Diffusion Policy

Recent advances in reinforcement learning (RL) have achieved great successes by leveraging the multimodality and exploration capability of diffusion policies. Among these approaches, one representative branch focuses on the sampling-based policy optimization. This design enables better exploration capability of the diffusion model, particularly at the beginning of training, but suffer from low exploitation in Q-value information, resulting in a slow policy convergence. Another branch pays attention to gradient-based policy optimization, which sufficiently exploits the gradient of the Q function yet tends to collapse into a unimodal policy with low diversity. To address this issue, we propose CGPO, \textbf{C}ritic-\textbf{G}uided diffusion \textbf{P}olicy \textbf{O}ptimization, which effectively balances exploration and exploitation with the training-free guidance technique integrated into the denoising process of diffusion policy. Concretely, CGPO steers action generation toward high-value regions defined by the critic network and uses the guided actions as regression objectives. In this manner, CGPO reduces the time required to obtain high-quality actions and improves final performance with better balance between the exploration-exploitation tradeoff. We validate the effectiveness of CGPO on 5 MuJoCo locomotion tasks, and CGPO achieves state-of-the-art performance compared with existing diffusion-based RL methods. Notably, CGPO is the first success to incorporate diffusion policy into real-world RL, with its superior performance on Franka robot arm grasping tasks. Our official page is released at https://dingsht.tech/cgpo-webpage.

Diffusion models are effective for waypoint prediction in visual navigation, but standard sampling and test time guidance can produce unreliable or inefficient trajectories when updates drift off the training manifold. We propose Fisher Preserving Guidance with Outer Product Span Projection, a training-free inference method that avoids large Fisher drift associated with off-distribution actions while optimizing a task objective. Our method computes the Fisher-preserving update via a low-rank Jacobian factorization, requiring only a single backward pass per step and enabling real-time use. We further introduce Truncated Fisher Denoising Sensitivity as an uncertainty signal and use it for robust multi-sample action blending. Experiments on toy and realistic navigation benchmarks, including Maze2D with TSDF-based guidance, PushT with official Diffusion Policy weights, and visual navigation in simulation and on real robots, demonstrate consistent improvements in performance over strong diffusion-policy baselines without additional training.

Learning visuomotor policies via behavior cloning typically involves mimicking expert demonstrations collected by human operators. However, natural human demonstrations inherently contain high-frequency noise, such as intermittent jerks, pauses, and action jitter. Training policies to directly imitate these raw trajectories inevitably causes the model to inherit these suboptimal behaviors. This pathology is particularly pronounced in diffusion-based policies, where iterative denoising steps can inadvertently amplify high-frequency artifacts at the expense of meaningful fine-grained details. To address these limitations, we present a novel frequency-based algorithm that enables implicit spectral maneuvering and smooth action generation. Our method, Frequency Guidance Operator (FGO), steers the generation process of diffusion polices by progressively driving the noisy samples through intermediate sub-frequency manifolds with expanding spectral bands. Validated on 15 robotic manipulation tasks from 5 benchmarks, FGO achieves superior performance in enhancing action smoothness and temporal consistency while preserving the details necessary for successful task execution. Project website: https://henrywjl.github.io/frequency-guidance-operator/

Model-based reinforcement learning (RL) can be effectively supported at scale through the use of world models. However, in practice, scaling such approaches remains fundamentally limited. A commonly recognized challenge is model bias and error compounding, which degrade long-horizon predictions. Beyond these issues, we identify a more critical yet underexplored bottleneck: a structural misalignment between search and value learning in existing world model approaches. In particular, policy improvement often relies on value functions induced by a separate, non-search policy, resulting in training inconsistency and ultimately suboptimal learning. To address this limitation, we propose Model-Based Diffusion Policy Optimization (MBDPO) in world models, a framework that unifies search and policy optimization through diffusion policy representations, thereby unlocking the potential of world models for scalable policy learning. Instead of constructing an explicit planner over a learned world model, we reformulate policy optimization as a diffusion process over searched trajectories in latent world models. In this view, we extract an implicit energy function from the collected dataset that anchors the policy, enabling MBDPO to refine the score field for policy optimization while mitigating misalignment. We evaluate MBDPO across a wide range of settings, including multi-task offline pretraining, online learning, and offline-to-online fine-tuning. In the offline regime, we further investigate its scaling behavior by pretraining on large-scale datasets, observing consistent and monotonic performance gains with increasing model capacity.

Diffusion models are increasingly used as powerful conditional generators, yet real deployments often involve multiple target distributions arising from different tasks, e.g., diverse prompt domains in text-to-image generation, or multiple environments in robotics with diffusion policies. This naturally leads to a multi-objective learning (MOL) problem. A key challenge is that achieving good Pareto trade-offs can require a generalist model class with substantially larger capacity than what suffices for solving any individual task, thereby increasing statistical cost since sample complexity typically scales with the model complexity. To reconcile this, we develop a principled MOL framework for diffusion models with limited data: a semi-supervised regime where paired (labeled) samples are scarce, but (unlabeled) condition data are abundant. We propose a two-stage training procedure that first fits lightweight specialist models from limited paired data, and then distills them into a generalist model by generating pseudo-samples. We establish generalization bounds showing that the required number of paired samples only depends on the complexity of the specialist model classes. We further extend the theory to diffusion policies for sequential decision making to account for distribution shift in on-policy rollouts. Extensive experiments on robotic control and image restoration tasks are conducted to verify our theoretical results.

Learning universal policies from cross-embodied data remains a fundamental challenge in robotics. Although Vision-Language-Action (VLA) models are pre-trained on large and diverse datasets, they typically rely on embodiment-specific fine-tuning to achieve strong performance in downstream tasks. This requirement severely limits their generalization capability and restricts knowledge transfer across embodiments performing similar tasks. To overcome these limitations, we focus on cross-embodied settings with shared robotic bases and heterogeneous end-effectors, and propose X-DiffVLA, a diffusion-based VLA model featuring a unified cross-embodied action head. X-DiffVLA can leverage the generative strengths of diffusion models to capture both the diversity and latent correlations in cross-embodied datasets. Specifically, we introduce Embodiment Forcing, a classifier-free guidance technique to implicitly steer action generation toward embodiment-specific functional components, capturing fine-grained structural nuances without explicit supervision. In addition, a Morphological Tree Diffusion approach is designed to strengthen behavioral correlations across diverse end-effectors, maximizing the transferability of heterogeneous demonstrations. Experimental results across RoboCasa and Isaac Gym, covering different embodiments from grippers to dexterous hands, show that X-DiffVLA achieves state-of-the-art performance, with improvements of 15.3% and 12.5%, respectively. Real-world evaluations further validate the robustness of the proposed framework and its effectiveness in scalable cross-embodied policy learning.

Diffusion models excel at generating diverse, multimodal trajectories for robotic control, yet their iterative denoising process introduces latency that can constrain real-time closed-loop execution. To address this problem, we propose a Dynamic Neural Koopman (DNK) distillation framework, which distills multistep diffusion inference into a single forward pass conditioned on observations and sampled noise. Specifically, we introduce a Factorized Dynamic Koopman (FDK) layer that models the denoising process through a latent linear transition. The noisy trajectory input is lifted into a latent space, where the FDK layer parameterizes a factorized linear operator with condition-dependent eigenvalues that adapt the noisy-to-denoised transition to the current context. We evaluate DNK across robot-control benchmarks that span locomotion, state-based, and image-based manipulation, comparing against accelerated generative-policy baselines. The results demonstrate that DNK achieves competitive or improved closed-loop performance relative to accelerated generative-policy baselines, while substantially reducing inference latency relative to the strongest high-performing one-step baselines. On long-horizon manipulation tasks, DNK achieves competitive performance with substantially fewer inference parameters than the one-step policy baselines. Hardware experiments on a physical Kinova manipulator further demonstrate millisecond-scale inference and reduced task completion time. A project page is available at https://fdkoopman.github.io/.

Diffusion-based policies have established a new standard for precise robotic manipulation but face a critical scalability bottleneck: high-performance models are computationally expensive, while lightweight alternatives often fail to generalize across diverse multi-task environments. Mixture-of-Experts (MoE) architectures offer a promising path to efficiency by activating only a subset of parameters. However, existing MoE routing mechanisms typically rely on low-level noise or latent statistics, ignoring the compositional nature of manipulation tasks. This can fragment reusable behaviors across experts, limiting interpretability and transferability. We introduce Semantically Structured Mixture-of-Experts Diffusion Policy (SMoDP) for compositional robotic manipulation, a framework that grounds expert specialization in semantic task structure. SMoDP leverages a lightweight, inference-time skill predictor, supervised by offline annotations from Vision-Language Models (VLMs), to route action chunks to experts specialized for specific behavioral phases. To ensure robust assignment, we propose a dual contrastive alignment strategy that grounds multi-modal observations in language-defined skill semantics (Inter-modal) while enforcing routing consistency across visually distinct but functionally related behaviors (Intra-modal). Our approach outperforms representative diffusion and MoE-based baselines on multi-task benchmarks with significantly improved parameter efficiency and demonstrates effective compositional transfer to novel tasks through parameter-efficient fine-tuning. Project website: https://deng-cy20.github.io/SMoDP/

Robotic tasks are typically specified by a tuple of factors, such as the object to be grasped, the obstacles to be avoided, the color of the target, and so on. Collecting expert demonstrations for every combination of factor values grows combinatorially. We present factored diffusion policies: a single shared diffusion network trained with per-factor null-token dropout, whose score decomposes additively across factors at inference. Under approximate conditional independence between factors given the action-observation pair, this composition approximates the true joint score with a bounded uniform error, reducing the training-task budget from a product of factor cardinalities to a sum. A trajectory-tube certificate chains this score-level bound through the reverse-time sampling ODE and a contracting tracking controller into a closed-loop state-trajectory tube whose radius factors into an ODE-sensitivity constant and a per-factor score-error budget. Unlike compositional-diffusion methods for control that combine separately trained networks, we use one shared network. Drone racing experiments confirm both the generalization bound and the certificate. On state-based multi-gate racing, the factored policy passes 90% of held-out gates -- matching an oracle -- while a K-network composition baseline collapses to 3%; on vision-based single-gate traversal, it transfers zero-shot to an unseen venue with +11.7pp success-rate gain and 2.4X crash-rate reduction.

Controlling physics-based humanoids from natural-language instructions is a critical step toward general-purpose embodied agents. However, existing methods remain constrained by a tension between semantic expressiveness and physical feasibility, often failing to jointly achieve faithful instruction following, high-quality motion, and stable long-horizon control. We propose SCRIPT, a scalable diffusion policy with a multi-stage training framework for language-driven physics-based humanoid control. The core of SCRIPT is a Joint Action-State-Text Diffusion Transformer (JAST-DiT), which represents actions, physical states, and text as dedicated token streams and couples them through joint attention, enabling direct interaction between language semantics and control dynamics. To stabilize autoregressive control, we introduce a nonlinear history conditioning mechanism, which preserves the dense recent context and samples increasingly sparse cues from long-term history. Beyond supervised imitation pre-training, we propose a post-training stage, further improving the performance using Reinforcement Learning with Hybrid Rewards (RLHR). By injecting learnable noise into the flow-sampling process, RLHR effectively improves motion quality and instruction following within closed-loop simulations using hybrid physical feedback and text rewards. Quantitative evaluations demonstrate that SCRIPT outperforms prior state-of-the-art methods, with gains across text alignment, motion quality, and physical realism metrics. Furthermore, scaling studies on the 1200-hour MotionMillion dataset demonstrate consistent performance gains with model scaling, highlighting SCRIPT's robust scalability for large-scale pre-training. Our code will be publicly available for future research.

Autonomous manipulation systems have achieved remarkable capabilities, yet the integration of human expertise with diffusion-based policies in shared control remains relatively unexplored. In this paper, we propose Human-In-The-Loop Diffusion (HITL-D), a shared control framework that enhances user performance in multi-step, insertion, and fine manipulation tasks. HITL-D leverages a novel combination of diffusion-based policies and human control to provide autonomous end effector orientation updates conditioned on a scene point cloud and the Cartesian position of the end effector. This approach reduces the number of joystick control axes required, thereby lowering mental workload. In a multi-task user study with 12 participants, HITL-D reduced average task completion times by 40%, decreased perceived workload by 37%, and improved Likert-scale ratings for independence, intuitiveness, and confidence compared to traditional teleoperation methods. These results demonstrate that HITL-D effectively integrates human expertise with autonomous assistance, improving both objective and subjective aspects of teleoperation.

Mobile imitation learning on portable demonstration interfaces faces two coupled bottlenecks: locomotion-contaminated action labels and inference-induced execution latency on a continuously moving base. Recent wrist-mounted interfaces lower the cost of tabletop data collection, yet a single wrist view does not capture the global context required for base navigation. Adding a body-mounted camera entangles human walking with hand motion. Meanwhile, generative policies introduce hundreds of milliseconds of inference latency, during which the base advances past predicted waypoints, forcing backward corrections at action splices. This paper presents Mobile UMI, a hardware-free demonstration framework that addresses both gaps through three components. First, a dual-camera capture system records chest-centric global context and wrist-centric local interaction without any robot present. Second, a one-shot ChArUco-based spatial anchor unifies the chest and hand visual-inertial frames; the hand pose is then re-expressed relative to the chest to extract decoupled SE(3) manipulation and SE(2) base trajectories. Third, an asynchronous receding-horizon executor performs online state matching: each generated action chunk is realigned with the current physical pose so that expired waypoints are discarded before execution. The full system is evaluated on four long-horizon household tasks, achieving an average success rate of 83.8% over 100 trials per task. Controlled comparisons against ACT and Diffusion Policy show that the chest-relative label alone closes much of the gap; online state matching closes the remainder. These results indicate that, for mobile imitation learning under the tested conditions, explicit kinematic factorization combined with state-level latency alignment provides an effective solution without requiring architectural changes to the underlying policy class.

Explainable robots require not only successful task execution but also the ability to expose internal decision-making process in a user-friendly manner. However, most imitation learning methods are trained solely on task-level demonstrations, without explicitly modeling subgoal structure or execution progress. This limitation is further exacerbated by the scarcity of subgoal-level supervision in standard robot learning datasets, which restricts the development of robots that can convey the subtasks they are executing during long-horizon manipulation. To address this issue, this paper proposes Subgoal-Aware Diffusion Policy (SADP), a framework that leverages foundation models to autonomously generate subgoal-annotated demonstrations and trains diffusion policies on these datasets. SADP structures policy execution around human-interpretable subgoals by conditioning action generation on both task-level and subgoal-level descriptions. A lightweight auxiliary head further predicts subgoal completion states, allowing the robot to expose its current execution stage and monitor subgoal progression. Experiments in RLBench simulations and real-world evaluations on a UR5e robot demonstrate that SADP achieves higher task success rates than strong task-conditioned diffusion baselines, while providing subgoal-level execution signals for monitoring progress and diagnosing failures. These results highlight that built-in, rather than post-hoc, interpretability can coexist with high task performance.

Recent work has framed decision-making as a sequence modeling problem using generative models such as diffusion models. Although promising, these approaches often overlook latent factors that exhibit evolving dynamics, elements that are fundamental to environment transitions, reward structures, and high-level agent behavior. Explicitly modeling these hidden processes is essential for both precise dynamics modeling and effective decision-making. In this paper, we propose a unified framework that explicitly incorporates latent dynamic inference into generative decision-making from minimal yet sufficient observations. We theoretically show that under mild conditions, the latent process can be identified from small temporal blocks of observations. Building on this insight, we introduce Ada-Diffuser, a causal diffusion model that learns the temporal structure of observed interactions and the underlying latent dynamics simultaneously, and furthermore, leverages them for planning and control. With a modular design, Ada-Diffuser supports both planning and policy learning tasks, enabling adaptation to latent variations in dynamics, rewards, and latent actions. Experiments on simulated control and robotic benchmarks demonstrate its effectiveness in accurate latent inference and adaptive policy learning.

Group Relative Policy Optimization has emerged as essential for aligning video diffusion models with human preferences, but faces a critical computational bottleneck: training a 14B parametered model typically demands hundreds of GPU days per experiment. Existing efficiency methods reduce costs through sliding window subsampling training timesteps, but fundamentally compromise optimization, exhibiting severe instability and failing to reach full trajectory performance. We present Flash-GRPO, a single-step training framework that outperforms full trajectory training in alignment quality under low computational budgets while substantially improving training efficiency. Flash-GRPO addresses two critical challenges: iso-temporal grouping eliminates timestep-confounded variance by enforcing prompt-wise temporal consistency, decoupling policy performance from timestep difficulty; temporal gradient rectification neutralizes the time-dependent scaling factor that causes vastly inconsistent gradient magnitudes across timesteps. Experiments on 1.3B to 14B parameter models validate Flash-GRPO's effectiveness, demonstrating substantial training acceleration with consistent stability and state-of-the-art alignment quality.

World models aim to improve robotic decision making by predicting the consequences of actions. However, in practice, their predictions often become unreliable once the robot encounters states outside the training distribution, limiting their effectiveness at deployment. We observe that execution itself provides a natural but underutilized signal: after each action, the robot directly observes the true next state, revealing the mismatch between predicted and actual outcomes. Building on this insight, we propose feedback world model, a new paradigm that closes the loop between prediction and observation at inference time. Instead of treating the world model as a static open-loop predictor, our method maintains a lightweight feedback state that is updated online to iteratively correct future predictions, compensating for model errors using real-time observations without additional training data or parameter updates. We show that this process can be interpreted as a latent-space observer and admits convergence guarantees under mild conditions. We further introduce action-aware guidance to better translate corrected predictions into control by emphasizing action-controllable components while suppressing irrelevant variations. Experiments on LIBERO-Plus, Robomimic, and real-world manipulation tasks demonstrate that our method substantially improves both prediction accuracy and policy performance under distribution shift. In particular, it reduces world model prediction error by up to 76.4% and improves out-of-distribution (OOD) success rate by 30%. These results show that incorporating real-time feedback at inference time provides a simple yet powerful alternative to static world modeling.

Diffusion-based imitation learning has shown strong promise for robot manipulation. However, most existing policies condition only on the current observation or a short window of recent observations, limiting their ability to resolve history-dependent ambiguities in long-horizon tasks. To address this, we introduce DSSP, a history-conditioned Diffusion State Space Policy that enables efficient, full-history conditioning for robot manipulation. Leveraging the continuous sequence modeling properties of State Space Models (SSMs), our history encoder effectively compresses the entire observation stream into a compact context representation. To ensure this context preserves critical information regarding future state evolution, the encoder is optimized with a dynamics-aware auxiliary training objective. This high-level context representation is then seamlessly fused with recent state observations to form a hierarchical conditioning mechanism for action generation. Furthermore, to maintain architectural consistency and minimize GPU memory overhead, we also instantiate the diffusion backbone itself using an SSM. Extensive experiments across simulation benchmarks and real-world manipulation tasks show that DSSP achieves state-of-the-art performance with a significantly smaller model size, demonstrating superior efficiency of the hierarchical conditioning in capturing crucial information as the history length increases.

Natural language is an intuitive interface for humanoid robots, yet streaming whole-body control requires control representations that are executable now and anticipatory of future physical transitions. Existing language-conditioned humanoid systems typically generate kinematic references that a low-level tracker must repair reactively, or use latent/action policies whose outputs do not explicitly encode upcoming contact changes, support transfers, and balance preparation. We propose \textbf{DAJI} (\emph{Dynamics-Aligned Joint Intent}), a hierarchical framework that learns an anticipatory joint-intent interface between language generation and closed-loop control. DAJI-Act distills a future-aware teacher into a deployable diffusion action policy through student-driven rollouts, while DAJI-Flow autoregressively generates future intent chunks from language and intent history. Experiments show that DAJI achieves strong results in anticipatory latent learning, single-instruction generation, and streaming instruction following, reaching 94.42% rollout success on HumanML3D-style generation and 0.152 subsequence FID on BABEL.

Generative policies based on diffusion and flow matching have become a dominant paradigm for visuomotor robotic control. We show that replacing the standard Gaussian source distribution with WarmPrior, a simple temporally grounded prior constructed from readily available recent action history, consistently improves success rates on robotic manipulation tasks. We trace this gain to markedly straighter probability paths, echoing the effect of optimal-transport couplings in Rectified Flow. Beyond standard behavior cloning, WarmPrior also reshapes the exploration distribution in prior-space reinforcement learning, improving both sample efficiency and final performance. Collectively, these results identify the source distribution as an important and underexplored design axis in generative robot control.

Action diffusion excels at high-fidelity action generation but incurs heavy computational costs owing to its iterative denoising nature. Despite current technologies showing promise in accelerating diffusion transformers by reusing the cached features, they struggle to adapt to policy dynamics arising from diverse perceptions and multi-round rollout iterations in open environments. We propose test-time sparsity to tackle this challenge, which aims to accelerate action diffusion by dynamically predicting prunable residual computations for each model forward at test time. However, two bottlenecks remain in this paradigm: 1) repetitive conditional encoding and pruning offset most potential speed gains, and 2) the features cached from previous denoising timesteps cannot constrain large pruning errors under aggressive sparsity. To address the first bottleneck, we design a highly parallelized inference pipeline that minimizes the non-decoder delay to milliseconds. Specifically, we first design a lightweight pruner that shares the encoder with the diffusion transformer. Then, we decouple the encoding and pruning from the autoregressive denoising loop by processing all denoising timesteps in parallel, and overlap the pruner with the decoder forward inference through asynchronism. To overcome the second bottleneck, we introduce an omnidirectional reusing strategy, which achieves 95% sparsity by selectively reusing features cached from the current forward, previous denoising timesteps, and earlier rollout iterations. To learn the rollout-level reusing strategies, we sample a few action trajectories to supervise the sparsified diffusion step by step. Extensive experiments demonstrate that our method reduces FLOPs by 92% and accelerates action generation by 5x, achieving lossless performance with an inference frequency of 47.5 Hz. Our code is available at https://github.com/ky-ji/Test-time-Sparsity.

Contact-rich assembly is fundamental in robotics but poses significant challenges due to uncertainties in relative poses, such as misalignments and small clearances in peg-in-hole tasks. Existing approaches typically address search and high-precision insertion separately, because these tasks involve distinct action patterns. However, supporting both tasks within a single model, without switching models or weights, is desirable for intelligent assembly systems. In this work, we propose SI-Diff, a framework that learns both search and high-precision insertion through a force-domain diffusion policy. To this end, we introduce a new mode-conditioning mechanism that enables the policy to capture distinct action behaviors under a single framework. Moreover, we develop a new search teacher policy that can generate diverse trajectories. By training on successful and efficient demonstrations provided by the teacher policy, the model learns the mapping from tactile and end-effector velocity observations to effective action behaviors. We conduct thorough experiments to show that SI-Diff extends the tolerance to x-y misalignments from 2 mm to 5 mm compared to the state-of-the-art baseline, TacDiffusion, while also demonstrating strong zero-shot transferability to unseen shapes.

Fine-tuning pre-trained robot policies with reinforcement learning (RL) often inherits the bottlenecks introduced by pre-training with behavioral cloning (BC), which produces narrow action distributions that lack the coverage necessary for downstream exploration. We present a unified framework that enables the exploration necessary to enable efficient robot policy finetuning by bridging BC pre-training and RL fine-tuning. Our pre-training method, Context-Smoothed Pre-training (CSP), injects forward-diffusion noise into policy inputs, creating a continuum between precise imitation and broad action coverage. We then fine-tune pre-trained policies via Timestep-Modulated Reinforcement Learning (TMRL), which trains the agent to dynamically adjust this conditioning during fine-tuning by modulating the diffusion timestep, granting explicit control over exploration. Integrating seamlessly with arbitrary policy inputs, e.g., states, 3D point clouds, or image-based VLA policies, we show that TMRL improves RL fine-tuning sample efficiency. Notably, TMRL enables successful real-world fine-tuning on complex manipulation tasks in under one hour. Videos and code available at https://weirdlabuw.github.io/tmrl/.

Imitation learning powered by generative models has proven effective for modeling complex single-agent behaviors. However, teaching multi-agent systems, like multiple arms or vehicles, to coordinate through imitation learning is hindered by a fundamental data bottleneck: as the joint state-action space grows exponentially with the number of agents, collecting a sufficient amount of coordinated multi-agent demonstrations becomes extremely costly. In this work, we ask: how can we leverage single-agent demonstration data to learn multi-agent policies? We present Coordinated Diffusion (CoDi), a framework that couples independently trained single-agent diffusion policies through a user-defined multi-agent cost function, without requiring any coordinated demonstrations. We derive a new diffusion-based sampling scheme wherein the diffusion score function decomposes into independent, single-agent pre-trained base policies plus a cost-driven guidance term that coordinates these base policies into cohesive multi-agent behavior. We show that this guidance term can be estimated in a gradient-free manner, making CoDi applicable to black-box, non-differentiable cost functions without additional training. Theoretically and empirically, we analyze the conditions under which this composition can faithfully approximate a target multi-agent behavior. We find a complementary role for demonstration data versus the cost function: single-agent demonstrations must cover the support of the desired multi-agent behavior, while the cost function must promote desired behavior from this product of single-agent policies. Our results in simulation and hardware experiments of a two-arm manipulation task show that CoDi discovers robust coordinated behavior from single-agent data, is more data-efficient than multi-agent baselines, and highlights the importance of joint guidance, base policy support, and cost design.

Generalizable manipulation involving cross-type object interactions is a critical yet challenging capability in robotics. To reliably accomplish such tasks, robots must address two fundamental challenges: "where to manipulate" (contact point localization) and "how to manipulate" (subsequent interaction trajectory planning). Existing foundation-model-based approaches often adopt end-to-end learning that obscures the distinction between these stages, exacerbating error accumulation in long-horizon tasks. Furthermore, they typically rely on a single uniform model, which fails to capture the diverse, category-specific features required for heterogeneous objects. To overcome these limitations, we propose HeteroGenManip, a task-conditioned, two-stage framework designed to decouple initial grasp from complex interaction execution. First, Foundation-Correspondence-Guided Grasp module leverages structural priors to align the initial contact state, thereby significantly reducing the pose uncertainty of grasping. Subsequently, Multi-Foundation-Model Diffusion Policy (MFMDP) routes objects to category-specialized foundation models, integrating fine-grained geometric information with highly-variable part features via a dual-stream cross-attention mechanism. Experimental evaluations demonstrate that HeteroGenManip achieves robust intra-category shape and pose generalization. The framework achieves an average 31% performance improvement in simulation tasks with broad type setting, alongside a 36.7% gain across four real-world tasks with different interaction types.

Diffusion policies have demonstrated exceptional performance in embodied AI. However, their iterative denoising process results in high latency, and existing acceleration methods often sacrifice physical consistency. To address this, we propose ElasticFlow, a distillation-free, physics-consistent one-step policy framework. We reconstruct the Mean Field Theory by directly modeling the average velocity field, enabling a direct single-step mapping from noise to action. Addressing the Temporal Heterogeneity of robotic tasks, we introduce the Elastic Time Horizons mechanism. This mechanism effectively overcomes Spectral Bias by explicitly encoding control granularity, achieving efficient alignment between semantic instructions and physical execution horizons. Experiments on benchmarks such as LIBERO, CALVIN, and RoboTwin demonstrate that ElasticFlow achieves efficient 1-NFE inference (approximately 71Hz). Furthermore, it outperforms state-of-the-art methods, including OpenVLA and $π_0$, on long-horizon tasks, highlighting its potential for efficient, robust, and semantically aligned control.

State-of-the-art physical AI models generate a chunk of actions per inference through diffusion or flow matching, iteratively refining an initial noise sample into an action trajectory. Because this inference process is inherently stochastic, committing to a single trajectory per round is brittle, and this brittleness compounds across the many sequential rounds that comprise a complete episode. We introduce KeyStone, an inference-time self-consistency method for diffusion-based action generation that draws $K$ candidate action chunks in parallel from a shared model context, clusters them in continuous action space, and returns the medoid of the largest cluster -- no additional model required. Two properties make this practical. First, the compact nature of action trajectories makes diffusion inference memory-bandwidth bound, leaving spare compute capacity to run $K$ chains in parallel with no additional wall-clock latency. Second, unlike token or pixel spaces where distance carries no semantic meaning and selection requires a learned judge, action chunks are geometrically structured such that Euclidean distance directly reflects physical similarity, making selection principled and judge-free. Across diverse vision-language-action models (VLAs) and world-action models (WAMs), KeyStone improves task success rates by up to \textbf{13.3%} over single-trajectory sampling with negligible latency overhead, while having on par accuracy with model-based selectors at no training cost. We open source KeyStone at https://github.com/dywsjtu/keystone.

Vision-language-action (VLA) models provide a promising paradigm for scalable robotic manipulation, yet their reliance on success-only behavioral cloning leaves them brittle; lacking corrective training signals, minor execution errors rapidly compound into unrecoverable, out-of-distribution failures. To address this limitation, we propose Adaptive Failure-Informed Learning (AFIL), an end-to-end framework that leverages failure trajectories as adaptive negative guidance for diffusion- and flow-based VLA policies. AFIL uses a pretrained VLA to generate failure rollouts online, avoiding the need for handcrafted failure-mode design or human-in-the-loop recovery. It then jointly trains Dual Action Generators (DAGs) for successful and failed behaviors while sharing a common vision-language backbone, enabling efficient failure-aware policy learning with limited parameter overhead. During sampling, the failure generator adaptively steers action generation away from failure-prone regions and toward more reliable success modes, with guidance strength determined by the per-diffusion-step distance between success and failure distributions. Experiments across in-domain and out-of-domain robotic manipulation tasks, covering both short- and long-horizon settings, show that AFIL consistently improves task success rates and robustness over existing VLA baselines, demonstrating its effectiveness, efficiency, and generality.

Cooperative multi-agent reinforcement learning (MARL) involves complex agent interactions and requires effective exploration strategies. A prominent class of MARL algorithms, decentralized softmax policy gradient (DecSPG), addresses this through energy-based policy updates. In practice, however, such energy-based policies are intractable to maintain and are commonly projected onto the Gaussian policy class. In this work, we show that the limited expressiveness of Gaussian policies severely hinders exploration in DecSPG, and this limitation worsens as the number of agents grows. To address this issue, we propose decentralized diffusion policy learning (DDPL), which parameterizes each agent's policy with a denoising diffusion probabilistic model, an expressive generative model that captures multi-modal action distributions for enhanced exploration. DDPL enables efficient online training of diffusion policies via importance sampling score matching (ISSM), a novel training method with theoretical guarantee. We evaluate DDPL on representative continuous-action MARL benchmarks, including multi-agent particle environment, multi-agent MuJoCo, IsaacLab, and JAX-reimplemented StarCraft multi-agent challenge, and observe consistently improved performance.

We introduce ReflectDrive-2, a masked discrete diffusion planner with separate action expert for autonomous driving that represents plans as discrete trajectory tokens and generates them through parallel masked decoding. This discrete token space enables in-place trajectory revision: AutoEdit rewrites selected tokens using the same model, without requiring an auxiliary refinement network. To train this capability, we use a two-stage procedure. First, we construct structure-aware perturbations of expert trajectories along longitudinal progress and lateral heading directions and supervise the model to recover the original expert trajectory. We then fine-tune the full decision--draft--reflect rollout with reinforcement learning (RL), assigning terminal driving reward to the final post-edit trajectory and propagating policy-gradient credit through full-rollout transitions. Full-rollout RL proves crucial for coupling drafting and editing: under supervised training alone, inference-time AutoEdit improves PDMS by at most $0.3$, whereas RL increases its gain to $1.9$. We also co-design an efficient reflective decoding stack for the decision--draft--reflect pipeline, combining shared-prefix KV reuse, Alternating Step Decode, and fused on-device unmasking. On NAVSIM, ReflectDrive-2 achieves $91.0$ PDMS with camera-only input and $94.8$ PDMS in a best-of-6 oracle setting, while running at $31.8$ ms average latency on NVIDIA Thor.

Diffusion-based visuomotor policies perform well in robotic manipulation, yet current methods still inherit image-generation-style decoders and multi-step sampling. We revisit this design from a frequency-domain perspective. Robot action trajectories are highly smooth, with most energy concentrated in a few low-frequency discrete cosine transform modes. Under this structure, we show that the error of the optimal denoiser is bounded by the low-frequency subspace dimension and residual high-frequency energy, implying that denoising error saturates after very few reverse steps. This also suggests that action denoising requires a much simpler denoising model than image generation. Motivated by this insight, we propose Hyper-DP3 (HDP3), a pocket-scale 3D diffusion policy with a lightweight Diffusion Mixer decoder that supports two-step DDIM inference. Our synthetic experiments validate the theory and support the sufficiency of two-step denoising. Futhermore, across RoboTwin2.0, Adroit, MetaWorld, and real-world tasks, HDP3 achieves state-of-the-art performance with fewer than 1% of the parameters of prior 3D diffusion-based policies and substantially lower inference latency.