Daily Papers

Accelerating diffusion model sampling is crucial for efficient AIGC deployment. While diffusion distillation methods -- based on distribution matching and trajectory matching -- reduce sampling to as few as one step, they fall short on complex tasks like text-to-image generation. Few-step generation offers a better balance between speed and quality, but existing approaches face a persistent trade-off: distribution matching lacks flexibility for multi-step sampling, while trajectory matching often yields suboptimal image quality. To bridge this gap, we propose learning few-step diffusion models by Trajectory Distribution Matching (TDM), a unified distillation paradigm that combines the strengths of distribution and trajectory matching. Our method introduces a data-free score distillation objective, aligning the student's trajectory with the teacher's at the distribution level. Further, we develop a sampling-steps-aware objective that decouples learning targets across different steps, enabling more adjustable sampling. This approach supports both deterministic sampling for superior image quality and flexible multi-step adaptation, achieving state-of-the-art performance with remarkable efficiency. Our model, TDM, outperforms existing methods on various backbones, such as SDXL and PixArt-alpha, delivering superior quality and significantly reduced training costs. In particular, our method distills PixArt-alpha into a 4-step generator that outperforms its teacher on real user preference at 1024 resolution. This is accomplished with 500 iterations and 2 A800 hours -- a mere 0.01% of the teacher's training cost. In addition, our proposed TDM can be extended to accelerate text-to-video diffusion. Notably, TDM can outperform its teacher model (CogVideoX-2B) by using only 4 NFE on VBench, improving the total score from 80.91 to 81.65. Project page: https://tdm-t2x.github.io/

Generative models have shown great promise in generating 3D geometric systems, which is a fundamental problem in many natural science domains such as molecule and protein design. However, existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. In this work, we propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories. Modeling such distribution is challenging as it requires capturing both the complex spatial interactions with physical symmetries and temporal correspondence encapsulated in the dynamics. We theoretically justify that diffusion models with equivariant temporal kernels can lead to density with desired symmetry, and develop a novel transition kernel leveraging SE(3)-equivariant spatial convolution and temporal attention. Furthermore, to induce an expressive trajectory distribution for conditional generation, we introduce a generalized learnable geometric prior into the forward diffusion process to enhance temporal conditioning. We conduct extensive experiments on both unconditional and conditional generation in various scenarios, including physical simulation, molecular dynamics, and pedestrian motion. Empirical results on a wide suite of metrics demonstrate that GeoTDM can generate realistic geometric trajectories with significantly higher quality.

End-to-end multi-modal planning is a promising paradigm in autonomous driving, enabling decision-making with diverse trajectory candidates. A key component is a robust trajectory scorer capable of selecting the optimal trajectory from these candidates. While recent trajectory scorers focus on scoring either large sets of static trajectories or small sets of dynamically generated ones, both approaches face significant limitations in generalization. Static vocabularies provide effective coarse discretization but struggle to make fine-grained adaptation, while dynamic proposals offer detailed precision but fail to capture broader trajectory distributions. To overcome these challenges, we propose GTRS (Generalized Trajectory Scoring), a unified framework for end-to-end multi-modal planning that combines coarse and fine-grained trajectory evaluation. GTRS consists of three complementary innovations: (1) a diffusion-based trajectory generator that produces diverse fine-grained proposals; (2) a vocabulary generalization technique that trains a scorer on super-dense trajectory sets with dropout regularization, enabling its robust inference on smaller subsets; and (3) a sensor augmentation strategy that enhances out-of-domain generalization while incorporating refinement training for critical trajectory discrimination. As the winning solution of the Navsim v2 Challenge, GTRS demonstrates superior performance even with sub-optimal sensor inputs, approaching privileged methods that rely on ground-truth perception. Code will be available at https://github.com/NVlabs/GTRS.

Predicting the future motion of dynamic agents is of paramount importance to ensuring safety and assessing risks in motion planning for autonomous robots. In this study, we propose a two-stage motion prediction method, called R-Pred, designed to effectively utilize both scene and interaction context using a cascade of the initial trajectory proposal and trajectory refinement networks. The initial trajectory proposal network produces M trajectory proposals corresponding to the M modes of the future trajectory distribution. The trajectory refinement network enhances each of the M proposals using 1) tube-query scene attention (TQSA) and 2) proposal-level interaction attention (PIA) mechanisms. TQSA uses tube-queries to aggregate local scene context features pooled from proximity around trajectory proposals of interest. PIA further enhances the trajectory proposals by modeling inter-agent interactions using a group of trajectory proposals selected by their distances from neighboring agents. Our experiments conducted on Argoverse and nuScenes datasets demonstrate that the proposed refinement network provides significant performance improvements compared to the single-stage baseline and that R-Pred achieves state-of-the-art performance in some categories of the benchmarks.

Generative models have shown great potential in trajectory planning. Recent studies demonstrate that anchor-guided generative models are effective in modeling the uncertainty of driving behaviors and improving overall performance. However, these methods rely on discrete anchor vocabularies that must sufficiently cover the trajectory distribution during testing to ensure robustness, inducing an inherent trade-off between vocabulary size and model performance. To overcome this limitation, we propose MeanFuser, an end-to-end autonomous driving method that enhances both efficiency and robustness through three key designs. (1) We introduce Gaussian Mixture Noise (GMN) to guide generative sampling, enabling a continuous representation of the trajectory space and eliminating the dependency on discrete anchor vocabularies. (2) We adapt ``MeanFlow Identity" to end-to-end planning, which models the mean velocity field between GMN and trajectory distribution instead of the instantaneous velocity field used in vanilla flow matching methods, effectively eliminating numerical errors from ODE solvers and significantly accelerating inference. (3) We design a lightweight Adaptive Reconstruction Module (ARM) that enables the model to implicitly select from all sampled proposals or reconstruct a new trajectory when none is satisfactory via attention weights.Experiments on the NAVSIM closed-loop benchmark demonstrate that MeanFuser achieves outstanding performance without the supervision of the PDM Score and exceptional inference efficiency, offering a robust and efficient solution for end-to-end autonomous driving. Our code and model are available at https://github.com/wjl2244/MeanFuser.

The problem of generalization in learning from demonstration (LfD) has received considerable attention over the years, particularly within the context of movement primitives, where a number of approaches have emerged. Recently, two important approaches have gained recognition. While one leverages via-points to adapt skills locally by modulating demonstrated trajectories, another relies on so-called task-parameterized models that encode movements with respect to different coordinate systems, using a product of probabilities for generalization. While the former are well-suited to precise, local modulations, the latter aim at generalizing over large regions of the workspace and often involve multiple objects. Addressing the quality of generalization by leveraging both approaches simultaneously has received little attention. In this work, we propose an interactive imitation learning framework that simultaneously leverages local and global modulations of trajectory distributions. Building on the kernelized movement primitives (KMP) framework, we introduce novel mechanisms for skill modulation from direct human corrective feedback. Our approach particularly exploits the concept of via-points to incrementally and interactively 1) improve the model accuracy locally, 2) add new objects to the task during execution and 3) extend the skill into regions where demonstrations were not provided. We evaluate our method on a bearing ring-loading task using a torque-controlled, 7-DoF, DLR SARA robot.

Diffusion-based planners have emerged as a promising approach for human-like trajectory generation in autonomous driving. Recent works incorporate reinforcement fine-tuning to enhance the robustness of diffusion planners through reward-oriented optimization in a generation-evaluation loop. However, they struggle to generate multi-modal, scenario-adaptive trajectories, hindering the exploitation efficiency of informative rewards during fine-tuning. To resolve this, we propose PlannerRFT, a sample-efficient reinforcement fine-tuning framework for diffusion-based planners. PlannerRFT adopts a dual-branch optimization that simultaneously refines the trajectory distribution and adaptively guides the denoising process toward more promising exploration, without altering the original inference pipeline. To support parallel learning at scale, we develop nuMax, an optimized simulator that achieves 10 times faster rollout compared to native nuPlan. Extensive experiments shows that PlannerRFT yields state-of-the-art performance with distinct behaviors emerging during the learning process.

Directly producing planning results from raw sensors has been a long-desired solution for autonomous driving and has attracted increasing attention recently. Most existing end-to-end autonomous driving methods factorize this problem into perception, motion prediction, and planning. However, we argue that the conventional progressive pipeline still cannot comprehensively model the entire traffic evolution process, e.g., the future interaction between the ego car and other traffic participants and the structural trajectory prior. In this paper, we explore a new paradigm for end-to-end autonomous driving, where the key is to predict how the ego car and the surroundings evolve given past scenes. We propose GenAD, a generative framework that casts autonomous driving into a generative modeling problem. We propose an instance-centric scene tokenizer that first transforms the surrounding scenes into map-aware instance tokens. We then employ a variational autoencoder to learn the future trajectory distribution in a structural latent space for trajectory prior modeling. We further adopt a temporal model to capture the agent and ego movements in the latent space to generate more effective future trajectories. GenAD finally simultaneously performs motion prediction and planning by sampling distributions in the learned structural latent space conditioned on the instance tokens and using the learned temporal model to generate futures. Extensive experiments on the widely used nuScenes benchmark show that the proposed GenAD achieves state-of-the-art performance on vision-centric end-to-end autonomous driving with high efficiency. Code: https://github.com/wzzheng/GenAD.

The current dominant paradigm in sensorimotor control, whether imitation or reinforcement learning, is to train policies directly in raw action spaces such as torque, joint angle, or end-effector position. This forces the agent to make decisions individually at each timestep in training, and hence, limits the scalability to continuous, high-dimensional, and long-horizon tasks. In contrast, research in classical robotics has, for a long time, exploited dynamical systems as a policy representation to learn robot behaviors via demonstrations. These techniques, however, lack the flexibility and generalizability provided by deep learning or reinforcement learning and have remained under-explored in such settings. In this work, we begin to close this gap and embed the structure of a dynamical system into deep neural network-based policies by reparameterizing action spaces via second-order differential equations. We propose Neural Dynamic Policies (NDPs) that make predictions in trajectory distribution space as opposed to prior policy learning methods where actions represent the raw control space. The embedded structure allows end-to-end policy learning for both reinforcement and imitation learning setups. We show that NDPs outperform the prior state-of-the-art in terms of either efficiency or performance across several robotic control tasks for both imitation and reinforcement learning setups. Project video and code are available at https://shikharbahl.github.io/neural-dynamic-policies/

High-level autonomous driving requires motion planners capable of modeling multimodal future uncertainties while remaining robust in closed-loop interactions. Although diffusion-based planners are effective at modeling complex trajectory distributions, they often suffer from stochastic instabilities and the lack of corrective negative feedback when trained purely with imitation learning. To address these issues, we propose RAD-2, a unified generator-discriminator framework for closed-loop planning. Specifically, a diffusion-based generator is used to produce diverse trajectory candidates, while an RL-optimized discriminator reranks these candidates according to their long-term driving quality. This decoupled design avoids directly applying sparse scalar rewards to the full high-dimensional trajectory space, thereby improving optimization stability. To further enhance reinforcement learning, we introduce Temporally Consistent Group Relative Policy Optimization, which exploits temporal coherence to alleviate the credit assignment problem. In addition, we propose On-policy Generator Optimization, which converts closed-loop feedback into structured longitudinal optimization signals and progressively shifts the generator toward high-reward trajectory manifolds. To support efficient large-scale training, we introduce BEV-Warp, a high-throughput simulation environment that performs closed-loop evaluation directly in Bird's-Eye View feature space via spatial warping. RAD-2 reduces the collision rate by 56% compared with strong diffusion-based planners. Real-world deployment further demonstrates improved perceived safety and driving smoothness in complex urban traffic.

We propose GoalFlow, an end-to-end autonomous driving method for generating high-quality multimodal trajectories. In autonomous driving scenarios, there is rarely a single suitable trajectory. Recent methods have increasingly focused on modeling multimodal trajectory distributions. However, they suffer from trajectory selection complexity and reduced trajectory quality due to high trajectory divergence and inconsistencies between guidance and scene information. To address these issues, we introduce GoalFlow, a novel method that effectively constrains the generative process to produce high-quality, multimodal trajectories. To resolve the trajectory divergence problem inherent in diffusion-based methods, GoalFlow constrains the generated trajectories by introducing a goal point. GoalFlow establishes a novel scoring mechanism that selects the most appropriate goal point from the candidate points based on scene information. Furthermore, GoalFlow employs an efficient generative method, Flow Matching, to generate multimodal trajectories, and incorporates a refined scoring mechanism to select the optimal trajectory from the candidates. Our experimental results, validated on the NavsimDauner2024_navsim, demonstrate that GoalFlow achieves state-of-the-art performance, delivering robust multimodal trajectories for autonomous driving. GoalFlow achieved PDMS of 90.3, significantly surpassing other methods. Compared with other diffusion-policy-based methods, our approach requires only a single denoising step to obtain excellent performance. The code is available at https://github.com/YvanYin/GoalFlow.

Aiming at promoting the safe real-world deployment of Reinforcement Learning (RL), research on safe RL has made significant progress in recent years. However, most existing works in the literature still focus on the online setting where risky violations of the safety budget are likely to be incurred during training. Besides, in many real-world applications, the learned policy is required to respond to dynamically determined safety budgets (i.e., constraint threshold) in real time. In this paper, we target at the above real-time budget constraint problem under the offline setting, and propose Trajectory-based REal-time Budget Inference (TREBI) as a novel solution that approaches this problem from the perspective of trajectory distribution. Theoretically, we prove an error bound of the estimation on the episodic reward and cost under the offline setting and thus provide a performance guarantee for TREBI. Empirical results on a wide range of simulation tasks and a real-world large-scale advertising application demonstrate the capability of TREBI in solving real-time budget constraint problems under offline settings.

Generative models have gained significant traction in offline reinforcement learning (RL) due to their ability to model complex trajectory distributions. However, existing generation-based approaches still struggle with long-horizon tasks characterized by sparse rewards. Some hierarchical generation methods have been developed to mitigate this issue by decomposing the original problem into shorter-horizon subproblems using one policy and generating detailed actions with another. While effective, these methods often overlook the multi-scale temporal structure inherent in trajectories, resulting in suboptimal performance. To overcome these limitations, we propose MAGE, a Multi-scale Autoregressive GEneration-based offline RL method. MAGE incorporates a condition-guided multi-scale autoencoder to learn hierarchical trajectory representations, along with a multi-scale transformer that autoregressively generates trajectory representations from coarse to fine temporal scales. MAGE effectively captures temporal dependencies of trajectories at multiple resolutions. Additionally, a condition-guided decoder is employed to exert precise control over short-term behaviors. Extensive experiments on five offline RL benchmarks against fifteen baseline algorithms show that MAGE successfully integrates multi-scale trajectory modeling with conditional guidance, generating coherent and controllable trajectories in long-horizon sparse-reward settings.

Robust planning in interactive scenarios requires predicting the uncertain future to make risk-aware decisions. Unfortunately, due to long-tail safety-critical events, the risk is often under-estimated by finite-sampling approximations of probabilistic motion forecasts. This can lead to overconfident and unsafe robot behavior, even with robust planners. Instead of assuming full prediction coverage that robust planners require, we propose to make prediction itself risk-aware. We introduce a new prediction objective to learn a risk-biased distribution over trajectories, so that risk evaluation simplifies to an expected cost estimation under this biased distribution. This reduces the sample complexity of the risk estimation during online planning, which is needed for safe real-time performance. Evaluation results in a didactic simulation environment and on a real-world dataset demonstrate the effectiveness of our approach. The code and a demo are available.

While few-step generative models have enabled powerful image and video generation at significantly lower cost, generic reinforcement learning (RL) paradigms for few-step models remain an unsolved problem. Existing RL approaches for few-step diffusion models strongly rely on back-propagating through differentiable reward models, thereby excluding the majority of important real-world reward signals, e.g., non-differentiable rewards such as humans' binary likeness, object counts, etc. To properly incorporate non-differentiable rewards to improve few-step generative models, we introduce TDM-R1, a novel reinforcement learning paradigm built upon a leading few-step model, Trajectory Distribution Matching (TDM). TDM-R1 decouples the learning process into surrogate reward learning and generator learning. Furthermore, we developed practical methods to obtain per-step reward signals along the deterministic generation trajectory of TDM, resulting in a unified RL post-training method that significantly improves few-step models' ability with generic rewards. We conduct extensive experiments ranging from text-rendering, visual quality, and preference alignment. All results demonstrate that TDM-R1 is a powerful reinforcement learning paradigm for few-step text-to-image models, achieving state-of-the-art reinforcement learning performances on both in-domain and out-of-domain metrics. Furthermore, TDM-R1 also scales effectively to the recent strong Z-Image model, consistently outperforming both its 100-NFE and few-step variants with only 4 NFEs. Project page: https://github.com/Luo-Yihong/TDM-R1

Accurately anticipating how complex, diverse scenes will evolve requires models that represent uncertainty, simulate along extended interaction chains, and efficiently explore many plausible futures. Yet most existing approaches rely on dense video or latent-space prediction, expending substantial capacity on dense appearance rather than on the underlying sparse trajectories of points in the scene. This makes large-scale exploration of future hypotheses costly and limits performance when long-horizon, multi-modal motion is essential. We address this by formulating the prediction of open-set future scene dynamics as step-wise inference over sparse point trajectories. Our autoregressive diffusion model advances these trajectories through short, locally predictable transitions, explicitly modeling the growth of uncertainty over time. This dynamics-centric representation enables fast rollout of thousands of diverse futures from a single image, optionally guided by initial constraints on motion, while maintaining physical plausibility and long-range coherence. We further introduce OWM, a benchmark for open-set motion prediction based on diverse in-the-wild videos, to evaluate accuracy and variability of predicted trajectory distributions under real-world uncertainty. Our method matches or surpasses dense simulators in predictive accuracy while achieving orders-of-magnitude higher sampling speed, making open-set future prediction both scalable and practical. Project page: http://compvis.github.io/myriad.

Camera-controllable video generation aims to synthesize videos with flexible and physically plausible camera movements. However, existing methods either provide imprecise camera control from text prompts or rely on labor-intensive manual camera trajectory parameters, limiting their use in automated scenarios. To address these issues, we propose a novel Vision-Language-Camera model, termed CT-1 (Camera Transformer 1), a specialized model designed to transfer spatial reasoning knowledge to video generation by accurately estimating camera trajectories. Built upon vision-language modules and a Diffusion Transformer model, CT-1 employs a Wavelet-based Regularization Loss in the frequency domain to effectively learn complex camera trajectory distributions. These trajectories are integrated into a video diffusion model to enable spatially aware camera control that aligns with user intentions. To facilitate the training of CT-1, we design a dedicated data curation pipeline and construct CT-200K, a large-scale dataset containing over 47M frames. Experimental results demonstrate that our framework successfully bridges the gap between spatial reasoning and video synthesis, yielding faithful and high-quality camera-controllable videos and improving camera control accuracy by 25.7% over prior methods.

Despite strong generalization capabilities, Vision-Language-Action (VLA) models remain constrained by the high cost of expert demonstrations and insufficient real-world interaction. While online reinforcement learning (RL) has shown promise in improving general foundation models, applying RL to VLA manipulation in real-world settings is still hindered by low exploration efficiency and a restricted exploration space. Through systematic real-world experiments, we observe that the effective exploration space of online RL is closely tied to the data distribution of supervised fine-tuning (SFT). Motivated by this observation, we propose TwinRL, a digital twin-real-world collaborative RL framework designed to scale and guide exploration for VLA models. First, a high-fidelity digital twin is efficiently reconstructed from smartphone-captured scenes, enabling realistic bidirectional transfer between real and simulated environments. During the SFT warm-up stage, we introduce an exploration space expansion strategy using digital twins to broaden the support of the data trajectory distribution. Building on this enhanced initialization, we propose a sim-to-real guided exploration strategy to further accelerate online RL. Specifically, TwinRL performs efficient and parallel online RL in the digital twin prior to deployment, effectively bridging the gap between offline and online training stages. Subsequently, we exploit efficient digital twin sampling to identify failure-prone yet informative configurations, which are used to guide targeted human-in-the-loop rollouts on the real robot. In our experiments, TwinRL approaches 100% success in both in-distribution regions covered by real-world demonstrations and out-of-distribution regions, delivering at least a 30% speedup over prior real-world RL methods and requiring only about 20 minutes on average across four tasks.

Diffusion transformers currently lead the field in high-quality video generation, but their slow iterative denoising process and prohibitive quadratic attention costs for long sequences create significant inference bottlenecks. While both step distillation and sparse attention mechanisms have shown promise as independent acceleration strategies, effectively combining these approaches presents critical challenges -- training-free integration yields suboptimal results, while separately training sparse attention after step distillation requires prohibitively expensive high-quality video data. To overcome these limitations, we propose BLADE, an innovative data-free joint training framework that introduces: (1) an Adaptive Block-Sparse Attention (ASA) mechanism for dynamically generating content-aware sparsity masks to focus computation on salient spatiotemporal features, and (2) a sparsity-aware step distillation paradigm built upon Trajectory Distribution Matching (TDM) that directly incorporates sparsity into the distillation process rather than treating it as a separate compression step, with fast convergence. We validate BLADE on text-to-video models like CogVideoX-5B and Wan2.1-1.3B. Our framework demonstrates remarkable efficiency gains across different scales. On Wan2.1-1.3B, BLADE achieves a 14.10x end-to-end inference acceleration over a 50-step baseline. Moreover, on models such as CogVideoX-5B with short video sequence lengths, our framework delivers a robust 8.89x speedup. Crucially, the acceleration is accompanied by a consistent quality improvement. On the VBench-2.0 benchmark, BLADE boosts the score of CogVideoX-5B to 0.569 (from 0.534) and Wan2.1-1.3B to 0.570 (from 0.563), results that are further corroborated by superior ratings in human evaluations. Our code and model weights are publicly available at: http://ziplab.co/BLADE-Homepage/.

Current diffusion-based super-resolution (SR) approaches achieve commendable performance at the cost of high inference overhead. Therefore, distillation techniques are utilized to accelerate the multi-step teacher model into one-step student model. Nevertheless, these methods significantly raise training costs and constrain the performance of the student model by the teacher model. To overcome these tough challenges, we propose Consistency Trajectory Matching for Super-Resolution (CTMSR), a distillation-free strategy that is able to generate photo-realistic SR results in one step. Concretely, we first formulate a Probability Flow Ordinary Differential Equation (PF-ODE) trajectory to establish a deterministic mapping from low-resolution (LR) images with noise to high-resolution (HR) images. Then we apply the Consistency Training (CT) strategy to directly learn the mapping in one step, eliminating the necessity of pre-trained diffusion model. To further enhance the performance and better leverage the ground-truth during the training process, we aim to align the distribution of SR results more closely with that of the natural images. To this end, we propose to minimize the discrepancy between their respective PF-ODE trajectories from the LR image distribution by our meticulously designed Distribution Trajectory Matching (DTM) loss, resulting in improved realism of our recovered HR images. Comprehensive experimental results demonstrate that the proposed methods can attain comparable or even superior capabilities on both synthetic and real datasets while maintaining minimal inference latency.

Most offline reinforcement learning (RL) algorithms return a target policy maximizing a trade-off between (1) the expected performance gain over the behavior policy that collected the dataset, and (2) the risk stemming from the out-of-distribution-ness of the induced state-action occupancy. It follows that the performance of the target policy is strongly related to the performance of the behavior policy and, thus, the trajectory return distribution of the dataset. We show that in mixed datasets consisting of mostly low-return trajectories and minor high-return trajectories, state-of-the-art offline RL algorithms are overly restrained by low-return trajectories and fail to exploit high-performing trajectories to the fullest. To overcome this issue, we show that, in deterministic MDPs with stochastic initial states, the dataset sampling can be re-weighted to induce an artificial dataset whose behavior policy has a higher return. This re-weighted sampling strategy may be combined with any offline RL algorithm. We further analyze that the opportunity for performance improvement over the behavior policy correlates with the positive-sided variance of the returns of the trajectories in the dataset. We empirically show that while CQL, IQL, and TD3+BC achieve only a part of this potential policy improvement, these same algorithms combined with our reweighted sampling strategy fully exploit the dataset. Furthermore, we empirically demonstrate that, despite its theoretical limitation, the approach may still be efficient in stochastic environments. The code is available at https://github.com/Improbable-AI/harness-offline-rl.

Recent studies suggest that Reinforcement Fine-Tuning (RFT) is inherently more resilient to catastrophic forgetting than Supervised Fine-Tuning (SFT). However, whether RFT (e.g., GRPO) can effectively overcome forgetting in challenging visual continual learning settings, such as class-incremental learning (CIL) and domain-incremental learning (DIL), remains an open problem. Through a pilot study, we confirm that while RFT consistently outperforms SFT, it still suffers from non-negligible forgetting. We empirically trace this bottleneck to Trajectory-level Drift Agnosticism: among candidate rollouts achieving identical task rewards, the KL divergence from the preceding-task policy varies substantially, which strongly correlates with catastrophic forgetting across sequential tasks. Motivated by this insight, we propose Retention-aware Policy Optimization (RaPO), a simple yet effective RFT method that explicitly mitigates forgetting through trajectory-level reward shaping. Specifically, RaPO comprises two core components: (1) Retention Reward that converts trajectory-level distribution drift into a continuous reward signal, preferentially reinforcing knowledge-preserving rollouts within each group; (2) Cross-Task Advantage Normalization (CTAN), which maintains a persistent exponential moving average of reward statistics across task boundaries to stabilize the optimization progress during continual learning. Leveraging the free-form textual generalization of MLLMs, we comprehensively evaluate RaPO across five visual continual learning settings. Extensive experiments demonstrate that RaPO achieves leading performance, substantially reducing catastrophic forgetting while preserving strong plasticity. To the best of our knowledge, this work represents the first systematic exploration of RFT in visual continual learning, offering insights that we hope will inspire future research.

Direct Preference Optimization (DPO) aligns text-to-image (T2I) generation models with human preferences using pairwise preference data. Although substantial resources are expended in collecting and labeling datasets, a critical aspect is often neglected: preferences vary across individuals and should be represented with more granularity. To address this, we propose SmPO-Diffusion, a novel method for modeling preference distributions to improve the DPO objective, along with a numerical upper bound estimation for the diffusion optimization objective. First, we introduce a smoothed preference distribution to replace the original binary distribution. We employ a reward model to simulate human preferences and apply preference likelihood averaging to improve the DPO loss, such that the loss function approaches zero when preferences are similar. Furthermore, we utilize an inversion technique to simulate the trajectory preference distribution of the diffusion model, enabling more accurate alignment with the optimization objective. Our approach effectively mitigates issues of excessive optimization and objective misalignment present in existing methods through straightforward modifications. Our SmPO-Diffusion achieves state-of-the-art performance in preference evaluation, outperforming baselines across metrics with lower training costs. The project page is https://jaydenlyh.github.io/SmPO-project-page/.

End-to-end multi-modal planning has become a transformative paradigm in autonomous driving, effectively addressing behavioral multi-modality and the generalization challenge in long-tail scenarios. We propose AnchDrive, a framework for end-to-end driving that effectively bootstraps a diffusion policy to mitigate the high computational cost of traditional generative models. Rather than denoising from pure noise, AnchDrive initializes its planner with a rich set of hybrid trajectory anchors. These anchors are derived from two complementary sources: a static vocabulary of general driving priors and a set of dynamic, context-aware trajectories. The dynamic trajectories are decoded in real-time by a Transformer that processes dense and sparse perceptual features. The diffusion model then learns to refine these anchors by predicting a distribution of trajectory offsets, enabling fine-grained refinement. This anchor-based bootstrapping design allows for efficient generation of diverse, high-quality trajectories. Experiments on the NAVSIM benchmark confirm that AnchDrive sets a new state-of-the-art and shows strong generalizability

Extrinsic calibration is essential for multi-sensor fusion, existing methods rely on structured targets or fully-excited data, limiting real-world applicability. Online calibration further suffers from weak excitation, leading to unreliable estimates. To address these limitations, we propose a reinforcement learning (RL)-based extrinsic calibration framework that formulates extrinsic calibration as a decision-making problem, directly optimizes SE(3) extrinsics to enhance odometry accuracy. Our approach leverages a probabilistic Bingham distribution to model 3D rotations, ensuring stable optimization while inherently retaining quaternion symmetry. A trajectory alignment reward mechanism enables robust calibration without structured targets by quantitatively evaluating estimated tightly-coupled trajectory against a reference trajectory. Additionally, an automated data selection module filters uninformative samples, significantly improving efficiency and scalability for large-scale datasets. Extensive experiments on UAVs, UGVs, and handheld platforms demonstrate that our method outperforms traditional optimization-based approaches, achieving high-precision calibration even under weak excitation conditions. Our framework simplifies deployment on diverse robotic platforms by eliminating the need for high-quality initial extrinsics and enabling calibration from routine operating data. The code is available at https://github.com/APRIL-ZJU/learn-to-calibrate.

The recent surge in popularity of Nano-Banana and Seedream 4.0 underscores the community's strong interest in multi-image composition tasks. Compared to single-image editing, multi-image composition presents significantly greater challenges in terms of consistency and quality, yet existing models have not disclosed specific methodological details for achieving high-quality fusion. Through statistical analysis, we identify Human-Object Interaction (HOI) as the most sought-after category by the community. We therefore systematically analyze and implement a state-of-the-art solution for multi-image composition with a primary focus on HOI-centric tasks. We present Skywork UniPic 3.0, a unified multimodal framework that integrates single-image editing and multi-image composition. Our model supports an arbitrary (1~6) number and resolution of input images, as well as arbitrary output resolutions (within a total pixel budget of 1024x1024). To address the challenges of multi-image composition, we design a comprehensive data collection, filtering, and synthesis pipeline, achieving strong performance with only 700K high-quality training samples. Furthermore, we introduce a novel training paradigm that formulates multi-image composition as a sequence-modeling problem, transforming conditional generation into unified sequence synthesis. To accelerate inference, we integrate trajectory mapping and distribution matching into the post-training stage, enabling the model to produce high-fidelity samples in just 8 steps and achieve a 12.5x speedup over standard synthesis sampling. Skywork UniPic 3.0 achieves state-of-the-art performance on single-image editing benchmark and surpasses both Nano-Banana and Seedream 4.0 on multi-image composition benchmark, thereby validating the effectiveness of our data pipeline and training paradigm. Code, models and dataset are publicly available.

Recent works for face editing usually manipulate the latent space of StyleGAN via the linear semantic directions. However, they usually suffer from the entanglement of facial attributes, need to tune the optimal editing strength, and are limited to binary attributes with strong supervision signals. This paper proposes a novel adaptive nonlinear latent transformation for disentangled and conditional face editing, termed AdaTrans. Specifically, our AdaTrans divides the manipulation process into several finer steps; i.e., the direction and size at each step are conditioned on both the facial attributes and the latent codes. In this way, AdaTrans describes an adaptive nonlinear transformation trajectory to manipulate the faces into target attributes while keeping other attributes unchanged. Then, AdaTrans leverages a predefined density model to constrain the learned trajectory in the distribution of latent codes by maximizing the likelihood of transformed latent code. Moreover, we also propose a disentangled learning strategy under a mutual information framework to eliminate the entanglement among attributes, which can further relax the need for labeled data. Consequently, AdaTrans enables a controllable face editing with the advantages of disentanglement, flexibility with non-binary attributes, and high fidelity. Extensive experimental results on various facial attributes demonstrate the qualitative and quantitative effectiveness of the proposed AdaTrans over existing state-of-the-art methods, especially in the most challenging scenarios with a large age gap and few labeled examples. The source code is available at https://github.com/Hzzone/AdaTrans.

Trajectory prediction models often fail in real-world automated driving due to distributional shifts between training and test conditions. Such distributional shifts, whether behavioural or environmental, pose a critical risk by causing the model to make incorrect forecasts in unfamiliar situations. We propose a self-supervised method that trains a decoder in a post-hoc fashion on the self-supervised task of forecasting the second half of observed trajectories from the first half. The L2 norm of the gradient of this forecasting loss with respect to the decoder's final layer defines a score to identify distribution shifts. Our approach, first, does not affect the trajectory prediction model, ensuring no interference with original prediction performance and second, demonstrates substantial improvements on distribution shift detection for trajectory prediction on the Shifts and Argoverse datasets. Moreover, we show that this method can also be used to early detect collisions of a deep Q-Network motion planner in the Highway simulator. Source code is available at https://github.com/Michedev/forecasting-the-past.

Accelerating the sampling speed of diffusion models remains a significant challenge. Recent score distillation methods distill a heavy teacher model into an one-step student generator, which is optimized by calculating the difference between the two score functions on the samples generated by the student model. However, there is a score mismatch issue in the early stage of the distillation process, because existing methods mainly focus on using the endpoint of pre-trained diffusion models as teacher models, overlooking the importance of the convergence trajectory between the student generator and the teacher model. To address this issue, we extend the score distillation process by introducing the entire convergence trajectory of teacher models and propose Distribution Backtracking Distillation (DisBack) for distilling student generators. DisBask is composed of two stages: Degradation Recording and Distribution Backtracking. Degradation Recording is designed to obtain the convergence trajectory of teacher models, which records the degradation path from the trained teacher model to the untrained initial student generator. The degradation path implicitly represents the intermediate distributions of teacher models. Then Distribution Backtracking trains a student generator to backtrack the intermediate distributions for approximating the convergence trajectory of teacher models. Extensive experiments show that DisBack achieves faster and better convergence than the existing distillation method and accomplishes comparable generation performance. Notably, DisBack is easy to implement and can be generalized to existing distillation methods to boost performance. Our code is publicly available on https://github.com/SYZhang0805/DisBack.

Distilling video generation models to extremely low inference budgets (e.g., 2--4 NFEs) is crucial for real-time deployment, yet remains challenging. Trajectory-style consistency distillation often becomes conservative under complex video dynamics, yielding an over-smoothed appearance and weak motion. Distribution matching distillation (DMD) can recover sharp, mode-seeking samples, but its local training signals do not explicitly regularize how denoising updates compose across timesteps, making composed rollouts prone to drift. To overcome this challenge, we propose Self-Consistent Distribution Matching Distillation (SC-DMD), which explicitly regularizes the endpoint-consistent composition of consecutive denoising updates. For real-time autoregressive video generation, we further treat the KV cache as a quality parameterized condition and propose Cache-Distribution-Aware training. This training scheme applies SC-DMD over multi-step rollouts and introduces a cache-conditioned feature alignment objective that steers low-quality outputs toward high-quality references. Across extensive experiments on both non-autoregressive backbones (e.g., Wan~2.1) and autoregressive real-time paradigms (e.g., Self Forcing), our method, dubbed Salt, consistently improves low-NFE video generation quality while remaining compatible with diverse KV-cache memory mechanisms. Source code will be released at https://github.com/XingtongGe/Salt{https://github.com/XingtongGe/Salt}.

Step distillation has become a leading technique for accelerating diffusion models, among which Distribution Matching Distillation (DMD) and Consistency Distillation are two representative paradigms. While consistency methods enforce self-consistency along the full PF-ODE trajectory to steer it toward the clean data manifold, vanilla DMD relies on sparse supervision at a few predefined discrete timesteps. This restricted discrete-time formulation and mode-seeking nature of the reverse KL divergence tends to exhibit visual artifacts and over-smoothed outputs, often necessitating complex auxiliary modules -- such as GANs or reward models -- to restore visual fidelity. In this work, we introduce Continuous-Time Distribution Matching (CDM), migrating the DMD framework from discrete anchoring to continuous optimization for the first time. CDM achieves this through two continuous-time designs. First, we replace the fixed discrete schedule with a dynamic continuous schedule of random length, so that distribution matching is enforced at arbitrary points along sampling trajectories rather than only at a few fixed anchors. Second, we propose a continuous-time alignment objective that performs active off-trajectory matching on latents extrapolated via the student's velocity field, improving generalization and preserving fine visual details. Extensive experiments on different architectures, including SD3-Medium and Longcat-Image, demonstrate that CDM provides highly competitive visual fidelity for few-step image generation without relying on complex auxiliary objectives. Code is available at https://github.com/byliutao/cdm.

Diffusion models are promising for joint trajectory prediction and controllable generation in autonomous driving, but they face challenges of inefficient inference steps and high computational demands. To tackle these challenges, we introduce Optimal Gaussian Diffusion (OGD) and Estimated Clean Manifold (ECM) Guidance. OGD optimizes the prior distribution for a small diffusion time T and starts the reverse diffusion process from it. ECM directly injects guidance gradients to the estimated clean manifold, eliminating extensive gradient backpropagation throughout the network. Our methodology streamlines the generative process, enabling practical applications with reduced computational overhead. Experimental validation on the large-scale Argoverse 2 dataset demonstrates our approach's superior performance, offering a viable solution for computationally efficient, high-quality joint trajectory prediction and controllable generation for autonomous driving. Our project webpage is at https://yixiaowang7.github.io/OptTrajDiff_Page/.

Executing complex terminal tasks remains a significant challenge for open-weight LLMs, constrained by two fundamental limitations. First, high-fidelity, executable training environments are scarce: environments synthesized from real-world repositories are not diverse and scalable, while trajectories synthesized by LLMs suffer from hallucinations. Second, standard instruction tuning uses expert trajectories that rarely exhibit simple mistakes common to smaller models. This creates a distributional mismatch, leaving student models ill-equipped to recover from their own runtime failures. To bridge these gaps, we introduce TermiGen, an end-to-end pipeline for synthesizing verifiable environments and resilient expert trajectories. Termi-Gen first generates functionally valid tasks and Docker containers via an iterative multi-agent refinement loop. Subsequently, we employ a Generator-Critic protocol that actively injects errors during trajectory collection, synthesizing data rich in error-correction cycles. Fine-tuned on this TermiGen-generated dataset, our TermiGen-Qwen2.5-Coder-32B achieves a 31.3% pass rate on TerminalBench. This establishes a new open-weights state-of-the-art, outperforming existing baselines and notably surpassing capable proprietary models such as o4-mini. Dataset is avaiable at https://github.com/ucsb-mlsec/terminal-bench-env.

State density distribution, in contrast to worst-case reachability, can be leveraged for safety-related problems to better quantify the likelihood of the risk for potentially hazardous situations. In this work, we propose a data-driven method to compute the density distribution of reachable states for nonlinear and even black-box systems. Our semi-supervised approach learns system dynamics and the state density jointly from trajectory data, guided by the fact that the state density evolution follows the Liouville partial differential equation. With the help of neural network reachability tools, our approach can estimate the set of all possible future states as well as their density. Moreover, we could perform online safety verification with probability ranges for unsafe behaviors to occur. We use an extensive set of experiments to show that our learned solution can produce a much more accurate estimate on density distribution, and can quantify risks less conservatively and flexibly comparing with worst-case analysis.

Generative flow networks (GFlowNets) are a method for learning a stochastic policy for generating compositional objects, such as graphs or strings, from a given unnormalized density by sequences of actions, where many possible action sequences may lead to the same object. We find previously proposed learning objectives for GFlowNets, flow matching and detailed balance, which are analogous to temporal difference learning, to be prone to inefficient credit propagation across long action sequences. We thus propose a new learning objective for GFlowNets, trajectory balance, as a more efficient alternative to previously used objectives. We prove that any global minimizer of the trajectory balance objective can define a policy that samples exactly from the target distribution. In experiments on four distinct domains, we empirically demonstrate the benefits of the trajectory balance objective for GFlowNet convergence, diversity of generated samples, and robustness to long action sequences and large action spaces.

Large Language Model (LLM) Red-Teaming, which proactively identifies vulnerabilities of LLMs, is an essential process for ensuring safety. Finding effective and diverse attacks in red-teaming is important, but achieving both is challenging. Generative Flow Networks (GFNs) that perform distribution matching are a promising methods, but they are notorious for training instability and mode collapse. In particular, unstable rewards in red-teaming accelerate mode collapse. We propose Stable-GFN (S-GFN), which eliminates partition function Z estimation in GFN and reduces training instability. S-GFN avoids Z-estimation through pairwise comparisons and employs a robust masking methodology against noisy rewards. Additionally, we propose a fluency stabilizer to prevent the model from getting stuck in local optima that produce gibberish. S-GFN provides more stable training while maintaining the optimal policy of GFN. We demonstrate the overwhelming attack performance and diversity of S-GFN across various settings.

Conventional supervised learning methods typically assume i.i.d samples and are found to be sensitive to out-of-distribution (OOD) data. We propose Generative Causal Representation Learning (GCRL) which leverages causality to facilitate knowledge transfer under distribution shifts. While we evaluate the effectiveness of our proposed method in human trajectory prediction models, GCRL can be applied to other domains as well. First, we propose a novel causal model that explains the generative factors in motion forecasting datasets using features that are common across all environments and with features that are specific to each environment. Selection variables are used to determine which parts of the model can be directly transferred to a new environment without fine-tuning. Second, we propose an end-to-end variational learning paradigm to learn the causal mechanisms that generate observations from features. GCRL is supported by strong theoretical results that imply identifiability of the causal model under certain assumptions. Experimental results on synthetic and real-world motion forecasting datasets show the robustness and effectiveness of our proposed method for knowledge transfer under zero-shot and low-shot settings by substantially outperforming the prior motion forecasting models on out-of-distribution prediction. Our code is available at https://github.com/sshirahmad/GCRL.

Best-of-N (BoN) Average Displacement Error (ADE)/ Final Displacement Error (FDE) is the most used metric for evaluating trajectory prediction models. Yet, the BoN does not quantify the whole generated samples, resulting in an incomplete view of the model's prediction quality and performance. We propose a new metric, Average Mahalanobis Distance (AMD) to tackle this issue. AMD is a metric that quantifies how close the whole generated samples are to the ground truth. We also introduce the Average Maximum Eigenvalue (AMV) metric that quantifies the overall spread of the predictions. Our metrics are validated empirically by showing that the ADE/FDE is not sensitive to distribution shifts, giving a biased sense of accuracy, unlike the AMD/AMV metrics. We introduce the usage of Implicit Maximum Likelihood Estimation (IMLE) as a replacement for traditional generative models to train our model, Social-Implicit. IMLE training mechanism aligns with AMD/AMV objective of predicting trajectories that are close to the ground truth with a tight spread. Social-Implicit is a memory efficient deep model with only 5.8K parameters that runs in real time of about 580Hz and achieves competitive results. Interactive demo of the problem can be seen at https://www.abduallahmohamed.com/social-implicit-amdamv-adefde-demo . Code is available at https://github.com/abduallahmohamed/Social-Implicit .

Discrete flow matching generates text by iteratively transforming noise tokens into coherent language, but may require hundreds of forward passes. Distillation uses the multi-step trajectory to train a student to reproduce the process in a few steps. When the student underperforms, the usual explanation is insufficient capacity. We argue the opposite: the trajectory is the bottleneck, not the student. Each training trajectory is built through a chain of blind stochastic jumps with no evaluation of sequence quality; a single bad decision at an early midpoint propagates through subsequent steps, yet the student must imitate the result. Trajectory-Shaped Discrete Flow Matching (TS-DFM) replaces these blind jumps with guided navigation: a lightweight energy compass evaluates candidate continuations at each midpoint, selecting the most coherent. All shaping is training-only; inference cost is unchanged. On 170M-parameter language modeling, the shaped student at 8 steps achieves 32% lower perplexity than the 1,024-step teacher while being 128x faster, with gains consistent across source distributions and three evaluators of increasing scale. TS-DFM achieves the best perplexity of any discrete-generation baseline we compare against, including methods trained on 6x more data or using 5x larger models.

Reliable multi-agent trajectory prediction is crucial for the safe planning and control of autonomous systems. Compared with single-agent cases, the major challenge in simultaneously processing multiple agents lies in modeling complex social interactions caused by various driving intentions and road conditions. Previous methods typically leverage graph-based message propagation or attention mechanism to encapsulate such interactions in the format of marginal probabilistic distributions. However, it is inherently sub-optimal. In this paper, we propose IPCC-TP, a novel relevance-aware module based on Incremental Pearson Correlation Coefficient to improve multi-agent interaction modeling. IPCC-TP learns pairwise joint Gaussian Distributions through the tightly-coupled estimation of the means and covariances according to interactive incremental movements. Our module can be conveniently embedded into existing multi-agent prediction methods to extend original motion distribution decoders. Extensive experiments on nuScenes and Argoverse 2 datasets demonstrate that IPCC-TP improves the performance of baselines by a large margin.

Reinforcement learning with stochastic optimal control offers a promising framework for diffusion fine-tuning, where a pre-trained diffusion model is optimized to generate paths that lead to a reward-tilted distribution. While these approaches enable optimization without access to explicit samples from the optimal distribution, they require training on rollouts under the current fine-tuned model, making them susceptible to reinforcing sub-optimal trajectories that yield poor rewards. To overcome this challenge, we introduce TRee Search Guided TRajectory-Aware Fine-Tuning for Discrete Diffusion (TR2-D2), a novel framework that optimizes reward-guided discrete diffusion trajectories with tree search to construct replay buffers for trajectory-aware fine-tuning. These buffers are generated using Monte Carlo Tree Search (MCTS) and subsequently used to fine-tune a pre-trained discrete diffusion model under a stochastic optimal control objective. We validate our framework on single- and multi-objective fine-tuning of biological sequence diffusion models, highlighting the overall effectiveness of TR2-D2 for reliable reward-guided fine-tuning in discrete sequence generation.

Multi-agent trajectory prediction at signalized intersections is crucial for developing efficient intelligent transportation systems and safe autonomous driving systems. Due to the complexity of intersection scenarios and the limitations of single-vehicle perception, the performance of vehicle-centric prediction methods has reached a plateau. In this paper, we introduce an Infrastructure-to-Everything (I2X) collaborative prediction scheme. In this scheme, roadside units (RSUs) independently forecast the future trajectories of all vehicles and transmit these predictions unidirectionally to subscribing vehicles. Building on this scheme, we propose I2XTraj, a dedicated infrastructure-based trajectory prediction model. I2XTraj leverages real-time traffic signal states, prior maneuver strategy knowledge, and multi-agent interactions to generate accurate, joint multi-modal trajectory prediction. First, a continuous signal-informed mechanism is proposed to adaptively process real-time traffic signals to guide trajectory proposal generation under varied intersection configurations. Second, a driving strategy awareness mechanism estimates the joint distribution of maneuver strategies by integrating spatial priors of intersection areas with dynamic vehicle states, enabling coverage of the full set of feasible maneuvers. Third, a spatial-temporal-mode attention network models multi-agent interactions to refine and adjust joint trajectory outputs.Finally, I2XTraj is evaluated on two real-world datasets of signalized intersections, the V2X-Seq and the SinD drone dataset. In both single-infrastructure and online collaborative scenarios, our model outperforms state-of-the-art methods by over 30\% on V2X-Seq and 15\% on SinD, demonstrating strong generalizability and robustness.

Generalization remains one of the most important desiderata for robust robot learning systems. While recently proposed approaches show promise in generalization to novel objects, semantic concepts, or visual distribution shifts, generalization to new tasks remains challenging. For example, a language-conditioned policy trained on pick-and-place tasks will not be able to generalize to a folding task, even if the arm trajectory of folding is similar to pick-and-place. Our key insight is that this kind of generalization becomes feasible if we represent the task through rough trajectory sketches. We propose a policy conditioning method using such rough trajectory sketches, which we call RT-Trajectory, that is practical, easy to specify, and allows the policy to effectively perform new tasks that would otherwise be challenging to perform. We find that trajectory sketches strike a balance between being detailed enough to express low-level motion-centric guidance while being coarse enough to allow the learned policy to interpret the trajectory sketch in the context of situational visual observations. In addition, we show how trajectory sketches can provide a useful interface to communicate with robotic policies: they can be specified through simple human inputs like drawings or videos, or through automated methods such as modern image-generating or waypoint-generating methods. We evaluate RT-Trajectory at scale on a variety of real-world robotic tasks, and find that RT-Trajectory is able to perform a wider range of tasks compared to language-conditioned and goal-conditioned policies, when provided the same training data.

Diffusion large language models (dLLMs) offer a promising paradigm for parallel text generation, but in practice they face an accuracy-parallelism trade-off, where increasing tokens per forward (TPF) often degrades generation quality. Existing acceleration methods often gain speed at the cost of accuracy. To address this limitation, we propose TAD, a Temporal-Aware trajectory self-Distillation framework. During data construction, we condition a teacher model on both the prompt and the ground-truth response to generate decoding trajectories, recording the intermediate masked states throughout the process. Based on how many decoding steps remain before each masked token is revealed, we partition masked positions into near and distant subsets. For near tokens, we train the student with a hard cross-entropy loss using the teacher trajectory tokens as labels, encouraging confident predictions for tokens that are about to be decoded. For distant tokens, we apply a soft KL divergence loss between the teacher and student token distributions, providing softer supervision and preserving future planning knowledge. This temporal-aware partition naturally gives rise to two deployment configurations: a Quality model that prioritizes accuracy and a Speed model that favors more aggressive acceleration. Experiments show that TAD consistently improves the accuracy-parallelism trade-off. On LLaDA, it raises average accuracy from 46.2\% to 51.6\% with the Quality model and average AUP from 46.2 to 257.1 with the Speed model. Our code is available at: https://github.com/BHmingyang/TAD

Timestep distillation is an effective approach for improving the generation efficiency of diffusion models. The Consistency Model (CM), as a trajectory-based framework, demonstrates significant potential due to its strong theoretical foundation and high-quality few-step generation. Nevertheless, current continuous-time consistency distillation methods still rely heavily on training data and computational resources, hindering their deployment in resource-constrained scenarios and limiting their scalability to diverse domains. To address this issue, we propose Trajectory-Backward Consistency Model (TBCM), which eliminates the dependence on external training data by extracting latent representations directly from the teacher model's generation trajectory. Unlike conventional methods that require VAE encoding and large-scale datasets, our self-contained distillation paradigm significantly improves both efficiency and simplicity. Moreover, the trajectory-extracted samples naturally bridge the distribution gap between training and inference, thereby enabling more effective knowledge transfer. Empirically, TBCM achieves 6.52 FID and 28.08 CLIP scores on MJHQ-30k under one-step generation, while reducing training time by approximately 40% compared to Sana-Sprint and saving a substantial amount of GPU memory, demonstrating superior efficiency without sacrificing quality. We further reveal the diffusion-generation space discrepancy in continuous-time consistency distillation and analyze how sampling strategies affect distillation performance, offering insights for future distillation research. GitHub Link: https://github.com/hustvl/TBCM.

On-policy reinforcement learning methods like GRPO suffer from mode collapse: they exhibit reduced solution diversity, concentrating probability mass on a single solution once discovered and ceasing exploration of alternative strategies. We show this stems from reverse KL minimization's mode-seeking behavior, which reinforces the first high-reward trajectory found rather than maintaining a distribution over multiple diverse solutions. We propose DMPO (Distribution-Matching Policy Optimization), which prevents mode collapse through principled approximation of forward KL minimization. DMPO constructs a group level target distribution over sampled trajectories proportional to their rewards, then aligns the policy distribution to this target. This provides mode-covering behavior without requiring sampling from the intractable global target distribution, enabling sustained exploration throughout training. We validate DMPO on NP-hard combinatorial optimization, where exponentially many feasible solutions exist but only a few approach optimality, an ideal testbed for evaluating exploration. DMPO achieves 43.9% Quality Ratio on text-based NP-Bench (vs. GRPO's 40.1%) and 43.1% on vision-based NP-Bench (vs. 38.4%), demonstrating 9% and 12% relative improvements respectively. These gains generalize to mathematical reasoning (+2.0%) and out-of-domain tasks (+2.3%), showing that diversity-preserving training enhances general reasoning capabilities across modalities. Our work establishes distribution matching as a practical, principled approach to preventing mode collapse in on-policy RL, with consistent quality improvements demonstrating sustained exploration across diverse reasoning tasks.

Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior distribution. In this paper, we identify several intriguing trajectory properties in the ODE-based sampling process of diffusion models. We characterize an implicit denoising trajectory and discuss its vital role in forming the coupled sampling trajectory with a strong shape regularity, regardless of the generated content. We also describe a dynamic programming-based scheme to make the time schedule in sampling better fit the underlying trajectory structure. This simple strategy requires minimal modification to any given ODE-based numerical solvers and incurs negligible computational cost, while delivering superior performance in image generation, especially in 5sim 10 function evaluations.

Policy-based optimizations are widely adopted today for the training and alignment of language models, where one of the most recent and effective approaches is Group-relative Policy Optimization (GRPO). In this paper, we reveals and analyze two major limitations of GRPO: (i) tokens frequently appear in completions with both positive and negative rewards, leading to conflicting gradient updates that can reduce their output probability, even though can be essential for maintaining proper structure; (ii) negatively rewarded completions may penalize confident responses and shift model decisions toward unlikely tokens, progressively flattening the output distribution and degrading learning. To address these issues and provide a more stable and effective policy optimization strategy, we introduce GTPO (Group-relative Trajectory-based Policy Optimization), which identifies conflict tokens, tokens appearing in the same position across completions with opposite rewards, protects them by skipping negative updates, while amplifying positive ones. To further prevent policy collapse, GTPO filters out completions whose entropy exceeds a provable threshold. Unlike GRPO, GTPO does not rely on KL-divergence regularization, eliminating the need for a reference model during training, while still ensuring greater training stability and improved performance, validated through multiple experiments on GSM8K, MATH and AIME 2024 benchmarks.

Recent advancements in 3D generation have leveraged synthetic datasets with ground truth 3D assets and predefined cameras. However, the potential of adopting real-world datasets, which can produce significantly more realistic 3D scenes, remains largely unexplored. In this work, we delve into the key challenge of the complex and scene-specific camera trajectories found in real-world captures. We introduce Director3D, a robust open-world text-to-3D generation framework, designed to generate both real-world 3D scenes and adaptive camera trajectories. To achieve this, (1) we first utilize a Trajectory Diffusion Transformer, acting as the Cinematographer, to model the distribution of camera trajectories based on textual descriptions. (2) Next, a Gaussian-driven Multi-view Latent Diffusion Model serves as the Decorator, modeling the image sequence distribution given the camera trajectories and texts. This model, fine-tuned from a 2D diffusion model, directly generates pixel-aligned 3D Gaussians as an immediate 3D scene representation for consistent denoising. (3) Lastly, the 3D Gaussians are refined by a novel SDS++ loss as the Detailer, which incorporates the prior of the 2D diffusion model. Extensive experiments demonstrate that Director3D outperforms existing methods, offering superior performance in real-world 3D generation.

In robotic manipulation, vision-language-action (VLA) models have emerged as a promising paradigm for learning generalizable and scalable robot policies. Most existing VLA frameworks rely on standard supervised objectives, typically cross-entropy for discrete actions and mean squared error (MSE) for continuous action regression, which impose strong pointwise constraints on individual predictions. In this work, we focus on continuous-action VLA models and move beyond conventional MSE-based regression by reshaping action error distributions during training. Drawing on information-theoretic principles, we introduce Minimum Error Entropy (MEE) into modern VLA architectures and propose a trajectory-level MEE objective, together with two weighted variants, combined with MSE for continuous-action VLA training. We evaluate our approaches across standard, few-shot, and noisy settings on multiple representative VLA architectures, using simulation benchmarks such as LIBERO and SimplerEnv as well as real-world robotic manipulation tasks. Experimental results demonstrate consistent improvements in success rates and robustness across these settings. Under imbalanced data regimes, the gains persist within a well-characterized operating range, while incurring negligible additional training cost and no impact on inference efficiency. We further provide theoretical analyses that explain why MEE-based supervision is effective and characterize its practical range. Project Page: https://cognition2actionlab.github.io/VLA-TMEE.github.io/

Recent large-scale Vision Language Action (VLA) models have shown superior performance in robotic manipulation tasks guided by natural language. However, their generalization remains limited when applied to novel objects or unfamiliar environments that lie outside the training distribution. To address this, many existing approaches integrate additional components such as depth estimation, segmentation, or even diffusion to improve generalization, at the cost of adding significant computation overhead, resulting in low efficiency. This motivates the exploration of efficient action prediction methods, which are independent of additional high-level visual representations or diffusion techniques. In this work, we propose VOTE, an efficient and general framework for the optimization and acceleration of VLA models. In details, we propose a novel tokenizer-free fine-tuning approach for parallel accurate action prediction, which reduces computational overhead and accelerates inference speed. Additionally, we adopt an ensemble voting strategy for the action sampling, which significantly improves model performance and enhances generalization. Experimental results show that our method achieves state-of-the-art performance with 35x faster inference and 145 Hz throughput. All the details and codes will be open-sourced.

Sampling from diffusion probabilistic models (DPMs) is often expensive for high-quality image generation and typically requires many steps with a large model. In this paper, we introduce sampling Trajectory Stitching T-Stitch, a simple yet efficient technique to improve the sampling efficiency with little or no generation degradation. Instead of solely using a large DPM for the entire sampling trajectory, T-Stitch first leverages a smaller DPM in the initial steps as a cheap drop-in replacement of the larger DPM and switches to the larger DPM at a later stage. Our key insight is that different diffusion models learn similar encodings under the same training data distribution and smaller models are capable of generating good global structures in the early steps. Extensive experiments demonstrate that T-Stitch is training-free, generally applicable for different architectures, and complements most existing fast sampling techniques with flexible speed and quality trade-offs. On DiT-XL, for example, 40% of the early timesteps can be safely replaced with a 10x faster DiT-S without performance drop on class-conditional ImageNet generation. We further show that our method can also be used as a drop-in technique to not only accelerate the popular pretrained stable diffusion (SD) models but also improve the prompt alignment of stylized SD models from the public model zoo. Code is released at https://github.com/NVlabs/T-Stitch

Accurate prediction of pedestrians' future motions is critical for intelligent driving systems. Developing models for this task requires rich datasets containing diverse sets of samples. However, the existing naturalistic trajectory prediction datasets are generally imbalanced in favor of simpler samples and lack challenging scenarios. Such a long-tail effect causes prediction models to underperform on the tail portion of the data distribution containing safety-critical scenarios. Previous methods tackle the long-tail problem using methods such as contrastive learning and class-conditioned hypernetworks. These approaches, however, are not modular and cannot be applied to many machine learning architectures. In this work, we propose a modular model-agnostic framework for trajectory prediction that leverages a specialized mixture of experts. In our approach, each expert is trained with a specialized skill with respect to a particular part of the data. To produce predictions, we utilise a router network that selects the best expert by generating relative confidence scores. We conduct experimentation on common pedestrian trajectory prediction datasets and show that besides achieving state-of-the-art performance, our method significantly performs better on long-tail scenarios. We further conduct ablation studies to highlight the contribution of different proposed components.

Vision Large Language Models (VLLMs) have achieved remarkable success in modern text-rich visual understanding. However, their perceptual robustness in the face of the continuous morphological evolution of historical writing systems remains largely unexplored. Existing ancient text datasets typically focus on isolated historical periods, failing to capture the systematic visual distribution shifts spanning thousands of years. To bridge this gap and empower Digital Humanities, we introduce Chronicles-OCR, the first comprehensive benchmark specifically designed to evaluate the cross-temporal visual perception capabilities of VLLMs across the complete evolutionary trajectory of Chinese characters, known as the Seven Chinese Scripts. Curated in collaboration with top-tier institutional domain experts, the dataset comprises 2,800 strictly balanced images encompassing highly diverse physical media, ranging from tortoise shells to paper-based calligraphy. To accommodate the drastic morphological and topological variations across different historical stages, we propose a novel Stage-Adaptive Annotation Paradigm. Based on this, Chronicles-OCR formulates four rigorous quantitative tasks: cross-period character spotting, fine-grained archaic character recognition via visual referring, ancient text parsing, and script classification. By isolating visual perception from semantic reasoning, Chronicles-OCR provides an authoritative platform to expose the limitations of current VLLMs, paving the way for robust, evolution-aware historical text perception. Chronicles-OCR is publicly available at https://github.com/VirtualLUOUCAS/Chronicles-OCR.

Agentic knowledge graph question answering (KGQA) requires an agent to iteratively interact with knowledge graphs (KGs), posing challenges in both training data scarcity and reasoning generalization. Specifically, existing approaches often restrict agent exploration: prompting-based methods lack autonomous navigation training, while current training pipelines usually confine reasoning to predefined trajectories. To this end, this paper proposes GraphWalker, a novel agentic KGQA framework that addresses these challenges through Automated Trajectory Synthesis and Stage-wise Fine-tuning. GraphWalker adopts a two-stage SFT training paradigm: First, the agent is trained on structurally diverse trajectories synthesized from constrained random-walk paths, establishing a broad exploration prior over the KG; Second, the agent is further fine-tuned on a small set of expert trajectories to develop reflection and error recovery capabilities. Extensive experiments demonstrate that our stage-wise SFT paradigm unlocks a higher performance ceiling for a lightweight reinforcement learning (RL) stage, enabling GraphWalker to achieve state-of-the-art performance on CWQ and WebQSP. Additional results on GrailQA and our constructed GraphWalkerBench confirm that GraphWalker enhances generalization to out-of-distribution reasoning paths. The code is publicly available at https://github.com/XuShuwenn/GraphWalker

The ability to conduct and learn from interaction and experience is a central challenge in robotics, offering a scalable alternative to labor-intensive human demonstrations. However, realizing such "play" requires (1) a policy robust to diverse, potentially out-of-distribution environment states, and (2) a procedure that continuously produces useful robot experience. To address these challenges, we introduce Tether, a method for autonomous functional play involving structured, task-directed interactions. First, we design a novel open-loop policy that warps actions from a small set of source demonstrations (<=10) by anchoring them to semantic keypoint correspondences in the target scene. We show that this design is extremely data-efficient and robust even under significant spatial and semantic variations. Second, we deploy this policy for autonomous functional play in the real world via a continuous cycle of task selection, execution, evaluation, and improvement, guided by the visual understanding capabilities of vision-language models. This procedure generates diverse, high-quality datasets with minimal human intervention. In a household-like multi-object setup, our method is the first to perform many hours of autonomous multi-task play in the real world starting from only a handful of demonstrations. This produces a stream of data that consistently improves the performance of closed-loop imitation policies over time, ultimately yielding over 1000 expert-level trajectories and training policies competitive with those learned from human-collected demonstrations.

Latent diffusion models excel at generating high-quality images but lose the benefits of end-to-end modeling. They discard information during image encoding, require a separately trained decoder, and model an auxiliary distribution to the raw data. In this paper, we propose Latent Forcing, a simple modification to existing architectures that achieves the efficiency of latent diffusion while operating on raw natural images. Our approach orders the denoising trajectory by jointly processing latents and pixels with separately tuned noise schedules. This allows the latents to act as a scratchpad for intermediate computation before high-frequency pixel features are generated. We find that the order of conditioning signals is critical, and we analyze this to explain differences between REPA distillation in the tokenizer and the diffusion model, conditional versus unconditional generation, and how tokenizer reconstruction quality relates to diffusability. Applied to ImageNet, Latent Forcing achieves a new state-of-the-art for diffusion transformer-based pixel generation at our compute scale.

Retrieval-augmented generation (RAG) systems have advanced large language models (LLMs) in complex deep search scenarios requiring multi-step reasoning and iterative information retrieval. However, existing approaches face critical limitations that lack high-quality training trajectories or suffer from the distributional mismatches in simulated environments and prohibitive computational costs for real-world deployment. This paper introduces SimpleDeepSearcher, a lightweight yet effective framework that bridges this gap through strategic data engineering rather than complex training paradigms. Our approach synthesizes high-quality training data by simulating realistic user interactions in live web search environments, coupled with a multi-criteria curation strategy that optimizes the diversity and quality of input and output side. Experiments on five benchmarks across diverse domains demonstrate that SFT on only 871 curated samples yields significant improvements over RL-based baselines. Our work establishes SFT as a viable pathway by systematically addressing the data-scarce bottleneck, offering practical insights for efficient deep search systems. Our code is available at https://github.com/RUCAIBox/SimpleDeepSearcher.

Reinforcement learning (RL) post-training is a dominant approach for improving the reasoning performance of large language models (LLMs), yet growing evidence suggests that its gains arise primarily from distribution sharpening rather than the acquisition of new capabilities. Recent work has shown that sampling from the power distribution of LLMs using Markov chain Monte Carlo (MCMC) can recover performance comparable to RL post-training without relying on external rewards; however, the high computational cost of MCMC makes such approaches impractical for widespread adoption. In this work, we propose a theoretically grounded alternative that eliminates the need for iterative MCMC. We derive a novel formulation showing that the global power distribution can be approximated by a token-level scaled low-temperature one, where the scaling factor captures future trajectory quality. Leveraging this insight, we introduce a training-free and verifier-free algorithm that sharpens the base model's generative distribution autoregressively. Empirically, we evaluate our method on math, QA, and code tasks across four LLMs, and show that our method matches or surpasses one-shot GRPO without relying on any external rewards, while reducing inference latency by over 10x compared to MCMC-based sampling.

As multimodal foundational models start being deployed experimentally in Self-Driving cars, a reasonable question we ask ourselves is how similar to humans do these systems respond in certain driving situations -- especially those that are out-of-distribution? To study this, we create the Robusto-1 dataset that uses dashcam video data from Peru, a country with one of the worst (aggressive) drivers in the world, a high traffic index, and a high ratio of bizarre to non-bizarre street objects likely never seen in training. In particular, to preliminarly test at a cognitive level how well Foundational Visual Language Models (VLMs) compare to Humans in Driving, we move away from bounding boxes, segmentation maps, occupancy maps or trajectory estimation to multi-modal Visual Question Answering (VQA) comparing both humans and machines through a popular method in systems neuroscience known as Representational Similarity Analysis (RSA). Depending on the type of questions we ask and the answers these systems give, we will show in what cases do VLMs and Humans converge or diverge allowing us to probe on their cognitive alignment. We find that the degree of alignment varies significantly depending on the type of questions asked to each type of system (Humans vs VLMs), highlighting a gap in their alignment.

This paper tackles the challenge of real-time 3D trajectory prediction for UAVs, which is critical for applications such as aerial surveillance and defense. Existing prediction models that rely primarily on position data struggle with accuracy, especially when UAV movements fall outside the position domain used in training. Our research identifies a gap in utilizing velocity estimates, first-order dynamics, to better capture the dynamics and enhance prediction accuracy and generalizability in any position domain. To bridge this gap, we propose a new trajectory prediction method using Gated Recurrent Units (GRUs) within sequence-based neural networks. Unlike traditional methods that rely on RNNs or transformers, this approach forecasts future velocities and positions based on historical velocity data instead of positions. This is designed to enhance prediction accuracy and scalability, overcoming challenges faced by conventional models in handling complex UAV dynamics. The methodology employs both synthetic and real-world 3D UAV trajectory data, capturing a wide range of flight patterns, speeds, and agility. Synthetic data is generated using the Gazebo simulator and PX4 Autopilot, while real-world data comes from the UZH-FPV and Mid-Air drone racing datasets. The GRU-based models significantly outperform state-of-the-art RNN approaches, with a mean square error (MSE) as low as 2 x 10^-8. Overall, our findings confirm the effectiveness of incorporating velocity data in improving the accuracy of UAV trajectory predictions across both synthetic and real-world scenarios, in and out of position data distributions. Finally, we open-source our 5000 trajectories dataset and a ROS 2 package to facilitate the integration with existing ROS-based UAV systems.

Diffusion and flow models achieve State-Of-The-Art (SOTA) generative performance, yet many practically important behaviors such as fine-grained prompt fidelity, compositional correctness, and text rendering are weakly specified by score or flow matching pretraining objectives. Reinforcement Learning (RL) fine-tuning with external, black-box rewards is a natural remedy, but diffusion RL is often brittle. Trajectory-based methods incur high memory cost and high-variance gradient estimates; forward-process approaches converge faster but can suffer from distribution drift, and hence reward hacking. In this work, we present Centered Reward Distillation (CRD), a diffusion RL framework derived from KL-regularized reward maximization built on forward-process-based fine-tuning. The key insight is that the intractable normalizing constant cancels under within-prompt centering, yielding a well-posed reward-matching objective. To enable reliable text-to-image fine-tuning, we introduce techniques that explicitly control distribution drift: (i) decoupling the sampler from the moving reference to prevent ratio-signal collapse, (ii) KL anchoring to a CFG-guided pretrained model to control long-run drift and align with the inference-time semantics of the pre-trained model, and (iii) reward-adaptive KL strength to accelerate early learning under large KL regularization while reducing late-stage exploitation of reward-model loopholes. Experiments on text-to-image post-training with GenEval and OCR rewards show that CRD achieves competitive SOTA reward optimization results with fast convergence and reduced reward hacking, as validated on unseen preference metrics.

With the success of flow matching in visual generation, sampling efficiency remains a critical bottleneck for its practical application. Among flow models' accelerating methods, ReFlow has been somehow overlooked although it has theoretical consistency with flow matching. This is primarily due to its suboptimal performance in practical scenarios compared to consistency distillation and score distillation. In this work, we investigate this issue within the ReFlow framework and propose FlowSteer, a method unlocks the potential of ReFlow-based distillation by guiding the student along teacher's authentic generation trajectories. We first identify that Piecewised ReFlow's performance is hampered by a critical distribution mismatch during the training and propose Online Trajectory Alignment(OTA) to resolve it. Then, we introduce a adversarial distillation objective applied directly on the ODE trajectory, improving the student's adherence to the teacher's generation trajectory. Furthermore, we find and fix a previously undiscovered flaw in the widely-used FlowMatchEulerDiscreteScheduler that largely degrades few-step inference quality. Our experiment result on SD3 demonstrates our method's efficacy.

We present EgoNav, a system that enables a humanoid robot to traverse diverse, unseen environments by learning entirely from 5 hours of human walking data, with no robot data or finetuning. A diffusion model predicts distributions of plausible future trajectories conditioned on past trajectory, a 360 deg visual memory fusing color, depth, and semantics, and video features from a frozen DINOv3 backbone that capture appearance cues invisible to depth sensors. A hybrid sampling scheme achieves real-time inference in 10 denoising steps, and a receding-horizon controller selects paths from the predicted distribution. We validate EgoNav through offline evaluations, where it outperforms baselines in collision avoidance and multi-modal coverage, and through zero-shot deployment on a Unitree G1 humanoid across unseen indoor and outdoor environments. Behaviors such as waiting for doors to open, navigating around crowds, and avoiding glass walls emerge naturally from the learned prior. We will release the dataset and trained models. Our website: https://egonav.weizhuowang.com

Diffusion Large Language Models (DLLMs) enable fully parallel token decoding but often remain impractical at inference time due to the many denoising iterations required to refine an information-free, fully masked initialization into coherent text. Most existing acceleration methods focus on traversing this generative trajectory more efficiently via improved solvers or sampling strategies. We advance a complementary perspective: shorten the trajectory itself by starting closer to the target distribution through context-aware initialization. We propose a training-free interface that injects prompt-conditioned priors from a lightweight auxiliary model into the diffusion initialization, and instantiate it with two mechanisms: discrete token injection and representation-level embedding interpolation. Because injected priors can be imperfect and unmask-only decoding can over-commit early, we also introduce a simple confidence-based remasking mechanism as a form of prior skepticism. Preliminary evidence on GSM8K suggests that context-aware initialization can substantially reduce denoising iterations (about 35\% fewer function evaluations in our setting), while also exposing a key open challenge: naive warm-starting can degrade final accuracy relative to strong diffusion baselines. We use these findings to motivate a research agenda around calibration, revision mechanisms, and representation alignment for reliable warm-started diffusion decoding.

Applying diffusion models in reinforcement learning for long-term planning has gained much attention recently. Several diffusion-based methods have successfully leveraged the modeling capabilities of diffusion for arbitrary distributions. These methods generate subsequent trajectories for planning and have demonstrated significant improvement. However, these methods are limited by their plain base distributions and their overlooking of the diversity of samples, in which different states have different returns. They simply leverage diffusion to learn the distribution of offline dataset, generate the trajectories whose states share the same distribution with the offline dataset. As a result, the probability of these models reaching the high-return states is largely dependent on the dataset distribution. Even equipped with the guidance model, the performance is still suppressed. To address these limitations, in this paper, we propose a novel method called CDiffuser, which devises a return contrast mechanism to pull the states in generated trajectories towards high-return states while pushing them away from low-return states to improve the base distribution. Experiments on 14 commonly used D4RL benchmarks demonstrate the effectiveness of our proposed method.

Large Reasoning Models (LRMs) have achieved impressive performance on challenging tasks, yet their deep reasoning often incurs substantial computational costs. To achieve efficient reasoning, existing reinforcement learning methods still struggle to construct short reasoning path during the rollout stage, limiting effective learning. Inspired by Evidence Accumulation Models, we find that LRMs have accumulated sufficient information early in reasoning, making further reasoning steps redundant. Based on this insight, we propose Just-Enough Thinking (JET), which trains models to proactively terminate unnecessary reasoning. JET performs trajectory truncation during rollout to expose the model to short, distributionally consistent reasoning paths. Besides, it uses a quality-controlled length reward to better encourage concise reasoning while maintaining correctness. Extensive experiments demonstrate that JET significantly improves reasoning efficiency without sacrificing accuracy. Especially, DeepSeek-Distill-Qwen-1.5B achieves a 4.6% accuracy gain while reducing output length by 46.3% on the Olympiad benchmark. Our code is available in the GitHub.

Reinforcement learning with verifiable rewards has shown notable effectiveness in enhancing large language models (LLMs) reasoning performance, especially in mathematics tasks. However, such improvements often come with reduced outcome diversity, where the model concentrates probability mass on a narrow set of solutions. Motivated by diminishing-returns principles, we introduce a set level diversity objective defined over sampled trajectories using kernelized similarity. Our approach derives a leave-one-out marginal contribution for each sampled trajectory and integrates this objective as a plug-in advantage shaping term for policy optimization. We further investigate the contribution of a single trajectory to language model diversity within a distribution perturbation framework. This analysis theoretically confirms a monotonicity property, proving that rarer trajectories yield consistently higher marginal contributions to the global diversity. Extensive experiments across a range of model scales demonstrate the effectiveness of our proposed algorithm, consistently outperforming strong baselines in both Pass@1 and Pass@K across various benchmarks.

Offline Reinforcement Learning (RL) is structured to derive policies from static trajectory data without requiring real-time environment interactions. Recent studies have shown the feasibility of framing offline RL as a sequence modeling task, where the sole aim is to predict actions based on prior context using the transformer architecture. However, the limitation of this single task learning approach is its potential to undermine the transformer model's attention mechanism, which should ideally allocate varying attention weights across different tokens in the input context for optimal prediction. To address this, we reformulate offline RL as a multi-objective optimization problem, where the prediction is extended to states and returns. We also highlight a potential flaw in the trajectory representation used for sequence modeling, which could generate inaccuracies when modeling the state and return distributions. This is due to the non-smoothness of the action distribution within the trajectory dictated by the behavioral policy. To mitigate this issue, we introduce action space regions to the trajectory representation. Our experiments on D4RL benchmark locomotion tasks reveal that our propositions allow for more effective utilization of the attention mechanism in the transformer model, resulting in performance that either matches or outperforms current state-of-the art methods.

Recent work suggests that large language models (LLMs) can perform multi-hop reasoning implicitly -- producing correct answers without explicitly verbalizing intermediate steps -- but the underlying mechanisms remain poorly understood. In this paper, we study how such implicit reasoning emerges by training transformers from scratch in a controlled symbolic environment. Our analysis reveals a three-stage developmental trajectory: early memorization, followed by in-distribution generalization, and eventually cross-distribution generalization. We find that training with atomic triples is not necessary but accelerates learning, and that second-hop generalization relies on query-level exposure to specific compositional structures. To interpret these behaviors, we introduce two diagnostic tools: cross-query semantic patching, which identifies semantically reusable intermediate representations, and a cosine-based representational lens, which reveals that successful reasoning correlates with the cosine-base clustering in hidden space. This clustering phenomenon in turn provides a coherent explanation for the behavioral dynamics observed across training, linking representational structure to reasoning capability. These findings provide new insights into the interpretability of implicit multi-hop reasoning in LLMs, helping to clarify how complex reasoning processes unfold internally and offering pathways to enhance the transparency of such models.

We present a Learning from Demonstration method for teaching robots to perform search strategies imitated from humans in scenarios where alignment tasks fail due to position uncertainty. The method utilizes human demonstrations to learn both a state invariant dynamics model and an exploration distribution that captures the search area covered by the demonstrator. We present two alternative algorithms for computing a search trajectory from the exploration distribution, one based on sampling and another based on deterministic ergodic control. We augment the search trajectory with forces learnt through the dynamics model to enable searching both in force and position domains. An impedance controller with superposed forces is used for reproducing the learnt strategy. We experimentally evaluate the method on a KUKA LWR4+ performing a 2D peg-in-hole and a 3D electricity socket task. Results show that the proposed method can, with only few human demonstrations, learn to complete the search task.

A central problem in learning from sequential data is representing cumulative history in an incremental fashion as more data is processed. We introduce a general framework (HiPPO) for the online compression of continuous signals and discrete time series by projection onto polynomial bases. Given a measure that specifies the importance of each time step in the past, HiPPO produces an optimal solution to a natural online function approximation problem. As special cases, our framework yields a short derivation of the recent Legendre Memory Unit (LMU) from first principles, and generalizes the ubiquitous gating mechanism of recurrent neural networks such as GRUs. This formal framework yields a new memory update mechanism (HiPPO-LegS) that scales through time to remember all history, avoiding priors on the timescale. HiPPO-LegS enjoys the theoretical benefits of timescale robustness, fast updates, and bounded gradients. By incorporating the memory dynamics into recurrent neural networks, HiPPO RNNs can empirically capture complex temporal dependencies. On the benchmark permuted MNIST dataset, HiPPO-LegS sets a new state-of-the-art accuracy of 98.3%. Finally, on a novel trajectory classification task testing robustness to out-of-distribution timescales and missing data, HiPPO-LegS outperforms RNN and neural ODE baselines by 25-40% accuracy.

One-step generative modeling seeks to generate high-quality data samples in a single function evaluation, significantly improving efficiency over traditional diffusion or flow-based models. In this work, we introduce Modular MeanFlow (MMF), a flexible and theoretically grounded approach for learning time-averaged velocity fields. Our method derives a family of loss functions based on a differential identity linking instantaneous and average velocities, and incorporates a gradient modulation mechanism that enables stable training without sacrificing expressiveness. We further propose a curriculum-style warmup schedule to smoothly transition from coarse supervision to fully differentiable training. The MMF formulation unifies and generalizes existing consistency-based and flow-matching methods, while avoiding expensive higher-order derivatives. Empirical results across image synthesis and trajectory modeling tasks demonstrate that MMF achieves competitive sample quality, robust convergence, and strong generalization, particularly under low-data or out-of-distribution settings.

A central statistical problem in population genetics is to infer evolutionary and biological parameters such as the strength of natural selection and allele age from DNA samples extracted from a contemporary population. That all samples come only from the present-day has long been known to limit statistical inference; there is potentially more information available if one also has access to ancient DNA so that inference is based on a time-series of historical changes in allele frequencies. We introduce a Markov Chain Monte Carlo (MCMC) method for Bayesian inference from allele frequency time-series data based on an underlying Wright--Fisher diffusion model of evolution, through which one can infer the parameters of essentially any selection model including those with frequency-dependent effects. The chief novelty is that we show this method to be exact in the sense that it is possible to augment the state space explored by MCMC with the unobserved diffusion trajectory, even though the transition function of this diffusion is intractable. Through careful design of a proposal distribution, we describe an efficient method in which updates to the trajectory and accept/reject decisions are calculated without error. We illustrate the method on data capturing changes in coat colour over the past 20,000 years, and find evidence to support previous findings that the mutant alleles ASIP and MC1R responsible for changes in coat color have experienced very strong, possibly overdominant, selection and further provide estimates for the ages of these genes.

The advent of large language models (LLMs) has sparked significant interest in using natural language for preference learning. However, existing methods often suffer from high computational burdens, taxing human supervision, and lack of interpretability. To address these issues, we introduce MAPLE, a framework for large language model-guided Bayesian active preference learning. MAPLE leverages LLMs to model the distribution over preference functions, conditioning it on both natural language feedback and conventional preference learning feedback, such as pairwise trajectory rankings. MAPLE also employs active learning to systematically reduce uncertainty in this distribution and incorporates a language-conditioned active query selection mechanism to identify informative and easy-to-answer queries, thus reducing human burden. We evaluate MAPLE's sample efficiency and preference inference quality across two benchmarks, including a real-world vehicle route planning benchmark using OpenStreetMap data. Our results demonstrate that MAPLE accelerates the learning process and effectively improves humans' ability to answer queries.

Continuous-valued Autoregressive (AR) image generation models have demonstrated notable superiority over their discrete-token counterparts, showcasing considerable reconstruction quality and higher generation fidelity. However, the computational demands of the autoregressive framework result in significant inference overhead. While speculative decoding has proven effective in accelerating Large Language Models (LLMs), their adaptation to continuous-valued visual autoregressive models remains unexplored. This work generalizes the speculative decoding algorithm from discrete tokens to continuous space. By analyzing the intrinsic properties of output distribution, we establish a tailored acceptance criterion for the diffusion distributions prevalent in such models. To overcome the inconsistency that occurred in speculative decoding output distributions, we introduce denoising trajectory alignment and token pre-filling methods. Additionally, we identify the hard-to-sample distribution in the rejection phase. To mitigate this issue, we propose a meticulous acceptance-rejection sampling method with a proper upper bound, thereby circumventing complex integration. Experimental results show that our continuous speculative decoding achieves a remarkable 2.33times speed-up on off-the-shelf models while maintaining the output distribution. Codes will be available at https://github.com/MarkXCloud/CSpD

Pre-trained vision-language models, such as CLIP, show impressive zero-shot recognition ability and can be easily transferred to specific downstream tasks via prompt tuning, even with limited training data. However, existing prompt tuning methods face two main challenges: (1) In few-shot scenarios, data scarcity often leads to overfitting, making the model sensitive to changes in the input domain. (2) To mitigate overfitting, these methods typically rely on complex task-specific model architectures and sensitive hyperparameter tuning, severely restricting their general applicability. To address these issues, we propose a simpler and more general framework called GLAD (Generalizable LoRA tuning with RegulArized GraDient). We show that merely applying LoRA achieves performance in downstream tasks comparable to current state-of-the-art prompt-based methods. While LoRA is effective and easy to use, it remains susceptible to overfitting in few-shot learning scenarios. To mitigate this risk, we introduce a gradient-based regularization technique. This technique effectively steers the optimization trajectory, encouraging the model to find a more stable parameter region that is robust to variations in data distribution. Through extensive experiments conducted on 15 benchmark datasets, we demonstrate that GLAD outperforms previous tuning approaches in terms of base-to-novel class generalization, image domain generalization, and cross-dataset generalization. The code will be publicly available.

Reasoning is central to purposeful action, yet most robotic foundation models map perception and instructions directly to control, which limits adaptability, generalization, and semantic grounding. We introduce Action Reasoning Models (ARMs), a class of vision-language-action models that integrate perception, planning, and control through a structured three-stage pipeline. Our model, MolmoAct, encodes observations and instructions into depth-aware perception tokens, generates mid-level spatial plans as editable trajectory traces, and predicts precise low-level actions, enabling explainable and steerable behavior. MolmoAct-7B-D achieves strong performance across simulation and real-world settings: 70.5% zero-shot accuracy on SimplerEnv Visual Matching tasks, surpassing closed-source Pi-0 and GR00T N1; 86.6% average success on LIBERO, including an additional 6.3% gain over ThinkAct on long-horizon tasks; and in real-world fine-tuning, an additional 10% (single-arm) and an additional 22.7% (bimanual) task progression over Pi-0-FAST. It also outperforms baselines by an additional 23.3% on out-of-distribution generalization and achieves top human-preference scores for open-ended instruction following and trajectory steering. Furthermore, we release, for the first time, the MolmoAct Dataset -- a mid-training robot dataset comprising over 10,000 high quality robot trajectories across diverse scenarios and tasks. Training with this dataset yields an average 5.5% improvement in general performance over the base model. We release all model weights, training code, our collected dataset, and our action reasoning dataset, establishing MolmoAct as both a state-of-the-art robotics foundation model and an open blueprint for building ARMs that transform perception into purposeful action through structured reasoning. Blogpost: https://allenai.org/blog/molmoact

Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent progress in designing fast samplers for DPMs achieves a trade-off between sampling speed and sample quality by knowledge distillation or adjusting the variance schedule or the denoising equation. However, it can't be optimal in both aspects and often suffer from mode mixture in short steps. To tackle this problem, we innovatively regard inverse diffusion as an optimal transport (OT) problem between latents at different stages and propose the DPM-OT, a unified learning framework for fast DPMs with a direct expressway represented by OT map, which can generate high-quality samples within around 10 function evaluations. By calculating the semi-discrete optimal transport map between the data latents and the white noise, we obtain an expressway from the prior distribution to the data distribution, while significantly alleviating the problem of mode mixture. In addition, we give the error bound of the proposed method, which theoretically guarantees the stability of the algorithm. Extensive experiments validate the effectiveness and advantages of DPM-OT in terms of speed and quality (FID and mode mixture), thus representing an efficient solution for generative modeling. Source codes are available at https://github.com/cognaclee/DPM-OT

Diffusion Language Models (DLMs) offer a promising alternative for language modeling by enabling parallel decoding through iterative refinement. However, most DLMs rely on hard binary masking and discrete token assignments, which hinder the revision of early decisions and underutilize intermediate probabilistic representations. In this paper, we propose EvoToken-DLM, a novel diffusion-based language modeling approach that replaces hard binary masks with evolving soft token distributions. EvoToken-DLM enables a progressive transition from masked states to discrete outputs, supporting revisable decoding. To effectively support this evolution, we introduce continuous trajectory supervision, which aligns training objectives with iterative probabilistic updates. Extensive experiments across multiple benchmarks show that EvoToken-DLM consistently achieves superior performance, outperforming strong diffusion-based and masked DLM baselines. Project webpage: https://aim-uofa.github.io/EvoTokenDLM.

We present MotionDiffuser, a diffusion based representation for the joint distribution of future trajectories over multiple agents. Such representation has several key advantages: first, our model learns a highly multimodal distribution that captures diverse future outcomes. Second, the simple predictor design requires only a single L2 loss training objective, and does not depend on trajectory anchors. Third, our model is capable of learning the joint distribution for the motion of multiple agents in a permutation-invariant manner. Furthermore, we utilize a compressed trajectory representation via PCA, which improves model performance and allows for efficient computation of the exact sample log probability. Subsequently, we propose a general constrained sampling framework that enables controlled trajectory sampling based on differentiable cost functions. This strategy enables a host of applications such as enforcing rules and physical priors, or creating tailored simulation scenarios. MotionDiffuser can be combined with existing backbone architectures to achieve top motion forecasting results. We obtain state-of-the-art results for multi-agent motion prediction on the Waymo Open Motion Dataset.

Self-improvement has emerged as a mainstream paradigm for advancing the reasoning capabilities of large vision-language models (LVLMs), where models explore and learn from successful trajectories iteratively. However, we identify a critical issue during this process: the model excels at generating high-quality trajectories for simple queries (i.e., head data) but struggles with more complex ones (i.e., tail data). This leads to an imbalanced optimization that drives the model to prioritize simple reasoning skills, while hindering its ability to tackle more complex reasoning tasks. Over iterations, this imbalance becomes increasingly pronounced--a dynamic we term the "Matthew effect"--which ultimately hinders further model improvement and leads to performance bottlenecks. To counteract this challenge, we introduce four efficient strategies from two perspectives: distribution-reshaping and trajectory-resampling, to achieve head-tail re-balancing during the exploration-and-learning self-improvement process. Extensive experiments on Qwen2-VL-7B-Instruct and InternVL2.5-4B models across visual reasoning tasks demonstrate that our methods consistently improve visual reasoning capabilities, outperforming vanilla self-improvement by 3.86 points on average.

Generative sequence models are often trained to plan motion in physical domains, from robotics to mechanical simulations. When constructing a dataset to train such a model, engineers may curate demonstrations to specify how trajectories should be distributed over a physical quantity like travel distance or mechanical energy. For example, a roboticist building a maze navigation agent might choose demonstrations whose travel distances cover a fixed range uniformly, hoping to constrain the agent's expected power usage. We find that standard deep learning can violate this intent: each generated trajectory can seem plausible on its own, but the aggregate distribution over the physical quantity is wrong. We call this failure physical misgeneralization, and develop an account of its mechanism. Using controlled synthetic tasks, we show that physical misgeneralization arises when local errors typical of the model class propagate through the physical measurement to shift the recovered distribution. We estimate these errors with a data deviation kernel, and we use it to predict which physical quantities gain or lose mass in both our synthetic and more applied maze navigation and double-pendulum motion tasks. Finally, our mechanistic interpretation helps identify which mitigation strategies are structurally promising, and we use it to propose a kernel-informed intervention.

Test-time scaling for code generation commonly relies on Best-of-N selection, in which multiple candidate solutions are sampled from a base model, and the best one is selected by an LLM judge. However, training reliable LLM judges is challenging due to severe distribution shifts, including imbalances between easy and hard problems, mismatches between training tasks and evaluation benchmarks, and trajectory mismatch arising from training data generated by cheaper models whose behavior differs from that of inference-time models. We propose DAJ, a reasoning-based LLM judge trained with verifiable rewards under a bi-level data-reweighted learning framework. The proposed framework learns data-importance weights (either domain-level or instance-level) to optimize generalization performance on a held-out meta set aligned with target benchmarks. To the best of our knowledge, this is the first application of data reweighting to LLM-as-a-Judge training for test-time scaling. Our approach automatically emphasizes hard problems, in-distribution samples, and trajectory-aligned data, without relying on hand-crafted heuristics. Empirically, DAJ achieves state-of-the-art performance on LiveCodeBench and BigCodeBench, outperforming strong test-time scaling baselines as well as leading proprietary models.

Neural rendering-based urban scene reconstruction methods commonly rely on images collected from driving vehicles with cameras facing and moving forward. Although these methods can successfully synthesize from views similar to training camera trajectory, directing the novel view outside the training camera distribution does not guarantee on-par performance. In this paper, we tackle the Extrapolated View Synthesis (EVS) problem by evaluating the reconstructions on views such as looking left, right or downwards with respect to training camera distributions. To improve rendering quality for EVS, we initialize our model by constructing dense LiDAR map, and propose to leverage prior scene knowledge such as surface normal estimator and large-scale diffusion model. Qualitative and quantitative comparisons demonstrate the effectiveness of our methods on EVS. To the best of our knowledge, we are the first to address the EVS problem in urban scene reconstruction. Link to our project page: https://vegs3d.github.io/.

We present UI-Venus, a native UI agent that takes only screenshots as input based on a multimodal large language model. UI-Venus achieves SOTA performance on both UI grounding and navigation tasks using only several hundred thousand high-quality training samples through reinforcement finetune (RFT) based on Qwen2.5-VL. Specifically, the 7B and 72B variants of UI-Venus obtain 94.1% / 50.8% and 95.3% / 61.9% on the standard grounding benchmarks, i.e., Screenspot-V2 / Pro, surpassing the previous SOTA baselines including open-source GTA1 and closed-source UI-TARS-1.5. To show UI-Venus's summary and planing ability, we also evaluate it on the AndroidWorld, an online UI navigation arena, on which our 7B and 72B variants achieve 49.1% and 65.9% success rate, also beating existing models. To achieve this, we introduce carefully designed reward functions for both UI grounding and navigation tasks and corresponding efficient data cleaning strategies. To further boost navigation performance, we propose Self-Evolving Trajectory History Alignment & Sparse Action Enhancement that refine historical reasoning traces and balances the distribution of sparse but critical actions, leading to more coherent planning and better generalization in complex UI tasks. Our contributions include the publish of SOTA open-source UI agents, comprehensive data cleaning protocols and a novel self-evolving framework for improving navigation performance, which encourage further research and development in the community. Code is available at https://github.com/inclusionAI/UI-Venus.

Sequential recommendation increasingly employs latent multi-step reasoning to enhance test-time computation. Despite empirical gains, existing approaches largely drive intermediate reasoning states via target-dominant objectives without imposing explicit feasibility constraints. This results in latent drift, where reasoning trajectories deviate into implausible regions. We argue that effective recommendation reasoning should instead be viewed as navigation on a collaborative manifold rather than free-form latent refinement. To this end, we propose ManCAR (Manifold-Constrained Adaptive Reasoning), a principled framework that grounds reasoning within the topology of a global interaction graph. ManCAR constructs a local intent prior from the collaborative neighborhood of a user's recent actions, represented as a distribution over the item simplex. During training, the model progressively aligns its latent predictive distribution with this prior, forcing the reasoning trajectory to remain within the valid manifold. At test time, reasoning proceeds adaptively until the predictive distribution stabilizes, avoiding over-refinement. We provide a variational interpretation of ManCAR to theoretically validate its drift-prevention and adaptive test-time stopping mechanisms. Experiments on seven benchmarks demonstrate that ManCAR consistently outperforms state-of-the-art baselines, achieving up to a 46.88% relative improvement w.r.t. NDCG@10. Our code is available at https://github.com/FuCongResearchSquad/ManCAR.

Single-shot neural decoders commit to answers without iterative refinement, while chain-of-thought methods introduce discrete intermediate steps but lack a scalar measure of reasoning progress. We propose Energy-Based Reasoning via Structured Latent Planning (EBRM), which models reasoning as gradient-based optimization of a multi-step latent trajectory z_{1:T} under a learned energy function E(h_x, z). The energy decomposes into per-step compatibility, transition consistency, and trajectory smoothness terms. Training combines supervised encoder-decoder learning with contrastive energy shaping using hard negatives, while inference performs gradient descent or Langevin dynamics over z and decodes from z_T. We identify a critical failure mode: on CNF logic satisfaction, latent planning reduces accuracy from approx 95% to approx 56%. This degradation arises from a distribution mismatch, where the decoder is trained on encoder outputs h_x but evaluated on planner outputs z_T that drift into unseen latent regions. We analyze this behavior through per-step decoding, latent drift tracking, and gradient decomposition. To address it, we propose dual-path decoder training and latent anchoring. We further introduce a six-part ablation protocol covering component contributions, trajectory length, planner dynamics, initialization, decoder training distribution, and anchor weight. Experiments on three synthetic tasks show that energy decreases monotonically and induces structured latent trajectories on graph and logic tasks, while remaining flat on arithmetic (r = 0.073), indicating a negative result. Code is available at https://github.com/dkjo8/ebr-via-structured-latent-planning.

We propose DemoDiffusion, a simple and scalable method for enabling robots to perform manipulation tasks in natural environments by imitating a single human demonstration. Our approach is based on two key insights. First, the hand motion in a human demonstration provides a useful prior for the robot's end-effector trajectory, which we can convert into a rough open-loop robot motion trajectory via kinematic retargeting. Second, while this retargeted motion captures the overall structure of the task, it may not align well with plausible robot actions in-context. To address this, we leverage a pre-trained generalist diffusion policy to modify the trajectory, ensuring it both follows the human motion and remains within the distribution of plausible robot actions. Our approach avoids the need for online reinforcement learning or paired human-robot data, enabling robust adaptation to new tasks and scenes with minimal manual effort. Experiments in both simulation and real-world settings show that DemoDiffusion outperforms both the base policy and the retargeted trajectory, enabling the robot to succeed even on tasks where the pre-trained generalist policy fails entirely. Project page: https://demodiffusion.github.io/

Reinforcement learning from verifiable rewards (RLVR) suffers from sparse outcome signals, creating severe exploration bottlenecks on complex reasoning tasks. Recent on-policy self-distillation methods attempt to address this by utilizing language feedback to generate dense, token-level supervision. However, these approaches rely on a fixed, passive teacher to interpret the feedback. As the student policy improves, the teacher's zero-shot assessment capabilities plateau, ultimately halting further learning. To overcome this, we propose Variational Policy Distillation (VPD), a framework that formalizes learning from language feedback as a Variational Expectation-Maximization (EM) problem. VPD co-evolves both policies: in the E-step, the teacher is actively refined on trajectory outcomes via an adaptive trust-region update, translating textual feedback into a dynamically improved target token distribution. In the M-step, the student internalizes this dense distributional guidance on its own on-policy rollouts. By continuously improving the teacher's ability to extract actionable signals from textual critique, VPD overcomes the limitations of passive distillation. Evaluated across diverse sources of diagnostic feedback on scientific reasoning and code generation tasks, VPD consistently outperforms both standard RLVR and existing self-distillation baselines. Finally, by stress-testing our framework on rigid mathematical reasoning and cold-start regimes, we illuminate the fundamental bounds of feedback-driven self-distillation compared to pure environment-driven RL.

Long-horizon LLM agents depend on intermediate information-gathering turns, yet training feedback is usually observed only at the final answer, because process-level rewards require high-quality human annotation. Existing turn-level shaping methods reward turns that increase the likelihood of a gold answer, but they require answer supervision or stable task-specific verifiers. Conversely, label-free RL methods extract self-signals from output distributions, but mainly at the answer or trajectory level and therefore cannot assign credit to intermediate turns. We propose Self-Induced Outcome Potential (SIOP), which treats semantic clusters of final answers as latent future outcome states for potential-based turn-level credit assignment. For each query, SIOP samples multiple rollouts, clusters final answers into semantic outcome modes, and builds a reliability-aware target distribution over these states. It then rewards turns for increasing posterior support for reliable future states using a tractable cluster-level approximation. The objective generalizes information-potential shaping from gold-answer supervision to settings without task-specific gold verifiers while avoiding the broadcasted rollout-level advantages used by standard GRPO. We formalize the framework, characterize its supervised gold-answer limit, and show that SIOP improves average performance over verifier-free outcome-level baselines on seven search-augmented agentic reasoning benchmarks while approaching a gold-supervised outcome baseline. Code is available at https://github.com/dl-m9/SIOP.git.

We propose Delta Velocity Rectified Flow (DVRF), a novel inversion-free, path-aware editing framework within rectified flow models for text-to-image editing. DVRF is a distillation-based method that explicitly models the discrepancy between the source and target velocity fields in order to mitigate over-smoothing artifacts rampant in prior distillation sampling approaches. We further introduce a time-dependent shift term to push noisy latents closer to the target trajectory, enhancing the alignment with the target distribution. We theoretically demonstrate that when this shift is disabled, DVRF reduces to Delta Denoising Score, thereby bridging score-based diffusion optimization and velocity-based rectified-flow optimization. Moreover, when the shift term follows a linear schedule under rectified-flow dynamics, DVRF generalizes the Inversion-free method FlowEdit and provides a principled theoretical interpretation for it. Experimental results indicate that DVRF achieves superior editing quality, fidelity, and controllability while requiring no architectural modifications, making it efficient and broadly applicable to text-to-image editing tasks. Code is available at https://github.com/gaspardbd/DeltaVelocityRectifiedFlow.

Autoregressive large language models achieve strong results on many benchmarks, but decoding remains fundamentally latency-limited by sequential dependence on previously generated tokens. Diffusion language models (DLMs) promise parallel generation but suffer from a fundamental static-to-dynamic misalignment: Training optimizes local transitions under fixed schedules, whereas efficient inference requires adaptive "long-jump" refinements through unseen states. Our goal is to enable highly parallel decoding for DLMs with low number of function evaluations while preserving generation quality. To achieve this, we propose CD4LM, a framework that decouples training from inference via Discrete-Space Consistency Distillation (DSCD) and Confidence-Adaptive Decoding (CAD). Unlike standard objectives, DSCD trains a student to be trajectory-invariant, mapping diverse noisy states directly to the clean distribution. This intrinsic robustness enables CAD to dynamically allocate compute resources based on token confidence, aggressively skipping steps without the quality collapse typical of heuristic acceleration. On GSM8K, CD4LM matches the LLaDA baseline with a 5.18x wall-clock speedup; across code and math benchmarks, it strictly dominates the accuracy-efficiency Pareto frontier, achieving a 3.62x mean speedup while improving average accuracy. Code is available at https://github.com/yihao-liang/CDLM

We present a novel data-driven simulation environment for modeling traffic in metropolitan street intersections. Using real-world tracking data collected over an extended period of time, we train trajectory forecasting models to learn agent interactions and environmental constraints that are difficult to capture conventionally. Trajectories of new agents are first coarsely generated by sampling from the spatial and temporal generative distributions, then refined using state-of-the-art trajectory forecasting models. The simulation can run either autonomously, or under explicit human control conditioned on the generative distributions. We present the experiments for a variety of model configurations. Under an iterative prediction scheme, the way-point-supervised TrajNet++ model obtained 0.36 Final Displacement Error (FDE) in 20 FPS on an NVIDIA A100 GPU.

Deep learning models achieve state-of-the art results in predicting blood glucose trajectories, with a wide range of architectures being proposed. However, the adaptation of such models in clinical practice is slow, largely due to the lack of uncertainty quantification of provided predictions. In this work, we propose to model the future glucose trajectory conditioned on the past as an infinite mixture of basis distributions (i.e., Gaussian, Laplace, etc.). This change allows us to learn the uncertainty and predict more accurately in the cases when the trajectory has a heterogeneous or multi-modal distribution. To estimate the parameters of the predictive distribution, we utilize the Transformer architecture. We empirically demonstrate the superiority of our method over existing state-of-the-art techniques both in terms of accuracy and uncertainty on the synthetic and benchmark glucose data sets.

Text-driven video generation has democratized film creation, but camera control in cinematic multi-shot scenarios remains a significant block. Implicit textual prompts lack precision, while explicit trajectory conditioning imposes prohibitive manual overhead and often triggers execution failures in current models. To overcome this bottleneck, we propose a data-centric paradigm shift, positing that aligned (Caption, Trajectory, Video) triplets form an inherent joint distribution that can connect automated plotting and precise execution. Guided by this insight, we present ShotVerse, a "Plan-then-Control" framework that decouples generation into two collaborative agents: a VLM (Vision-Language Model)-based Planner that leverages spatial priors to obtain cinematic, globally aligned trajectories from text, and a Controller that renders these trajectories into multi-shot video content via a camera adapter. Central to our approach is the construction of a data foundation: we design an automated multi-shot camera calibration pipeline aligns disjoint single-shot trajectories into a unified global coordinate system. This facilitates the curation of ShotVerse-Bench, a high-fidelity cinematic dataset with a three-track evaluation protocol that serves as the bedrock for our framework. Extensive experiments demonstrate that ShotVerse effectively bridges the gap between unreliable textual control and labor-intensive manual plotting, achieving superior cinematic aesthetics and generating multi-shot videos that are both camera-accurate and cross-shot consistent.

Existing Reinforcement Learning from Verifiable Rewards (RLVR) methods, such as Group Relative Policy Optimization (GRPO), have achieved remarkable progress in improving the reasoning capabilities of Large Reasoning Models (LRMs). However, they exhibit limited exploration due to reliance on on-policy rollouts where confined to the current policy's distribution, resulting in narrow trajectory diversity. Recent approaches attempt to expand policy coverage by incorporating trajectories generated from stronger expert models, yet this reliance increases computational cost and such advaned models are often inaccessible. To address these issues, we propose In-Context Steered Policy Optimization (ICPO), a unified framework that leverages the inherent in-context learning capability of LRMs to provide expert guidance using existing datasets. ICPO introduces Mixed-Policy GRPO with Implicit Expert Forcing, which expands exploration beyond the current policy distribution without requiring advanced LRM trajectories. To further stabilize optimization, ICPO integrates Expert Region Reject Sampling to filter unreliable off-policy trajectories and Annealed Expert-Bonus Reward Shaping to balance early expert guidance with later autonomous improvement. Results demonstrate that ICPO consistently enhances reinforcement learning performance and training stability on mathematical reasoning benchmarks, revealing a scalable and effective RLVR paradigm for LRMs.

Diffusion models have demonstrated exceptional visual quality in video generation, making them promising for autonomous driving world modeling. However, existing video diffusion-based world models struggle with flexible-length, long-horizon predictions and integrating trajectory planning. This is because conventional video diffusion models rely on global joint distribution modeling of fixed-length frame sequences rather than sequentially constructing localized distributions at each timestep. In this work, we propose Epona, an autoregressive diffusion world model that enables localized spatiotemporal distribution modeling through two key innovations: 1) Decoupled spatiotemporal factorization that separates temporal dynamics modeling from fine-grained future world generation, and 2) Modular trajectory and video prediction that seamlessly integrate motion planning with visual modeling in an end-to-end framework. Our architecture enables high-resolution, long-duration generation while introducing a novel chain-of-forward training strategy to address error accumulation in autoregressive loops. Experimental results demonstrate state-of-the-art performance with 7.4\% FVD improvement and minutes longer prediction duration compared to prior works. The learned world model further serves as a real-time motion planner, outperforming strong end-to-end planners on NAVSIM benchmarks. Code will be publicly available at https://github.com/Kevin-thu/Epona/{https://github.com/Kevin-thu/Epona/}.

Recent years have witnessed significant progress in developing efficient training and fast sampling approaches for diffusion models. A recent remarkable advancement is the use of stochastic differential equations (SDEs) to describe data perturbation and generative modeling in a unified mathematical framework. In this paper, we reveal several intriguing geometric structures of diffusion models and contribute a simple yet powerful interpretation to their sampling dynamics. Through carefully inspecting a popular variance-exploding SDE and its marginal-preserving ordinary differential equation (ODE) for sampling, we discover that the data distribution and the noise distribution are smoothly connected with an explicit, quasi-linear sampling trajectory, and another implicit denoising trajectory, which even converges faster in terms of visual quality. We also establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm, with which we can characterize the asymptotic behavior of diffusion models and identify the score deviation. These new geometric observations enable us to improve previous sampling algorithms, re-examine latent interpolation, as well as re-explain the working principles of distillation-based fast sampling techniques.

Long-horizon manipulation remains challenging for vision-language-action (VLA) policies: real tasks are multi-step, progress-dependent, and brittle to compounding execution errors. We present LoHo-Manip, a modular framework that scales short-horizon VLA execution to long-horizon instruction following via a dedicated task-management VLM. The manager is decoupled from the executor and is invoked in a receding-horizon manner: given the current observation, it predicts a progress-aware remaining plan that combines (i) a subtask sequence with an explicit done + remaining split as lightweight language memory, and (ii) a visual trace -- a compact 2D keypoint trajectory prompt specifying where to go and what to approach next. The executor VLA is adapted to condition on the rendered trace, thereby turning long-horizon decision-making into repeated local control by following the trace. Crucially, predicting the remaining plan at each step yields an implicit closed loop: failed steps persist in subsequent outputs, and traces update accordingly, enabling automatic continuation and replanning without hand-crafted recovery logic or brittle visual-history buffers. Extensive experiments spanning embodied planning, long-horizon reasoning, trajectory prediction, and end-to-end manipulation in simulation and on a real Franka robot demonstrate strong gains in long-horizon success, robustness, and out-of-distribution generalization. Project page: https://www.liuisabella.com/LoHoManip

Reinforcement Learning from Verifiable Rewards (RLVR) has emerged as a powerful paradigm for enhancing the complex reasoning capabilities of Large Reasoning Models. However, standard outcome-based supervision suffers from a critical limitation that penalizes trajectories that are largely correct but fail due to several missteps as heavily as completely erroneous ones. This coarse feedback signal causes the model to discard valuable largely correct rollouts, leading to a degradation in rollout diversity that prematurely narrows the exploration space. Process Reward Models have demonstrated efficacy in providing reliable step-wise verification for test-time scaling, naively integrating these signals into RLVR as dense rewards proves ineffective.Prior methods attempt to introduce off-policy guided whole-trajectory replacement that often outside the policy model's distribution, but still fail to utilize the largely correct rollouts generated by the model itself and thus do not effectively mitigate the narrowing of the exploration space. To address these issues, we propose SCOPE (Step-wise Correction for On-Policy Exploration), a novel framework that utilizes Process Reward Models to pinpoint the first erroneous step in suboptimal rollouts and applies fine-grained, step-wise off-policy rectification. By applying precise refinement on partially correct rollout, our method effectively salvages partially correct trajectories and increases diversity score by 13.5%, thereby sustaining a broad exploration space. Extensive experiments demonstrate that our approach establishes new state-of-the-art results, achieving an average accuracy of 46.6% on math reasoning and exhibiting robust generalization with 53.4% accuracy on out-of-distribution reasoning tasks.

Diffusion models have found widespread adoption in various areas. However, their sampling process is slow because it requires hundreds to thousands of network evaluations to emulate a continuous process defined by differential equations. In this work, we use neural operators, an efficient method to solve the probability flow differential equations, to accelerate the sampling process of diffusion models. Compared to other fast sampling methods that have a sequential nature, we are the first to propose parallel decoding method that generates images with only one model forward pass. We propose diffusion model sampling with neural operator (DSNO) that maps the initial condition, i.e., Gaussian distribution, to the continuous-time solution trajectory of the reverse diffusion process. To model the temporal correlations along the trajectory, we introduce temporal convolution layers that are parameterized in the Fourier space into the given diffusion model backbone. We show our method achieves state-of-the-art FID of 4.12 for CIFAR-10 and 8.35 for ImageNet-64 in the one-model-evaluation setting.

Pixel-space generative models are often more difficult to train and generally underperform compared to their latent-space counterparts, leaving a persistent performance and efficiency gap. In this paper, we introduce a novel two-stage training framework that closes this gap for pixel-space diffusion and consistency models. In the first stage, we pre-train encoders to capture meaningful semantics from clean images while aligning them with points along the same deterministic sampling trajectory, which evolves points from the prior to the data distribution. In the second stage, we integrate the encoder with a randomly initialized decoder and fine-tune the complete model end-to-end for both diffusion and consistency models. Our training framework demonstrates strong empirical performance on ImageNet dataset. Specifically, our diffusion model reaches an FID of 2.04 on ImageNet-256 and 2.35 on ImageNet-512 with 75 number of function evaluations (NFE), surpassing prior pixel-space methods by a large margin in both generation quality and efficiency while rivaling leading VAE-based models at comparable training cost. Furthermore, on ImageNet-256, our consistency model achieves an impressive FID of 8.82 in a single sampling step, significantly surpassing its latent-space counterpart. To the best of our knowledge, this marks the first successful training of a consistency model directly on high-resolution images without relying on pre-trained VAEs or diffusion models.

Unsupervised anomaly detection (UAD) in brain imaging is crucial for identifying pathologies without the need for labeled data. However, accurately localizing anomalies remains challenging due to the intricate structure of brain anatomy and the scarcity of abnormal examples. In this work, we introduce REFLECT, a novel framework that leverages rectified flows to establish a direct, linear trajectory for correcting abnormal MR images toward a normal distribution. By learning a straight, one-step correction transport map, our method efficiently corrects brain anomalies and can precisely localize anomalies by detecting discrepancies between anomalous input and corrected counterpart. In contrast to the diffusion-based UAD models, which require iterative stochastic sampling, rectified flows provide a direct transport map, enabling single-step inference. Extensive experiments on popular UAD brain segmentation benchmarks demonstrate that REFLECT significantly outperforms state-of-the-art unsupervised anomaly detection methods. The code is available at https://github.com/farzad-bz/REFLECT.

The post-training pipeline for diffusion models currently has two stages: supervised fine-tuning (SFT) on curated data and reinforcement learning (RL) with reward models. A fundamental gap separates them. SFT optimizes the denoiser only on ground-truth states sampled from the forward noising process; once inference deviates from these ideal states, subsequent denoising relies on out-of-distribution generalization rather than learned correction, exhibiting the same exposure bias that afflicts autoregressive models, but accumulated along the denoising trajectory instead of the token sequence. RL can in principle address this mismatch, yet its terminal reward signal is sparse, suffers from credit-assignment difficulty, and risks reward hacking. We propose SOAR (Self-Correction for Optimal Alignment and Refinement), a bias-correction post-training method that fills this gap. Starting from a real sample, SOAR performs a single stop-gradient rollout with the current model, re-noises the resulting off-trajectory state, and supervises the model to steer back toward the original clean target. The method is on-policy, reward-free, and provides dense per-timestep supervision with no credit-assignment problem. On SD3.5-Medium, SOAR improves GenEval from 0.70 to 0.78 and OCR from 0.64 to 0.67 over SFT, while simultaneously raising all model-based preference scores. In controlled reward-specific experiments, SOAR surpasses Flow-GRPO in final metric value on both aesthetic and text-image alignment tasks, despite having no access to a reward model. Since SOAR's base loss subsumes the standard SFT objective, it can directly replace SFT as a stronger first post-training stage after pretraining, while remaining fully compatible with subsequent RL alignment.

Large language models are transforming systems research by automating the discovery of performance-critical algorithms for computer systems. Despite plausible codes generated by LLMs, producing solutions that meet the stringent correctness and performance requirements of systems demands iterative optimization. Test-time reinforcement learning offers high search efficiency but requires parameter updates infeasible under API-only access, while existing training-free evolutionary methods suffer from inefficient context utilization and undirected search. We introduce ContextEvolve, a multi-agent framework that achieves RL-level search efficiency under strict parameter-blind constraints by decomposing optimization context into three orthogonal dimensions: a Summarizer Agent condenses semantic state via code-to-language abstraction, a Navigator Agent distills optimization direction from trajectory analysis, and a Sampler Agent curates experience distribution through prioritized exemplar retrieval. This orchestration forms a functional isomorphism with RL-mapping to state representation, policy gradient, and experience replay-enabling principled optimization in a textual latent space. On the ADRS benchmark, ContextEvolve outperforms state-of-the-art baselines by 33.3% while reducing token consumption by 29.0%. Codes for our work are released at https://anonymous.4open.science/r/ContextEvolve-ACC

Reinforcement learning, including reinforcement learning with verifiable rewards (RLVR), has emerged as a powerful approach for LLM post-training. Central to these approaches is the design of the importance sampling (IS) ratio used in off-policy policy-gradient estimation. Existing methods face a fundamental bias-variance dilemma: token-level IS ratios, as adopted by PPO (Schulman et al., 2017) and GRPO (Shao et al., 2024), introduce bias by ignoring prefix state distribution mismatch; full sequence ratios provide exact trajectory-level correction but suffer from high variance due to the multiplicative accumulation of per-token ratios, while GSPO (Zheng et al., 2025) improves numerical stability via length normalization at the cost of deviating from the exact full-sequence IS correction. In this work, we identify the cumulative token IS ratio, the product of per-token ratios up to position t, as a theoretically principled solution to this dilemma. We prove that, under the token-level policy-gradient formulation, this ratio provides an unbiased prefix correction for each token-level gradient term and has strictly lower variance than the full sequence ratio. Building on this insight, we propose CTPO (Cumulative Token Policy Optimization), which combines the cumulative token IS ratio with position-adaptive clipping that scales log-space clip bounds according to the natural t growth of the cumulative log-ratio. This yields more consistent regularization across token positions. We implement and evaluate CTPO in the tool-integrated reasoning setting on several challenging mathematical reasoning benchmarks, achieving the best average performance across both model scales compared with strong GRPO and GSPO baselines. Code will be available at https://github.com/horizon-llm/CTPO.

Density of the reachable states can help understand the risk of safety-critical systems, especially in situations when worst-case reachability is too conservative. Recent work provides a data-driven approach to compute the density distribution of autonomous systems' forward reachable states online. In this paper, we study the use of such approach in combination with model predictive control for verifiable safe path planning under uncertainties. We first use the learned density distribution to compute the risk of collision online. If such risk exceeds the acceptable threshold, our method will plan for a new path around the previous trajectory, with the risk of collision below the threshold. Our method is well-suited to handle systems with uncertainties and complicated dynamics as our data-driven approach does not need an analytical form of the systems' dynamics and can estimate forward state density with an arbitrary initial distribution of uncertainties. We design two challenging scenarios (autonomous driving and hovercraft control) for safe motion planning in environments with obstacles under system uncertainties. We first show that our density estimation approach can reach a similar accuracy as the Monte-Carlo-based method while using only 0.01X training samples. By leveraging the estimated risk, our algorithm achieves the highest success rate in goal reaching when enforcing the safety rate above 0.99.

In reinforcement learning and imitation learning, an object of central importance is the state distribution induced by the policy. It plays a crucial role in the policy gradient theorem, and references to it--along with the related state-action distribution--can be found all across the literature. Despite its importance, the state distribution is mostly discussed indirectly and theoretically, rather than being modeled explicitly. The reason being an absence of appropriate density estimation tools. In this work, we investigate applications of a normalizing flow-based model for the aforementioned distributions. In particular, we use a pair of flows coupled through the optimality point of the Donsker-Varadhan representation of the Kullback-Leibler (KL) divergence, for distribution matching based imitation learning. Our algorithm, Coupled Flow Imitation Learning (CFIL), achieves state-of-the-art performance on benchmark tasks with a single expert trajectory and extends naturally to a variety of other settings, including the subsampled and state-only regimes.

In trajectory forecasting tasks for traffic, future output trajectories can be computed by advancing the ego vehicle's state with predicted actions according to a kinematics model. By unrolling predicted trajectories via time integration and models of kinematic dynamics, predicted trajectories should not only be kinematically feasible but also relate uncertainty from one timestep to the next. While current works in probabilistic prediction do incorporate kinematic priors for mean trajectory prediction, variance is often left as a learnable parameter, despite uncertainty in one time step being inextricably tied to uncertainty in the previous time step. In this paper, we show simple and differentiable analytical approximations describing the relationship between variance at one timestep and that at the next with the kinematic bicycle model. These approximations can be easily incorporated with negligible additional overhead into any existing trajectory forecasting framework utilizing probabilistic predictions, whether it is autoregressive or one-shot prediction. In our results, we find that encoding the relationship between variance across timesteps works especially well in unoptimal settings, such as with small or noisy datasets. We observe up to a 50% performance boost in partial dataset settings and up to an 8% performance boost in large-scale learning compared to previous kinematic prediction methods on SOTA trajectory forecasting architectures out-of-the-box, with no fine-tuning. In this paper, we show four analytical formulations of probabilistic kinematic priors which can be used for any Gaussian Mixture Model (GMM)-based deep learning models, quantify the error bound on linear approximations applied during trajectory unrolling, and show results to evaluate each formulation in trajectory forecasting.

We introduce a learning-guided motion planning framework that generates seed trajectories using a diffusion model for trajectory optimization. Given a workspace, our method approximates the configuration space (C-space) obstacles through an environment representation consisting of a sparse set of task-related key configurations, which is then used as a conditioning input to the diffusion model. The diffusion model integrates regularization terms that encourage smooth, collision-free trajectories during training, and trajectory optimization refines the generated seed trajectories to correct any colliding segments. Our experimental results demonstrate that high-quality trajectory priors, learned through our C-space-grounded diffusion model, enable the efficient generation of collision-free trajectories in narrow-passage environments, outperforming previous learning- and planning-based baselines. Videos and additional materials can be found on the project page: https://kiwi-sherbet.github.io/PRESTO.

User profiling and region analysis are two tasks of significant commercial value. However, in practical applications, modeling different features typically involves four main steps: data preparation, data processing, model establishment, evaluation, and optimization. This process is time-consuming and labor-intensive. Repeating this workflow for each feature results in abundant development time for tasks and a reduced overall volume of task development. Indeed, human mobility data contains a wealth of information. Several successful cases suggest that conducting in-depth analysis of population movement data could potentially yield meaningful profiles about users and areas. Nonetheless, most related works have not thoroughly utilized the semantic information within human mobility data and trained on a fixed number of the regions. To tap into the rich information within population movement, based on the perspective that Regions Are Who walk them, we propose a large spatiotemporal model based on trajectories (RAW). It possesses the following characteristics: 1) Tailored for trajectory data, introducing a GPT-like structure with a parameter count of up to 1B; 2) Introducing a spatiotemporal fine-tuning module, interpreting trajectories as collection of users to derive arbitrary region embedding. This framework allows rapid task development based on the large spatiotemporal model. We conducted extensive experiments to validate the effectiveness of our proposed large spatiotemporal model. It's evident that our proposed method, relying solely on human mobility data without additional features, exhibits a certain level of relevance in user profiling and region analysis. Moreover, our model showcases promising predictive capabilities in trajectory generation tasks based on the current state, offering the potential for further innovative work utilizing this large spatiotemporal model.

We present Orbit-Space Geometric Probability Paths (OGPP), a particle-native flow-matching framework for generative modeling of particle systems. OGPP is motivated by two insights: (i) particles are defined up to permutation symmetries, so anonymous indexing inflates per-index target variance and yields curved, hard-to-learn flows; and (ii) particles live in physical space, so the flow terminal velocity has physical meaning and can encode geometric attributes, e.g., surface normals. OGPP instantiates three key components: (1) orbit-space canonicalization of the probability-path terminal endpoint, (2) particle index embeddings for role specialization, and (3) geometric probability paths with arc-length-aware terminal velocities that generate normals as a byproduct of the flow. We evaluate OGPP on minimal-surface benchmarks, where it reduces metric error by up to two orders of magnitude in a single inference step; on ShapeNet, where it matches the state of the art with 5x fewer steps and reaches airplane EMD comparable to DiT-3D with 26x fewer parameters and 5x fewer steps; and on single-shape encoding, where it produces normals and reconstructions competitive with 6D generators while operating entirely in 3D.

Diffusion models have shown strong competitiveness in offline reinforcement learning tasks by formulating decision-making as sequential generation. However, the practicality of these methods is limited due to the lengthy inference processes they require. In this paper, we address this problem by decomposing the sampling process of diffusion models into two decoupled subprocesses: 1) generating a feasible trajectory, which is a time-consuming process, and 2) optimizing the trajectory. With this decomposition approach, we are able to partially separate efficiency and quality factors, enabling us to simultaneously gain efficiency advantages and ensure quality assurance. We propose the Trajectory Diffuser, which utilizes a faster autoregressive model to handle the generation of feasible trajectories while retaining the trajectory optimization process of diffusion models. This allows us to achieve more efficient planning without sacrificing capability. To evaluate the effectiveness and efficiency of the Trajectory Diffuser, we conduct experiments on the D4RL benchmarks. The results demonstrate that our method achieves it 3-it 10 times faster inference speed compared to previous sequence modeling methods, while also outperforming them in terms of overall performance. https://github.com/RenMing-Huang/TrajectoryDiffuser Keywords: Reinforcement Learning and Efficient Planning and Diffusion Model

Capturing high-dimensional social interactions and feasible futures is essential for predicting trajectories. To address this complex nature, several attempts have been devoted to reducing the dimensionality of the output variables via parametric curve fitting such as the B\'ezier curve and B-spline function. However, these functions, which originate in computer graphics fields, are not suitable to account for socially acceptable human dynamics. In this paper, we present EigenTrajectory (ET), a trajectory prediction approach that uses a novel trajectory descriptor to form a compact space, known here as ET space, in place of Euclidean space, for representing pedestrian movements. We first reduce the complexity of the trajectory descriptor via a low-rank approximation. We transform the pedestrians' history paths into our ET space represented by spatio-temporal principle components, and feed them into off-the-shelf trajectory forecasting models. The inputs and outputs of the models as well as social interactions are all gathered and aggregated in the corresponding ET space. Lastly, we propose a trajectory anchor-based refinement method to cover all possible futures in the proposed ET space. Extensive experiments demonstrate that our EigenTrajectory predictor can significantly improve both the prediction accuracy and reliability of existing trajectory forecasting models on public benchmarks, indicating that the proposed descriptor is suited to represent pedestrian behaviors. Code is publicly available at https://github.com/inhwanbae/EigenTrajectory .

The field of trajectory forecasting has grown significantly in recent years, partially owing to the release of numerous large-scale, real-world human trajectory datasets for autonomous vehicles (AVs) and pedestrian motion tracking. While such datasets have been a boon for the community, they each use custom and unique data formats and APIs, making it cumbersome for researchers to train and evaluate methods across multiple datasets. To remedy this, we present trajdata: a unified interface to multiple human trajectory datasets. At its core, trajdata provides a simple, uniform, and efficient representation and API for trajectory and map data. As a demonstration of its capabilities, in this work we conduct a comprehensive empirical evaluation of existing trajectory datasets, providing users with a rich understanding of the data underpinning much of current pedestrian and AV motion forecasting research, and proposing suggestions for future datasets from these insights. trajdata is permissively licensed (Apache 2.0) and can be accessed online at https://github.com/NVlabs/trajdata

Trajectory planning is commonly used as part of a local planner in autonomous driving. This paper considers the problem of planning a continuous-curvature-rate trajectory between fixed start and goal states that minimizes a tunable trade-off between passenger comfort and travel time. The problem is an instance of infinite dimensional optimization over two continuous functions: a path, and a velocity profile. We propose a simplification of this problem that facilitates the discretization of both functions. This paper also proposes a method to quickly generate minimal-length paths between start and goal states based on a single tuning parameter: the second derivative of curvature. Furthermore, we discretize the set of velocity profiles along a given path into a selection of acceleration way-points along the path. Gradient-descent is then employed to minimize cost over feasible choices of the second derivative of curvature, and acceleration way-points, resulting in a method that repeatedly solves the path and velocity profiles in an iterative fashion. Numerical examples are provided to illustrate the benefits of the proposed methods.

Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite intervals, circles, cylinders, spheres, other manifolds, and graphs. This paper introduces an approach for detecting differences between two collections of distributions over such general domains. To this end, we propose the intrinsic slicing construction that yields a novel class of Wasserstein distances on manifolds and graphs. These distances are Hilbert embeddable, allowing us to reduce the distribution collection comparison problem to a more familiar mean testing problem in a Hilbert space. We provide two testing procedures one based on resampling and another on combining p-values from coordinate-wise tests. Our experiments in various synthetic and real data settings show that the resulting tests are powerful and the p-values are well-calibrated.

Recent successful generative models are trained by fitting a neural network to an a-priori defined tractable probability density path taking noise to training examples. In this paper we investigate the space of Gaussian probability paths, which includes diffusion paths as an instance, and look for an optimal member in some useful sense. In particular, minimizing the Kinetic Energy (KE) of a path is known to make particles' trajectories simple, hence easier to sample, and empirically improve performance in terms of likelihood of unseen data and sample generation quality. We investigate Kinetic Optimal (KO) Gaussian paths and offer the following observations: (i) We show the KE takes a simplified form on the space of Gaussian paths, where the data is incorporated only through a single, one dimensional scalar function, called the data separation function. (ii) We characterize the KO solutions with a one dimensional ODE. (iii) We approximate data-dependent KO paths by approximating the data separation function and minimizing the KE. (iv) We prove that the data separation function converges to 1 in the general case of arbitrary normalized dataset consisting of n samples in d dimension as n/drightarrow 0. A consequence of this result is that the Conditional Optimal Transport (Cond-OT) path becomes kinetic optimal as n/drightarrow 0. We further support this theory with empirical experiments on ImageNet.

Straight line equation y=mx with slope m, when singularly perturbed as ay^3+y=mx with a positive parameter a, results in S-shaped curves or S-curves on a real plane. As arightarrow 0, we get back y=mx which is a cumulative distribution function of a continuous uniform distribution that describes the occurrence of every event in an interval to be equally probable. As arightarrowinfty, the derivative of y has finite support only at y=0 resembling a degenerate distribution. Based on these arguments, in this work, we propose that these S-curves can represent maximum entropy uniform distribution to a zero entropy single value. We also argue that these S-curves are superposable as they are only parametrically nonlinear but fundamentally linear. So far, the superposed forms have been used to capture the patterns of natural systems such as nonlinear dynamics of biological growth and kinetics of enzyme reactions. Here, we attempt to use the S-curve and its superposed form as statistical models. We fit the models on a classical dataset containing flower measurements of iris plants and analyze their usefulness in pattern recognition. Based on these models, we claim that any non-uniform pattern can be represented as a singular perturbation to uniform distribution. However, our parametric estimation procedure have some limitations such as sensitivity to initial conditions depending on the data at hand.