Diffusion Planning

Pretrained driving vision-language models (VLMs) integrate visual, route, language, and driving context into rich driving priors, yet their representation objectives remain separated from continuous driving planning. Existing methods typically begin trajectory generation only after the VLM has formed a final condition, leaving depth-wise condition computation outside the stepwise formation of trajectory state. We introduce DiffAdapterVLA, which realizes Planning in the Backbone: it injects explicit trajectory tokens into selected VLM late layers, bringing trajectory state into backbone forward computation, where it co-evolves with driving conditions at different depths. Lightweight layer-wise DiffAdapters organize this computation into recursive trajectory refinement, while asymmetric joint attention preserves directed guidance from the condition stream to trajectory planning. By placing planning within existing backbone computation rather than relying on an independent trajectory planner, DiffAdapterVLA adapts only lightweight trajectory modules to turn existing driving priors into efficient continuous planning capability. NAVSIM results show that it achieves high-quality closed-loop planning with low end-to-end latency using few trainable parameters, and demonstrate that jointly evolving trajectory state and depth-wise driving conditions in VLM late-layer computation effectively realizes continuous trajectory planning.

Many diffusion-based planners enforce safety through inference-time guidance, but such interleaved trajectory deformations often degrade kinematic feasibility due to manifold rupture. We propose Graph-Guided Safe Diffuser (G2SD), a hierarchical framework that leverages a high-level topological graph planner to guide a low-level diffusion model. G2SD enforces safety at a structural level by abstracting the data manifold into a learned latent graph, on which high-level planning is performed. Continuous trajectories are generated by diffusion planners, which are conditioned on the graph node representations selected by the high-level planner. Theoretical analyses demonstrate conditions under which manifold rupture occurs in diffusion planners, and show that G2SD improves safety by reducing the constraint violation probability as the number of segments increases. Experiments demonstrate that G2SD substantially outperforms baselines, increasing goal-reaching rate without any collision from 40-50% to 98% in Maze2D navigation and also achieving superior task scores in locomotion.

Large video diffusion models provide rich spatiotemporal priors for autonomous driving, but existing world-action models often inherit the cost of iterative future-video generation even though deployment only requires an ego trajectory. We ask a more basic question: how much of a video diffusion model must be executed to make a reliable driving decision? Through a controlled study of video denoising timesteps and Diffusion Transformer (DiT) depth, we find that planning performance is largely insensitive to the tested video-noise levels, whereas strong trajectories can already be decoded from intermediate layers. Based on this observation, we introduce Adaptive-WAM, a quality-aware multi-exit planner built on a Wan2.2-5B backbone. Trajectory diffusion heads are attached to selected DiT blocks, and a lightweight trajectory-quality scorer terminates inference once the best trajectory decoded so far satisfies a quality threshold; otherwise, computation continues from the cached hidden state to a deeper exit. The deployed planner therefore avoids the iterative classifier-free denoising loop and VAE decoding required for future-video synthesis, while dynamically allocating backbone depth according to trajectory quality. On NAVSIM, the adaptive single-trajectory planner achieves 90.8 PDMS; a separate fixed-exit variant reaches 92.6 PDMS with 64 proposals. It further obtains 89.9 EPDMS on NAVSIM v2, yielding the best reported results among the compared front-view video world-model planners. Without target-domain fine-tuning, Adaptive-WAM transfers to nuScenes with 0.88 m average L2 error and a 0.08% collision rate. On an A100, adaptive routing improves PDMS from 90.62 to 90.79 while averaging 170 ms end-to-end planning latency, approximately 10% below the 190 ms fixed block-15 planner and 47% below the 320 ms fixed full-depth planner. Code will be released.

Vehicle-to-everything-aided autonomous driving (V2X-AD) significantly enhances driving performance through information sharing. However, existing collaborative perception methods only optimize module-level perception capabilities and fail to effectively serve the ultimate planning and control tasks. We propose an end-to-end collaborative driving system that directly optimizes planning task performance. The system employs MotionNetwork to fuse historical temporal information, utilizes attention mechanisms to efficiently compress spatial features into compact tokens, and adaptively fuses multi-agent features through an autoregressive decoder. Additionally, we introduce Mixture-of-Experts (MoE) architecture to enhance the model's representation capacity for heterogeneous features. Experiments demonstrate that our method achieves a driving score of 79.72, surpassing the state-of-the-art CoDriving baseline (77.15) by 3.33% in closed-loop evaluation while maintaining communication efficiency.

Generating closed-loop traffic scenarios that are both realistic and controllable is crucial for evaluating autonomous driving systems, especially under rare safety-critical interactions. Existing learning-based methods often struggle to balance controllability and realism, offering either limited fine-grained control over traffic behavior or controllable scenarios at the expense of behavioral plausibility. This paper presents E2E-CDiff, an end-to-end conditional diffusion framework for controllable and realistic scenario generation. Conditioned on front-view visual observations, E2E-CDiff jointly denoises future motion states and executable low-level controls for route-interacting background vehicles. This unified state-action generation mitigates the planning-control mismatch in conventional two-stage trajectory-then-controller pipelines. Differentiable guidance further regulates speed, enforces drivable-area compliance, and supports collision-avoidance or collision-seeking behaviors, enabling both naturalistic and safety-critical scenario generation. Experiments on Bench2Drive show that E2E-CDiff achieves a favorable controllability-realism trade-off compared with representative reinforcement- and imitation-learning baselines, while its collision-guided variant induces challenging interactions across multiple autonomous driving systems. E2E-CDiff also performs competitively as a learning-based ego planner, demonstrating the generality of end-to-end state-action diffusion.

Robots in cluttered indoor spaces often fail not because they cannot generate collision-free paths, but because a fixed safety margin is mis-calibrated: conservative margins cause detours and timeouts, while permissive margins lead to near-boundary shortcuts under perception bias. Diffusion-based planners propose diverse trajectory candidates from egocentric RGB-D, yet reliable selection remains the bottleneck. We propose a context-conditioned safety critic that learns an adaptive clearance preference for ranking diffusion proposals, decomposed into three complementary terms: (i) a safety term with a clearance-budget penalty and a control-barrier-function residual for waypoint- and transition-wise safety, (ii) an efficiency term combining a smoothness penalty with a safety-gated detour-ratio penalty that avoids detours without incentivizing risky shortcuts, and (iii) a distance-constraint matching term that anchors the learned budget to realized ESDF clearances to prevent margin collapse. We train the critic with privileged ESDF geometry in simulation and distill it into a perception-only selector via a two-stage teacher-student procedure. On PointGoal navigation in HM3D and MP3D, including cross-dataset transfer, our method achieves the highest success rate (SR) and success weighted by path length (SPL) among strong diffusion, optimization, and RL baselines. Trained purely in simulation, it transfers to a Unitree G1 humanoid and navigates cluttered indoor scenes without task-specific tuning.

End-to-end trajectory planners need to represent multiple plausible driving behaviors while producing a single executable trajectory under real-time constraints. Proposal-based approaches address this ambiguity by generating multiple candidates, but converting the proposal set into a final plan remains a key design problem. We present DRIFT, a fixed-depth planner that combines one-step drifting in a compact trajectory latent space with scene-aware proposal aggregation. Conditioned on features from a pretrained visual encoder, the DRIFT Decoder generates 48 proposal features in a single batched pass, with 32 samples at alpha=0.5 and 16 samples at alpha=0.9. A lightweight Aggregation Head integrates these features with scene, navigation, and ego-state information and directly predicts the final trajectory without requiring trajectory-level quality labels for aggregation. Its output is trained with expert-trajectory imitation and a map-derived boundary regularizer that penalizes waypoints outside the drivable polygon and inside waypoints near its boundary. On NAVSIM navtest, DRIFT achieves 89.6 PDMS and 90.4 EPDMS, with strong drivable-area compliance and ego progress among the methods compared. The proposal-generation and aggregation module runs in 10.82 ms on an NVIDIA RTX 4090, while full-model inference including the visual backbone takes 66.43 ms. These results show that one-step latent proposal generation and direct aggregation provide an efficient design for multi-hypothesis motion planning.

Multi-Robot Motion Planning in continuous environments, where robots must generate dynamically feasible, collision-free trajectories, is challenging due to the combinatorial growth of the joint trajectory space and the difficulty of enforcing dynamic feasibility and hard safety constraints. Recent approaches recast trajectory planning as probabilistic inference, sampling from a posterior over trajectories using diffusion models whose score functions are learned from demonstration data. While showing promising performance, these approaches are limited: they often rely on sizable demonstration datasets and struggle to rigorously enforce dynamics and hard safety constraints during sampling. To this end, we introduce Model-Based Diffusion Optimal Control (MDOC), a model-based diffusion planner that efficiently produces dynamically feasible trajectories without relying on data. Crucially, we show that MDOC's safety mechanism -- combining known dynamics models with Control Barrier Function-constrained projections -- naturally scales to multi-robot planning settings through Conflict-Based Search. Across simulation experiments, this integrated method consistently outperforms representative baseline planners in sample efficiency, geometric smoothness, and success rate, while reducing computation time and producing collision-free trajectories.

A key limitation on the use of diffusion models in robotic planning is their inability to inherently enforce safety or dynamical constraints, which often results in physically infeasible or unsafe outputs. Hybrid approaches that employ model predictive control (MPC) to address this problem can be unstable, as poor trajectory initializations from the diffusion model prevent the MPC from converging to a safe and feasible solution. To overcome these challenges, we propose D-SafeMPC, which enhances the interaction between diffusion and control. Our method guides the reverse diffusion process with control barrier functions (CBFs) and control Lyapunov functions (CLFs) and employs an iterative-projection scheme where an MPC refines the trajectory at each denoising step. This steers sampling toward safe, goal-directed regions and provides reliable MPC warm starts. In simulations on a Franka manipulator across four scenarios (one static-obstacle and three dynamic-obstacle settings) and in a sim-to-real experiment on a physical Franka robot, D-SafeMPC improves safety, task success rates, and planning efficiency over state-of-the-art baselines. To facilitate reproducibility, our source code and experimental configurations are available in a repository at https://github.com/erdiphd/D-SafeMPC

Autonomous driving planning is a key component of IoT-enabled intelligent transportation systems, requiring vehicles to generate safe, efficient, and executable trajectories in complex urban environments from multi-source contextual information. While imitation learning (IL) has shown promise on large-scale datasets, IL-based planners still suffer from limited coverage of complex long-tail interactions, weak consistency with downstream constrained refinement, and insufficient use of high level scene semantics under real time constraints. To address these issues, this paper proposes a large language model (LLM) enhanced differentiable trajectory planning framework for IoT-enabled autonomous driving. Specifically, we introduce a surrounding agent centric data augmentation strategy to reorganize sur rounding agent trajectories as additional planning supervision, thereby improving the training distribution without collecting additional raw data. We further design a complexity-aware asyn chronous LLM-based semantic enhancement module to extract scene-related high-level semantic features with controlled online overhead. In addition, a differentiable optimization module is incorporated to refine generated trajectories with explicit residual penalties while backpropagating optimization gradients to the upstream planner. Experiments show that the proposed method achieves the best overall scores of 83.63 and 78.29 on the nuPlan closed-loop nonreactive and reactive Hard20 benchmarks, respectively, and CARLA-ROS tests further verify its online deployment and real time closed-loop execution capability.

Diffusion-based trajectory planners have shown strong performance in offline reinforcement learning, but their iterative denoising process often incurs high inference cost. Consistency-based planners reduce the number of sampling steps, yet they typically rely on a two-stage teacher--student distillation pipeline that increases training cost and may introduce instability. We propose Shortcut Trajectory Planning (STP), an offline model-based reinforcement learning framework that incorporates shortcut models as efficient trajectory generators. STP trains a conditional shortcut trajectory model in a single stage, supports adjustable one-step and few-step inference through step-size conditioning, and selects candidate plans using a critic augmented with feasibility-aware correction. Across standard D4RL benchmarks, including locomotion, navigation, manipulation, and dexterous control tasks, STP achieves strong performance while simplifying the training pipeline for fast generative planning.

Diffusion-based motion planners have demonstrated strong performance in generating diverse and high-quality robot trajectories in cluttered environments with multiple feasible solutions. However, existing approaches typically operate on fixed-length waypoint sequences, making the learned model resolution-dependent, thereby preventing zero-shot generalization across resolutions. In this work, we propose Function-Space Diffusion for Motion Planning (FSD-MP), a diffusion-based motion planner that models trajectories as continuous functions and performs diffusion directly in function space, achieving discretization-invariant trajectory generation. We define a mode-wise forward process in the spectral domain, driven by Gaussian noise with a Matérn-type covariance, and parameterize the reverse process with a boundary-compatible Discrete Sine Transform-based Fourier Neural Operator (DST-FNO) that preserves start-goal constraints across resolutions. We evaluate FSD-MP on 2D point robot and 7-DoF Franka manipulator planning benchmarks. Our method achieves competitive planning performance at the training resolution and generalizes zero-shot across resolutions up to 16$\times$ higher, preserving consistent planning behavior without retraining. These results demonstrate that function-space diffusion provides an effective framework for discretization-invariant motion planning.

World-model-based autonomous driving endows the model with the ability to understand scene evolution. Yet this promise is undermined by the prevailing imagine-then-act paradigm, which allows errors from the more challenging visual generation stage to cascade into action planning. We introduce ForgeDrive, a unified autoregressive diffusion framework with visual-action cross-conditioning that closes this gap through act-then-imagine paradigm. ForgeDrive factorizes the future as a sequence of per-timestep frame-action pairs, intertwining each action with its corresponding visual observation. During training, we decouple the diffusion timesteps of the two modalities and introduce a UniDiffuser-style noise scheduler to get the ability to infer either modality from its counterpart and deepen understanding of relationships between images and actions. At inference, we propose a novel act-then-imagine inference paradigm, and find that at each step, action generation is a capability internalized during training, requiring no clean future frame as a prerequisite at inference time; instead, the generated action can improve the accuracy of future frame generation, which in turn enhances the quality of the next action. Additionally, we augment each step with future ego-status prediction, further sharpening planning ability. Extensive experiments on NAVSIM demonstrate that ForgeDrive not only unifies driving simulation, planning, and visual odometry into a single model, but also outperforms existing strong planners without any post-training strategy.

Generative models have recently seen rapid adoption in End-to-End (E2E) autonomous driving (AD), with diffusion-based denoising and vocabulary-based retrieval becoming the dominant trajectory-decoding paradigms. Despite their architectural diversity, current generative AD planners share a common inference pattern: a fixed set of candidate trajectories (anchors, vocabulary entries, or proposal queries) is scored by one or more learned heads conditioned on the Bird's-Eye-View (BEV) features, and the highest-scored candidate is returned as the final trajectory. Under this design, the scoring head is the only barrier between perception and the motion command, and its decision margins between competing candidates are often small. We introduce \textsc{Derail}, an adversarial framework that exploits this scoring-head attack surface. Evaluated on various generative planners, \textsc{Derail} flips the trajectory selection from a safe to an unsafe candidate, with score drops of $39$--$80\%$ and collision rates of up to $50\%$, consistently outperforming generic loss-maximization and feature-divergence attacks. Our analysis suggests that safety-violating objectives govern attack effectiveness against generative AD planners, and that the scoring-head inference pattern itself is a recurring attack surface worth explicit defensive consideration.

Autonomous driving systems are steadily moving toward end-to-end paradigms to mitigate the limited adaptability of rule-based pipelines in complex traffic environments. However, most existing learning-based methods still make decisions from static representations of the current scene, without explicit future rollouts or modeling of the temporal causal dynamics in traffic interactions. This limitation often results in unstable or overly conservative planning under high-uncertainty conditions, such as occlusions and unexpected events. To overcome these challenges, we introduce OWMDrive, a generative end-to-end driving framework built upon an Occupancy World Model for multi-step 3D occupancy forecasting, which serves as a conditional prior to guide diffusion-based planning. Conditioned on both current observations and predicted future states, the planner iteratively refines trajectory candidates to generate a reinforced driving trajectory. By explicitly modeling scene evolution over future horizons, OWMDrive captures key spatiotemporal causal dependencies, which leads to more foresighted and robust trajectory generation. Extensive experiments demonstrate that OWMDrive significantly improves planning reliability and safety, especially in challenging and partially observable driving scenarios.

Traffic signal control at urban intersections inherently introduces stop-and-go behavior, resulting in increased delays and reduced traffic efficiency, especially under high traffic demand. With the emergence of connected and automated vehicles (CAVs), trajectory-level coordination has emerged as a high-potential strategy to augment or transcend conventional phase-based management. This paper proposes DSIP (Diffusion-model-based Signal-free Intersection Planner), a multi-agent motion planning framework driven by a generative diffusion process. DSIP shifts the intersection management paradigm from discrete temporal phasing to continuous multi-vehicle trajectory optimization. This work evaluates the theoretical upper-bound performance of this coordination strategy under idealized communication and execution conditions to isolate the core benefits of the diffusion-driven approach. Using the SUMO platform, we evaluate DSIP across diverse four-leg intersection configurations. Experimental results demonstrate that DSIP significantly reduces average delay and maintains higher average speed compared to both fixed-time signal control and state-of-the-art reinforcement-learning-based controllers, particularly in medium- to high-density traffic. These findings suggest that diffusion-based trajectory planning provides a scalable and robust foundation for future autonomous intersection management. By unlocking latent intersection capacity through software-defined coordination, this approach offers a cost-effective pathway to improve urban traffic flow efficiency without requiring physical infrastructure expansion.

Closed-loop traffic simulation remains challenging because it must generate interactive multi-agent behaviors that are scene-consistent and controllable throughout rollout. Prior diffusion-based approaches achieve strong realism, but their computational cost can hinder deployment in time-constrained replanning loops for autonomous vehicle planning and simulation. We present a diffusion-based scenario generation framework conditioned on instance-centric scene context and multimodal proposal priors, with optional test-time guidance for shaping safety-critical behaviors. A compact action-latent representation and proposal-based initialization improve sampling efficiency and reduce per-step runtime without retraining. Experiments on the Waymo Open Motion Dataset demonstrate a favorable balance among realism, safety, and controllability across diverse interactive scenarios, while showing that test-time guidance enables systematic trade-offs among competing objectives.

In autonomous driving, diffusion-based planners have emerged as a promising paradigm for robust motion planning in dense and interactive traffic, as they can effectively model diverse driving behaviors. However, their inherent stochasticity often requires explicit guidance during denoising to ensure safety and route adherence for robust closed-loop execution. Existing guidance typically relies on sparse, entity-centric geometric queries or post-hoc refinement, yielding limited situational awareness and fragile performance in interactive scenes. To address this issue, we propose G2DP (Grid-Guided Diffusion Planning), a diffusion-based planner that directly enforces dense environmental constraints through inference-time guidance. Specifically, G2DP constructs a differentiable spatio-temporal cost volume by fusing probabilistic future occupancy distributions with a route-progress map. By formulating this volume as a continuous safety energy functional, it injects dense gradients directly into the denoising loop, actively steering trajectory generation toward collision-free and progress-optimal regions. Extensive closed-loop evaluations show that G2DP achieves state-of-the-art performance on nuPlan, outperforming the strongest imitation-learning baseline by +7.2 points in reactive score. It further maintains top scores in zero-shot transfers to interPlan and DeepScenario benchmarks, with collision avoidance improving by +10.15 over the unguided approach on interPlan. These results demonstrate that spatio-temporal cost grids serve as an effective representation for robust guidance in diffusion-based planning.

Diffusion models have shown strong potential for multi-modal planning in end-to-end autonomous driving. However, most existing methods confine diffusion to the planning module, conditioning on fixed outputs from separate discriminative perception networks. This decoupled design propagates perception errors to the planner, increasing optimization difficulty and reducing robustness. To overcome these limitations, we propose UniTeD, a Unified Temporal Diffusion framework that jointly models perception and planning through iterative denoising in a shared generative space. By enabling bidirectional information exchange, the framework facilitates mutual refinement between tasks and improves robustness via noise-conditioned multi-task training. We further extend this unified diffusion paradigm to a streaming setting by incorporating temporal context. A Temporal Transition Module (TTM) is introduced to resolve the noise-level mismatch between historical and current frames. In addition, we propose an Anchor Refresh Strategy (ARS) to alleviate the training-inference distribution shift commonly observed in sparse diffusion-based end-to-end driving frameworks. Without bells and whistles, UniTeD achieves state-of-the-art performance across multiple benchmarks, surpassing both recent discriminative end-to-end methods and diffusion-based planning approaches.

Recent Vision-Language-Action (VLA) models have advanced end-to-end autonomous driving by incorporating reasoning for better interpretability and planning quality. However, most existing approaches directly generate the final trajectory without explicitly examining its future consequences, which limits their reliability in complex and dynamic environments. To address this limitation, we propose IRR-Drive (Intend, Reflect, Refine), an adaptive multimodal reflection framework for autonomous driving. Specifically, to tightly couple high-level reasoning with physical constraints, IRR-Drive first generates a preliminary textual intention and anticipates potential interactions by predicting future semantic bird's-eye view (BEV) representations. This dual-modality (Text + BEV) reflection space explicitly models anticipated scene evolution, enabling the model to rigorously self-correct and refine its initial intent before generating the final trajectory. Furthermore, to balance planning performance and computational efficiency, we construct reflection-oriented training data and design an adaptive reflection reward, enabling the model to adaptively select its reasoning mode according to scene complexity. Instead of using reasoning primarily as an auxiliary interpretation, IRR-Drive directly integrates an adaptive reflection mechanism into the planning framework, enabling grounded, decision-aware trajectory correction that is driven by scene complexity. Our method achieves state-of-the-art performance on the NAVSIM benchmark in both PDMS and EPDMS. Extensive experiments demonstrate the effectiveness of our multimodal reflection framework and validate the efficacy of the proposed adaptive reflection strategy.

Manipulation in confined environments, such as threading a manipulator through narrow apertures, remains a fundamental challenge, especially for conventional rigid robots. Hybrid rigid-soft manipulators offer promise but face two compounding planning challenges: backbone shapes feasible in free space become infeasible under environmental contact, and planning rigid and soft segments independently ignores their kinematic coupling. We present THREAD, the first diffusion-based trajectory planner for hybrid manipulation, learning a generative prior over physically realizable backbone trajectories conditioned on local environment geometry, with physics-inspired losses encoding curvature, smoothness, and collision constraints jointly across both segments. Trained in simulation, THREAD achieves 92.4% task success with 5x fewer collisions than the strongest baseline. We show cross-embodiment real-world transfer with minimal online updates, successfully threading through apertures as small as 1.3x the soft segment diameter.

Compositional diffusion planners aim to solve long-horizon robotic tasks using short training trajectories. Yet, current approaches often rely on the heuristic stitching of local predictions. We show that the resulting stitched update is generally a non-conservative field} that does not mathematically correspond to any valid global trajectory log-density function. We propose Energy-based Compositional Diffuser (ECD), a framework that formulates the global trajectory as the minimizer of the sum of local bridge potentials. This energy-based perspective defines a conservative correction field and contains a boundary reaction term that heuristic stitching omits. To enable efficient inference, we further introduce a Markov-based score approximation that computes the reaction term via a single block-tridiagonal solve, maintaining time complexity linear in the planning horizon. Empirically, ECD achieves state-of-the-art success rates on a range of OGBench stitching tasks, while nearly matching the inference speed of heuristic stitching methods. Code is available at https://github.com/GradientSpaces/ECD.

Planning under uncertainty is an essential capability for autonomous robots. The Partially Observable Markov Decision Process (POMDP) provides a powerful framework for such a capability. Although POMDP-based planning has advanced significantly, its application to real-world problems is often limited by the difficulty of obtaining faithful POMDP models. We present Vectorized Online planning wIth Learned diffusion model for POMDP Agents (VOiLA), a framework that learns task-agnostic POMDP models for online planning under uncertainty. VOiLA learns transition and observation samplers using conditional diffusion models and learns observation-likelihood models for particle-based belief updates. To enable efficient online planning, the diffusion samplers are distilled into compact feedforward generators and integrated with Vectorized Online POMDP Planner (VOPP), an online POMDP planner designed to leverage GPU parallelization. Experimental results indicate the distillation strategy reduces sampling cost by up to nearly three orders of magnitude, making learned generative POMDP models practical for online planning. Evaluation of VOiLA on three benchmark problems indicate that VOiLA achieves equal or better performance than Recurrent Soft Actor Critic while using less than 10% training data, and generalizes much better to unseen environment configurations. Physical robot evaluation indicates VOiLA uses the models learned using only simulated data and generates a policy that successfully accomplish the task in 10 of 10 runs.

Navigation in partially observable environments presents a significant challenge for autonomous agents, requiring effective decision-making with limited sensory information in unknown environments. Belief-based methods, particularly those using neural networks to approximate the belief space, often fail to capture the inherent multimodality of belief spaces, especially in high-dimensional cases with perceptual aliasing. While generative models present a compelling alternative, they typically require substantial data or expert demonstrations and lack explicit mechanisms for long-term planning. In this paper, we introduce BeliefDiffusion, a novel framework that combines the benefits of both generation and planning. BeliefDiffusion leverages diffusion models to explicitly characterize multimodal belief distributions and utilizes Model Predictive Control (MPC) to simultaneously plan ahead. It consists of two steps: (1) Imagining plausible environment configurations based on observation history and (2) Planning efficient navigation strategies across an aggregated configurations. Through extensive experiments in synthetic map environments, we demonstrate that BeliefDiffusion significantly outperforms both model-free reinforcement learning baselines and other generative approaches in navigation success rate and path efficiency. Our results validate that explicitly incorporating multimodal belief representations into planning enables more robust navigation in partially observable settings.

Exploration and object search require robots to perceive their environment, identify regions of interest, and plan trajectories that improve target-detection likelihood or maximize information gain. Many IPP methods, especially in continuous environmental monitoring, rely on Gaussian-process belief models, while object-search settings often produce complex, multimodal belief maps from semantic or open-vocabulary perception. Global trajectory generation directly conditioned on such non-Gaussian belief maps remains comparatively underexplored. Although diffusion-based planners offer strong capabilities for modeling such distributions, their use in informative path planning remains limited. In this work, we propose DIFF-IPPO, a pipeline that integrates an open-vocabulary belief map generator with a diffusion-based planner for global trajectory generation over belief maps. The method generates trajectories that concentrate sensor coverage over high-belief regions, achieving normalized detection scores between 81.49% and 86.55% across different dataset scenarios. We validate the system in a simulated search-and-rescue scenario where the planner searches candidate building regions to locate a burning building. In this setting, a team of five drones using batched belief-map-conditioned trajectory generation achieves first detections in 3.5 minutes.

Shared-space transportation operation requires low-speed autonomous platforms to navigate safely and efficiently among pedestrians, service robots, micromobility users, carts, and other road users. Most existing systems decompose this problem into trajectory prediction followed by motion planning, which creates one-way information flow: predicted participant futures influence the robot plan, but the selected robot plan cannot influence the predicted multi-agent evolution. This paper presents a joint prediction-planning diffusion framework that treats participant prediction and robot planning as a single conditional trajectory generation problem, where the model samples the future robot trajectory and all participant trajectories from one coupled distribution using a causal Transformer with cross-trajectory attention. To replace heuristic repulsive post-processing, the framework introduces differentiable safety potential guidance, a time-varying occupancy-probability potential whose gradient directly guides the joint sampler, and conditional flow matching is used to reduce inference steps while preserving multimodal trajectory diversity. The evaluation emphasizes shared-space operational effects, including near misses, blockage time, induced participant deviation, hard-braking events, and embedded latency, rather than treating average displacement error and final displacement error as the main result. Experiments in scenario-grounded simulation, naturalistic pedestrian replay, Isaac Sim validation, and ROS/Orin deployment show that joint sampling improves tail safety and runtime efficiency over a separated prediction-then-planning baseline.

We study the problem of human gaze modeling, which aims to generate the gaze patterns a viewer produces while observing a visual stimulus. Gaze is primarily captured through two modalities: continuous eye-tracking trajectories, which describe fine-grained motion dynamics, and discrete scanpaths, which describe high-level fixation structure. Because gaze varies substantially across viewers and trials, we treat this variability as a defining property rather than noise and model gaze as a stochastic generative process. Existing generative gaze models supervise on only one of these two representations in isolation. We hypothesize that trajectories and scanpaths describe gaze at complementary scales and are jointly informative during training, and test this hypothesis through ST-DiffEye, a joint trajectory-scanpath diffusion framework that couples both modalities by concatenating them as an additional raw input channel, requiring no architectural overhead beyond an input and output channel expansion. We further introduce a principled evaluation framework based on the Continuous Ranked Probability Score (CRPS), which generalizes any existing sequence similarity metric into a proper scoring rule that jointly assesses the accuracy and diversity of generated gaze. Experiments on task-driven visual search, covering both target-present and target-absent scenarios, and on free-viewing benchmarks demonstrate state-of-the-art performance. These results, along with detailed ablations, confirm the benefit of joint modeling and the value of distribution-aware evaluation in capturing the intrinsic variability of human gaze. Project webpage: https://st-diffeye.github.io/

Diffusion models have emerged as powerful tools for planning and control by learning multimodal distributions over actions and trajectories. Yet reliable inference-time safety enforcement remains a key barrier to their deployment in safety-critical tasks. Existing approaches typically project each denoising iterate onto the feasible set, even though constraints are defined only on the final clean trajectory. Enforcing feasibility on noisy intermediate samples can therefore overconstrain the sampling dynamics, substantially degrading sample quality. To address this limitation, we introduce DiRecT (Diffusion-based planning via Receding-horizon denoising with Terminal constraints), a training-free algorithm for constrained sampling from diffusion models via stochastic optimal control (SOC). DiRecT enforces constraints only on the final clean sample, avoiding unnecessary restrictions on the intermediate denoising dynamics. Inspired by model predictive control, we derive a principled receding-horizon surrogate for the otherwise intractable constrained SOC formulation, yielding an efficient algorithm that cleanly separates stochastic denoising from constraint satisfaction, progressively steering samples toward feasible final trajectories without distorting the learned diffusion dynamics. Furthermore, DiRecT is highly flexible: it can leverage off-the-shelf or domain-specific optimizers, incorporate priors over environment dynamics, and optimize additional soft rewards. Extensive experiments on safe planning benchmarks demonstrate that DiRecT substantially improves deployment safety and task performance over existing diffusion-based planning baselines.

Autonomous UAV navigation is conventionally solved by pipelines that separate perception, mapping, and planning into distinct stages, which propagates errors, accumulates latency, and requires environment-specific retuning. End-to-end generative models remove these interfaces by mapping raw observations directly to trajectories, but inherit a subtle failure mode: trained on clean data, they cannot recognise when an observation is unreliable, and treat degraded regions such as glass, mirrors, and overexposed surfaces as valid evidence for planning. We present a reliability-aware diffusion planner for 3D UAV navigation. It conditions trajectory generation on the observation together with a scene-level reliability heatmap that marks where perception cannot be trusted, produced by a lightweight network that distils the open-vocabulary reasoning of a vision-language model within the real-time planning budget. To generalise to unseen environments without retraining, we steer the denoising process with a differentiable two-stage ESDF cost that treats physical obstacles from depth and virtual obstacles from highly unreliable regions on equal footing. In simulation and on a real quadrotor, our planner produces markedly safer trajectories than a state-of-the-art diffusion baseline, reducing the obstacle-violation rate from 40.3% to 9.6% and raising the mean reliability of traversed regions from 0.588 to 0.925. Ablating the reliability term alone drops mean reliability from 0.898 to 0.783, confirming it as the decisive component, while distillation runs the framework up to 2 times faster than the full vision-language model.

Learning-based motion planners, despite recent progress, often suffer from temporal inconsistency. Small perturbations across frames can accumulate into unstable trajectories, degrading comfort and safety in closed-loop driving. Several methods attempt to inject history as a static conditioning signal to stabilize outputs, only to induce the planner to copy historical patterns instead of adapting to environment contexts. To address this limitation, we propose Diffusion Forcing Planner (DFP), a diffusion-based planning framework driven by history-guided control. Specifically, DFP decomposes the full trajectory into history, current and future segments, and assign independent noise levels to each segment. The model jointly denoises the historical and the future segments, enforcing a heterogeneous joint diffusion process. At inference, classifier-free guidance (CFG) is applied to steer future sampling using annealed history in a controllable manner. Closed-loop evaluation and comprehensive ablations on nuPlan show that DFP achieves competitive performance while producing continuous, stable, and controllable motion plans in complex driving scenarios.

How can we plan long-horizon routes that reach designated goals, visit required waypoints, and remain short when only short-horizon offline trajectories are available? This problem matters in offline navigation because collecting sufficiently rich long-horizon data is difficult, yet real agents must still solve long-range tasks with route-level efficiency rather than mere feasibility. The difficulty is twofold: at the microscopic level, composing many short-horizon segments creates a trade-off between search cost and path quality, while at the macroscopic level, waypoint ordering requires comparing pairwise travel costs among start, goal, and waypoint anchors that are unknown before planning and increasingly unreliable when estimated only from long-range temporal distance. In this paper, we propose ChronoForest, a closed-loop planning system that couples local bridge search and online route re-solving through an anchor-chaining tree diffusion planner and an online multi-tree orchestrator. ChronoForest uses temporal distance for short-range guidance and node evaluation, while using search-time bridge evidence to validate long-range anchor connectivity and repeatedly re-solve the route. On OGBench AntMaze-Stitch, ChronoForest achieves 99.8%, 99.3%, and 99.5% success on the medium, large, and giant splits and improves giant-stitch success by up to 34.5 points over prior reported diffusion-based results. On Hamiltonian route-composition benchmarks, online re-solving corrects poor temporal orderings and improves route quality while remaining substantially cheaper than exhaustive planning.

End-to-end autonomous driving models often struggle to balance multi-modal maneuver generation with real-time inference constraints. While diffusion models successfully capture diverse driving behaviors, their iterative denoising process incurs unacceptable latency for safety-critical deployment. To address this, we propose CLEAR (Cognition and Latent Evaluation for Adaptive Routing), a framework that combines ultra-fast generative planning with deep semantic reasoning. CLEAR employs Drive-JEPA as the visual encoder and replaces the multi-step denoising chain with a single-step conditional drift in a VAE latent space, introducing a conditioning coefficient to balance diversity and expert precision. Meanwhile, we fully fine-tune Qwen3.50.8B on driving QA pairs to extract scene-aware hidden states. These states guide both an Adaptive Scheduler, which selects the conditioning coefficient $α$ and sample count $N$ from a discrete set of predefined schemes, and a cross-attention scorer that selects the optimal trajectory from candidates. On the NAVSIM v1 benchmark, CLEAR achieves a state-of-the-art PDMS of 93.7. Our results demonstrate that high-fidelity, multi-modal planning can be executed efficiently without dense geometric annotations or iterative sampling.

Traditional end-to-end autonomous driving frameworks frequently suffer from the "style-averaging" dilemma when trained on high-variance human demonstrations, yielding homogenized, style-uncontrollable, and even kinematically unsafe policies. To overcome this limitation, we present D$^3$-MoE (Dual Disentangled Diffusion Mixture-of-Experts), which disentangles trajectory modeling along two complementary axes. On the behavioral axis, generation is decoupled from selection: a style-conditioned diffusion process synthesizes multi-style candidate trajectories in parallel within a single scene, allowing a downstream module to select the optimal trajectory based on user preference or an evaluation score. On the physical axis, decoupled longitudinal and lateral routers activate their respective experts during inference time, trained without manual labels using self-supervised targets from orthogonal ground-truth kinematics. These activated experts, architected as Diffusion Transformers (DiT) and equipped with style-conditioned AdaLN and asymmetric lateral-fusion cross-attention, independently predict their corresponding physical state before being reassembled into a unified, kinematically coherent trajectory. Extensive evaluations on the challenging NAVSIM benchmark demonstrate that D$^3$-MoE achieves state-of-the-art planning performance, reaching 88.2 PDMS and 84.3 EPDMS by default. Moreover, our Best-of-Three ensemble strategy effectively broadens the multi-modal solution space, raising performance to 91.3 PDMS and 87.5 EPDMS. Both quantitative and qualitative analyses jointly confirm the framework's advantages in planning quality and style controllability.

Indoor UAV navigation requires efficient exploration, scene understanding, and reliable trajectory execution under limited field-of-view observations. Existing vision-based navigation frameworks typically rely on single-view observations, limiting their ability to reason about occlusions, target visibility, and global scene structure. In this work, we propose AgenticDiffusion, a multi-view UAV navigation framework that coordinates language-guided reasoning, open-vocabulary target grounding, vision-based diffusion planning, and NMPC within a unified aerial navigation pipeline. Given a natural language instruction and synchronized first-person-view (FPV) and top-view observations, the framework determines the most informative viewpoint for navigation and generates a mission plan prior to trajectory execution. The targets are localized using an open-vocabulary grounding model, after which viewpoint-specific diffusion planners generate navigation trajectories for UAV execution. Using complementary viewpoints, the proposed framework reduces repeated target exploration and improves navigation efficiency in cluttered indoor environments. The framework was validated in four real-world UAV navigation scenarios involving adaptive viewpoint selection, multi-stage mission execution, long-horizon navigation, and safe landing-site selection. The experimental results demonstrated an overall mission success rate of 80% in 40 real-world trials, while the diffusion planners achieved a trajectory generation success rate of 100%.

Complex, dynamic, and interactive driving environments pose significant challenges for autonomous driving, primarily due to the pervasive uncertainty of surrounding traffic. A fundamental bottleneck in current systems is the disconnect between highly expressive uncertainty modeling and interpretable, safe motion planning. In this paper, we propose a novel sample-conditioned differentiable planning framework that bridges this gap by explicitly incorporating diffusion-generated future trajectories into the optimization process. Rather than compressing predictions into a single deterministic future or relying on black-box end-to-end architectures, our approach leverages a conditional diffusion model to generate a diverse set of plausible future scenarios. Crucially, these samples are directly fed into a differentiable planner, which explicitly mitigates predictive uncertainty via an empirical Conditional Value-at-Risk (CVaR) tail-risk constraint. This allows the planner to optimize a physically interpretable trajectory that is robust to rare yet safety-critical interactions. Furthermore, we introduce a directed graph representation for scene context that yields substantial improvements in both predictive effectiveness and computational efficiency. Validated through extensive open-loop and closed-loop evaluations on the Waymo Open Motion and Argoverse 2 datasets, our framework significantly outperforms state-of-the-art baselines in safety, efficiency, and ride comfort.

Discrete visual tokens should provide a compact representation for both token-based world modeling and planning in autonomous driving. However, most tokenizers are inherited from image generation and are optimized mainly for pixel reconstruction, which may leave a gap between what is easy to generate and what is useful to decode for driving decisions. We present a representation-guided and geometry-enhanced tokenizer that learns discrete tokens under joint supervision. The tokenizer aligns its discrete bottleneck with a frozen DINO feature space through feature decoding, while preserving appearance via RGB reconstruction with perceptual and adversarial losses. To inject geometric state-related cues, we add adjacent-frame depth and relative-pose supervision during training and stabilize joint objectives with multi-codebook quantization. We evaluate the same learned tokens with a lightweight planning readout and a GPT-style next-token world model. Experiments on NAVSIM show improved reconstruction fidelity and representation consistency, competitive planning performance under a fixed decoder, and better generative quality under matched settings.

Coordinating multiple robots in shared environments requires generating feasible trajectories for each agent while accounting for interactions among agents. Centralized planning approaches become difficult to scale as the number of robots increases, while decentralized approaches that allow each agent to plan independently do not inherently account for inter-agent interactions. This paper presents a framework for coordinated multi-robot motion planning that combines decentralized generative trajectory planning with multi-agent reinforcement learning (MARL)-based coordination. Each robot independently generates candidate trajectories using a diffusion model trained on single-agent motion data, leveraging the generative model's ability to produce feasible and diverse trajectories. To reduce conflicts between agents, a centralized value function trained via MARL guides the reverse diffusion process through gradient-based steering, enabling interaction-aware trajectory generation without centralized joint planning or retraining of the generative model. This guidance follows an exponential tilting formulation, in which the value function biases the denoising distribution toward trajectories with higher expected multi-agent return. The framework is evaluated in a simulated maze environment with four mobile robots. Experimental results show that the proposed value-guided diffusion planning reduces the inter-agent interference rate from 55.4% to 41.8%, demonstrating that coordination can be effectively achieved while preserving the scalability of decentralized trajectory generation. These results suggest that MARL-based value guidance can effectively introduce coordination into decentralized generative planners without requiring a fully joint multi-robot model.

Diffusion models provide strong priors for generating structured data, but many tasks require outputs beyond the scale on which these models are typically trained. Compositional generation addresses this by composing overlapping local plans from a pretrained short-horizon prior into a long-horizon output. However, standard composition primarily enforces agreement between neighboring local plans, yielding local consistency without directly specifying the global structure of the full composition. As a result, locally compatible plans may still form an implausible route, task sequence, or temporal evolution. Existing methods improve global coherence by repeatedly propagating local consistency signals or by adding inference-time optimization, but these procedures become expensive as the number or dimensionality of local plans increases. We propose Coarse-to-Fine Compositional Diffusion (CoFi), an inference-time sampler that separates global structure formation from local detail refinement. CoFi first aligns local denoised estimates around a shared coarse structure, producing a global scaffold that captures the long-range task-level arrangement. It then diffuses this scaffold to an intermediate noise level and denoises it with the same pretrained local prior, restoring local fine structure while preserving the scaffold-induced global coherence. Across long-horizon robotic planning, panoramic image generation, and long video generation, CoFi not only improves both global coherence and local sample quality over prior compositional baselines, but also requires 2-8x fewer denoiser evaluations.

We present DriveAnchor, a three-stage framework for autonomous driving planning that achieves behavioral diversity, controllability, and safety in a composable pipeline. Demonstration Flow Pretraining replaces the unstructured Gaussian prior with a vocabulary of 2,398 trajectory shapes constructed by farthest-point sampling, structurally grounding behavioral diversity in vocabulary coverage. Guided Flow Post-training jointly post-trains an Energy Field module with flow matching (FM), conditioning the Energy Field on static road geometry alone, to relocate anchors toward user-specified corridor polygons before flow generation, adding controllability without differentiable guidance; after Stage 2, new corridor presets require only Energy Field updates, not FM retraining. Reward-Refined Flow Fine-tuning applies zeroth-order reinforcement learning to align each anchor's output with collision-avoidance objectives: because the flow-matching model is a deterministic feedforward network in single-step mode, each anchor uniquely determines the output trajectory, reducing reward optimization to a direction search in anchor space without log-likelihood computation or ODE-to-SDE conversion. Evaluated on approximately 2 million held-out driving scenarios, DriveAnchor reduces near-range collision rates by 89% and improves mean reward by 32% without degradation in imitation accuracy, with 2.06 ms inference on NVIDIA Drive Orin. DriveAnchor has been validated through real-world vehicle testing, confirming its practicality for production deployment.

Recent perception-free end-to-end (E2E) autonomous driving methods bypass explicit perception outputs by compressing dense image patch tokens into compact scene tokens for downstream trajectory generation and scoring. While these scene tokens form a compact visual bottleneck for the planner, they receive supervision solely from the planning objective, providing limited constraints on the encoded visual information. To address this limitation, we introduce Neural Token Reconstruction (NTR), a representation learning framework to directly constrain the compact scene-token bottleneck in perception-free driving. NTR introduces a self-distillation masked latent reconstruction objective that reconstructs masked patch-level latent features using only compact scene tokens as reconstruction memory. This forces reconstruction gradients to pass exclusively through the scene-token bottleneck, encouraging scene tokens to preserve richer and less redundant visual representations for planning. We further introduce semantic priors derived from foundation-model annotations as a weak semantic interface biasing reconstruction targets toward driving-related structures without introducing explicit perception heads. All auxiliary reconstruction components are removed at inference time, leaving the deployed planner unchanged. NTR achieves state-of-the-art performance on three public autonomous driving benchmarks, including 8.0461 RFS on Waymo E2E and 94.1 PDMS / 90.9 EPDMS on NavSim1&2. The learned scene tokens exhibit lower pairwise redundancy and higher effective rank, indicating that effective bottleneck supervision improves both compact visual representation learning and planning performance.

We propose Drift-Resistant Navigation World Model, a generative model that mitigates both perceptual drift and geometric drift in conventional rollout-based navigation world models. Existing methods recursively feed generated content into subsequent steps, causing noise accumulation and degraded predictions, i.e., perceptual drift. Meanwhile, their predictions often deviate from the agent's motion, resulting in geometry drift. We address both types of drift by redesigning world-model prediction as an anchor-guided rollout. Instead of rolling out every frame sequentially, we first predict sparse future anchors that serve as stable long-range targets, and then generate intermediate frames within each chunk conditioned on both past context and future anchors. Importantly, these sparse anchors also provide geometric constraints, supported by bidirectional epipolar geometry, to localize where corresponding content should appear in the intermediate frames. Experiments on four benchmarks demonstrate consistent improvements over strong baselines in long-horizon visual quality, geometric consistency, and multi-view coherence. These gains further translate into improved downstream planning performance under the same planners, highlighting the importance of drift-resistant, geometry-aware prediction for reliable navigation world models.

Current end-to-end autonomous driving systems are fundamentally limited by a mismatch between temporal causal reasoning and global trajectory consistency. Autoregressive (AR) models capture interaction-aware temporal dependencies via causal factorization, but their step-wise decoding leads to error accumulation and suboptimal global structure. In contrast, diffusion models optimize trajectories globally but lack explicit causal constraints, making them unreliable in interactive and safety-critical scenarios. This dichotomy reveals a deeper issue: existing methods treat causal modeling and global optimization as separate paradigms, without a principled way to unify them within a single trajectory distribution. To address this, we propose ChainFlow-VLA, which unifies causal generation and global refinement within a unified probabilistic framework. We formulate planning as a mixture over AR-induced modes and learn Vision-Language Model (VLM)-conditioned residual distributions over these modes. An autoregressive generator (Chain) produces a discrete set of causal trajectory modes, followed by a diffusion-based refiner (Flow) that leverages VLM hidden states as semantic priors to perform mode-conditioned correction in residual space while preserving causal structure. This straightforward conditioning seamlessly injects high-level scene understanding into fine-grained trajectory adjustments. Experiments demonstrate that ChainFlow-VLA achieves robust planning in ambiguous and long-tail scenarios, achieving a state-of-the-art score of 94.85 on the NAVSIM v1 leaderboard, matching human-level performance (94.8). Code will be available at https://github.com/AFARI-Research/ChainFlow-VLA.

End-to-end autonomous driving via Vision-Language-Action (VLA) models demands a precarious balance between high-fidelity trajectory planning and efficient inference. Existing paradigms typically fall short: autoregressive (AR) VLAs are memory-bandwidth-bound on edge hardware and prone to exposure-bias drift, while full-sequence diffusion models preclude KV-cache reuse and suffer from "logical leakage" that violates the fundamental perceive-then-plan causality. We present Fast-dDrive, a block-diffusion VLA that performs bidirectional refinement within semantic units while enforcing strict causal ordering across them. Leveraging the observation that driving VLAs often emit structured JSON-like outputs, Fast-dDrive freezes structural tokens into a section scaffold and employs a section-aware training recipe that prioritizes safety-critical planning. We further introduce Scaffold Speculative Decoding to achieve AR-equivalent quality at significantly higher throughput. Finally, we propose a low-overhead test-time scaling scheme: by forking $N$ stochastic trajectory rollouts from a single shared-prefix KV cache and averaging them, we effectively suppress prediction variance at a fractional computational cost. Empirical results demonstrate that Fast-dDrive redefines the speed-accuracy frontier for driving agents. On the WOD-E2E test set, Fast-dDrive achieves SOTA ADE@3s and ADE@5s, alongside the highest RFS among diffusion-based VLAs; on nuScenes, it reduces average L2 error to $0.32$m (a $22\%$ improvement). When integrated with SGLang, our framework delivers $12\times$ throughput speedup over the AR baseline, narrowing the gap between high-capacity VLAs and the efficiency demands of real-time on-vehicle deployment.

Compositional diffusion models offer a promising route to long-horizon planning by denoising multiple overlapping sub-trajectories while ensuring that together they constitute a global solution. However, enforcing local behavior over long chains is often insufficient for a coherent global structure to emerge. Recent works tackle this limitation through intrinsic search, which explores multiple paths during the denoising process. While intrinsic search improves global coherence, it comes at the cost of repeated evaluations of an already compute-heavy model. In this work, we argue that extrinsic search, performed outside the denoising process, offers a more effective mode of exploration for long-horizon planning while naturally enabling the use of classical algorithms to solve unseen combinatorial tasks at test time. Our eXtrinsic search-guided Diffuser (XDiffuser) first computes a plan over a state-space graph -- serving as a lightweight local connectivity oracle for the diffusion model. The plan is then used to guide denoising for a single trajectory, effectively offloading the burden of exploration. XDiffuser outperforms diffusion-based baselines on long-horizon tasks, with particularly large gains in the low-quality data regime and on unseen tasks beyond goal-reaching, including multi-agent coordination and TSP-style reasoning. Project website: https://yanivhass.github.io/XDiffuser-site/

End-to-End (E2E) autonomous driving models have shown growing capability in recent years, with performance improving on increasingly challenging benchmarks. However, modern generative E2E planners still suffer from a substantial number of catastrophic failures in safety-critical scenarios. We find that many such failures arise from violations of physical constraints and safety requirements, leading to unsafe behavior. Motivated by this finding, in this paper, we focus on improving safety outcomes in generative end-to-end driving with a targeted reduction of catastrophic planning failures, instead of enhancing average planning quality. Towards this end, we propose DriveSafer, a failure-aware safety framework for end-to-end planners. DriveSafer explicitly steers generative planners towards safe behaviors leveraging both training-time safety constraints and inference-time safety guidance. Compared to the state-of-the-art DiffusionDrive model, on the NAVSIM benchmark, DriveSafer reduces the number of catastrophic failures (PDMS=0) by 48%, with over 65% reduction in drivable-area compliance failures.

We present a flow-matching planner for autonomous driving that directly outputs actionable control trajectories defined by acceleration and curvature profiles. The model is conditioned on a bird's-eye-view (BEV) raster of the surrounding scene and generates control sequences in a small number of Ordinary Differential Equations (ODE) integration steps, enabling low-latency inference suitable for real-time closed-loop re-planning. We train exclusively on urban scenarios (real urban city streets, intersections and roundabouts of the city of Parma, Italy) collected from a 2D traffic simulator with reactive agents, and evaluate in closed-loop on both in-distribution and markedly out-of-distribution environments, including multi-lane highways and unseen urban scenarios. Our results show that the model generalizes reliably to these unseen conditions, maintaining stable closed-loop control and successfully completing scenarios that differ substantially from the training distribution. We attribute this to the BEV representation, which provides a geometry-centric view of the scene that is inherently less sensitive to distributional shifts, and to the flow-matching formulation, which learns a smooth vector field that degrades gracefully under distribution shift. We provide video demonstrations of closed-loop behavior at https://marcelloceresini.github.io/DirectControlFlowMatching.

Volumetric Modulated Arc Therapy (VMAT) is a cornerstone of modern radiation therapy, enabling highly conformal tumor irradiation and healthy-tissue sparing. Yet, its planning solves inverse and nested optimization for multi-leaf collimators, monitor units and dose parameters, while enforcing their consistency to ensure mechanical deliverability. Nevertheless, this process often requires repeated re-optimization when treatment configurations change, resulting in substantial planning time per patient. To address these problems, we present a diffusion-driven Learning-to-Optimize (L2O) method for end-to-end VMAT planning. A distribution-matching distilled diffusion model learns a clinically feasible manifold of fluence maps, enabling their one-shot generation. On top of this, an LSTM-based L2O module learns gradient update dynamics to swiftly refine fluence maps toward prescribed dose objectives during inference. Experimental results on clinical and public prostate cancer cohorts demonstrate improved planning efficiency, flexibility, and machine deliverability over currently available end-to-end VMAT planners.

Multi-Agent Path Finding (MAPF) is a coordination problem that requires computing globally consistent, collision-free trajectories from individual start positions to assigned goal positions under combinatorial planning complexity. In dense environments, suboptimal initial plans induce compound conflicts that hinder feasible repair. For repair-based solvers like LNS2, initial plan quality critically affects downstream repair, yet this factor remains underexplored. We propose DiffLNS, a hybrid framework that integrates a discrete denoising diffusion probabilistic model (D3PM) with LNS2. The D3PM serves as an initializer with sparse social attention that learns a spatiotemporal prior over coordinated multi-agent action trajectories from expert demonstrations and samples multiple joint plans. Operating directly on the categorical action space, our discrete diffusion preserves the MAPF action structure and samples from a multimodal joint-plan distribution to produce diverse drafts well suited for neighborhood repair. These drafts act as warm starts for downstream repair, which completes unfinished trajectories and resolves remaining conflicts under hard MAPF constraints. Experimental results show that despite being trained only on instances with at most 96 agents, the initializer generalizes to scenarios with up to 312 agents at inference time. Across 20 complex and congested settings, DiffLNS achieves an average success rate of 95.8%, outperforming the strongest tested baseline by 9.6 percentage points and matching or exceeding all baselines in all 20 settings. To the best of our knowledge, this is the first work to leverage discrete diffusion for warm-starting an LNS-based MAPF solver.

Multi-agent trajectory modeling traditionally focuses on forecasting, often neglecting more general tasks like trajectory completion, which is essential for real-world applications such as correcting tracking data. Existing methods also generally predict agents' states without offering any state-wise measure of heteroscedastic uncertainty. Moreover, popular multi-modal sampling methods lack error probability estimates for each generated scene under the same prior observations, which makes it difficult to rank the predictions at inference time. We introduce U2Diffine, a unified diffusion model built to perform trajectory completion while simultaneously offering state-wise heteroscedastic uncertainty estimates. This is achieved by augmenting the standard denoising loss with the negative log-likelihood of the predicted noise, and then propagating the latent space uncertainty to the real state space using a first-order Taylor approximation. We also propose U2Diff, a faster baseline that avoids gradient computation during sampling. This approach significantly increases inference speed, making it as efficient as a standard generative-only diffusion model. For post-processing, we integrate a Rank Neural Network (RankNN) that enables error probability estimation for each generated mode, demonstrating strong correlation with ground truth errors. Our method outperforms state-of-the-art solutions in both trajectory completion and forecasting across four challenging sports datasets (NBA, Basketball-U, Football-U, Soccer-U), underscoring the effectiveness of our uncertainty and error probability estimation.

Vision-Language-Action (VLA) models have emerged as a promising paradigm for end-to-end autonomous driving. However, existing reasoning mechanisms still struggle to provide planning-oriented intermediate representations: textual Chain-of-Thought (CoT) fails to preserve continuous spatiotemporal structure, while latent world reasoning remains difficult to use as a direct condition for action generation. In this paper, we propose CoWorld-VLA, a multi-expert world reasoning framework for autonomous driving, where world representations serve as explicit conditions to guide action planning. CoWorld-VLA extracts complementary world information through multi-source supervision and encodes it into expert tokens within the VLA, thereby providing planner-accessible conditioning signals. Specifically, we construct four types of tokens: semantic interaction, geometric structure, dynamic evolution, and ego trajectory tokens, which respectively model interaction intent, spatial structure, future temporal dynamics, and behavioral goals. During action generation, CoWorld-VLA employs a diffusion-based hierarchical multi-expert fusion planner, which is coupled with scene context throughout the joint denoising process to generate continuous ego trajectories. Experiments show that CoWorld-VLA achieves competitive results in both future scene generation and planning on the NAVSIM v1 benchmark, demonstrating strong performance in collision avoidance and trajectory accuracy. Ablation studies further validate the complementarity of expert tokens and their effectiveness as planning conditions for action generation. Code will be available at https://github.com/AFARI-Research/CoWorld-VLA.

Diffusion-based trajectory planners can synthesize rich, multimodal robot motions, but their iterative denoising makes online planning and control prohibitively slow. Existing accelerations either modify the sampler or compress the network--sacrificing plan quality or requiring retraining without accounting for downstream control risk. We address the problem of making diffusion-based trajectory planners fast enough for real-time robot use without retraining the model or sacrificing trajectory quality, and in a way that works across diverse state-space diffusion architectures. Our key insight is that diffusion trajectory planners expose two signals we can exploit: a cheap probe of how their internal trajectory representation changes across steps, and analytic coefficients that describe how denoiser errors affect the sampler's state update. By calibrating the first signal against the second on offline runs, we obtain a per-step score that upper-bounds how far the final trajectory can deviate when we reuse a cached denoiser output, and we treat this bound as an uncertainty budget that we can spend over the denoising process. Building on this insight, we present Muninn, a training-free caching wrapper that tracks this uncertainty budget during sampling and, at each diffusion step, chooses between reusing a cached denoiser output when the predicted deviation is small and recomputing the denoiser when it is not. Across standard benchmarks Muninn delivers up to 4.6x wall-clock speedups across several trajectory diffusion models by reducing denoiser evaluations, while preserving task performance and safety metrics. Muninn further certifies that cached rollouts remain within a specified distance of their full-compute counterparts, and we validate these gains in real-time closed-loop navigation and manipulation hardware deployments. Project page: https://github.com/gokulp01/Muninn.

Existing latent world models for autonomous driving have opened a promising path toward future-aware driving intelligence. However, they typically treat future latent states as prediction targets or auxiliary signals, rather than directly conditioning trajectory planning. This can entangle current and future features in latent space. In this work, we propose DriveFuture, a future-aware latent world modeling framework for autonomous driving that explicitly learns planning-oriented foresight by conditioning the current latent state modeling process on future world states. Specifically, during training, the model first predicts future latent world states from the current latent state and ego action, and then refines the prediction against the ground-truth future latent state via cross-attention. The resulting future-aware latent serves as an explicit condition for a diffusion-based trajectory planner. During inference, DriveFuture conditions on the predicted future latent state instead of the ground-truth future state. DriveFuture achieves SOTA performance on the public NAVSIM benchmarks, reaching \textbf{55.5} EPDMS on NAVSIM-v2 {\textcolor{blue}{\textit{navhard}}}, \textbf{89.9} EPDMS on NAVSIM-v2 {\textcolor{blue}{\textit{navtest}}}, and \textbf{90.7} PDMS on NAVSIM-v1 {\textcolor{blue}{\textit{navtest}}}, respectively. These results suggest that the key to latent world modeling lies not merely in simulating future states, but more importantly in conditioning current decision-making on future states. Notably, as of April 2026, DriveFuture ranks \textbf{1st} on the \href{https://huggingface.co/spaces/AGC2025/e2e-driving-navhard}{NAVSIM-v2 {\textcolor{blue}{\textit{navhard}}}} leaderboard and achieves SOTA performance on \href{https://huggingface.co/spaces/AGC2024-P/e2e-driving-navtest}{NAVSIM-v1 {\textcolor{blue}{\textit{navtest}}}}.

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.

Recent advances in generative models have shown promise in generating behavior plans for long-horizon, sparse reward tasks. While these approaches have achieved promising results, they often lack a principled framework for hierarchical decomposition and struggle with the computational demands of real-time execution, due to their iterative denoising process. In this work, we introduce Hierarchical Diffusion-Flow (HDFlow), a novel hierarchical planning framework that optimally leverages the strengths of diffusion and rectified flow models to overcome the limitations of single-paradigm generative planners. HDFlow employs a high-level diffusion planner to generate sequences of strategic subgoals in a learned latent space, capitalizing on diffusion's powerful exploratory capabilities. These subgoals then guide a low-level rectified flow planner that generates smooth and dense trajectories, exploiting the speed and efficiency of ordinary differential equation (ODE)-based trajectory generation. We evaluate HDFlow on four challenging furniture assembly tasks in both simulation and real-world, where it significantly outperforms state-of-the-art methods. Furthermore, we also showcase our method's generalizability on two long-horizon benchmarks comprising diverse locomotion and manipulation tasks. Project website: https://hdflow-page.github.io/

Compositional diffusion planning generates long-horizon trajectories by stitching together overlapping short-horizon segments through score composition. However, when local plan distributions are multimodal, existing compositional methods suffer from mode-averaging, where averaging incompatible local modes leads to plans that are neither locally feasible nor globally coherent. We propose Refining Compositional Diffusion (RCD), a training-free guidance method that steers compositional sampling toward high-density, globally coherent plans. RCD leverages the self-reconstruction error of a pretrained diffusion model as a proxy for the log-density of composed plans, combined with an overlap consistency term that enforces consistency at segment boundaries. We show that the combined guidance concentrates sampling on high-density plans that mitigate mode-averaging. Experiments on challenging long-horizon tasks from OGBench, including locomotion, object manipulation, and pixel-based observations, demonstrate that RCD consistently outperforms existing methods.

End-to-end autonomous driving planners typically generate trajectories from current observations alone. However, real-world driving is highly dynamic, and such reactive planning cannot anticipate future scene evolution, often leading to myopic decisions and safety-critical failures. We propose ProDrive, a world-model-based proactive planning framework that enables ego-environment co-evolution for autonomous driving. ProDrive jointly trains a query-centric trajectory planner and a bird's-eye-view (BEV) world model end-to-end: the planner generates diverse candidate trajectories and planning-aware ego tokens, while the world model predicts future scene evolution conditioned on them. By injecting planner features into the world model and evaluating all candidates in parallel, ProDrive preserves end-to-end gradient flow and allows future outcome assessment to directly shape planning. This bidirectional coupling enables proactive planning beyond current-observation-driven decision-making. Experiments on NAVSIM v1 show that ProDrive outperforms strong baselines in both safety and planning efficiency, while ablations validate the effectiveness of the proposed ego-environment coupling design.

Multi-modal trajectory generation is essential for safe autonomous driving, yet existing diffusion-based planners suffer from high inference latency due to iterative neural function evaluations. This paper presents MISTY (Mixer-based Inference for Single-step Trajectory-drifting Yield), a high-throughput generative motion planner that achieves state-of-the-art closed-loop performance with pure single-step inference. MISTY integrates a vectorized Sub-Graph encoder to capture environment context, a Variational Autoencoder to structure expert trajectories into a compact 32-dimensional latent manifold, and an ultra-lightweight MLP-Mixer decoder to eliminate quadratic attention complexity. Importantly, we introduce a latent-space drifting loss that shifts the complex distribution evolution entirely to the training phase. By formulating explicit attractive and repulsive forces, this mechanism empowers the model to synthesize novel, proactive maneuvers, such as active overtaking, that are virtually absent from the raw expert demonstrations. Extensive evaluations on the nuPlan benchmark demonstrate that MISTY achieves state-of-the-art results on the challenging Test14-hard split, with comprehensive scores of 80.32 and 82.21 in non-reactive and reactive settings, respectively. Operating at over 99 FPS with an end-to-end latency of 10.1 ms, MISTY offers an order-of-magnitude speedup over iterative diffusion planners while while achieving significantly robust generation.

Safe and agile trajectory planning is essential for autonomous systems, especially during complex aerobatic maneuvers. Motivated by the recent success of diffusion models in generative tasks, this paper introduces AeroTrajGen, a novel framework for diffusion-based trajectory generation that incorporates control barrier function (CBF)-guided sampling during inference, specifically designed for unmanned aerial vehicles (UAVs). The proposed CBF-guided sampling addresses two critical challenges: (1) mitigating the inherent unpredictability and potential safety violations of diffusion models, and (2) reducing reliance on extensively safety-verified training data. During the reverse diffusion process, CBF-based guidance ensures collision-free trajectories by seamlessly integrating safety constraint gradients with the diffusion model's score function. The model features an obstacle-aware diffusion transformer architecture with multi-modal conditioning, including trajectory history, obstacles, maneuver styles, and goal, enabling the generation of smooth, highly agile trajectories across 14 distinct aerobatic maneuvers. Trained on a dataset of 2,000 expert demonstrations, AeroTrajGen is rigorously evaluated in simulation under multi-obstacle environments. Simulation results demonstrate that CBF-guided sampling reduces collision rates by 94.7% compared to unguided diffusion baselines, while preserving trajectory agility and diversity. Our code is open-sourced at https://github.com/RoboticsPolyu/CBF-DMP.

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.

Generalization is a central challenge in autonomous driving, as real-world deployment requires robust performance under unseen scenarios, sensor domains, and environmental conditions. Recent world-model-based planning methods have shown strong capabilities in scene understanding and multi-modal future prediction, yet their generalization across datasets and sensor configurations remains limited. In addition, their loosely coupled planning paradigm often leads to poor video-trajectory consistency during visual imagination. To overcome these limitations, we propose DriveVA, a novel autonomous driving world model that jointly decodes future visual forecasts and action sequences in a shared latent generative process. DriveVA inherits rich priors on motion dynamics and physical plausibility from well-pretrained large-scale video generation models to capture continuous spatiotemporal evolution and causal interaction patterns. To this end, DriveVA employs a DiT-based decoder to jointly predict future action sequences (trajectories) and videos, enabling tighter alignment between planning and scene evolution. We also introduce a video continuation strategy to strengthen long-duration rollout consistency. DriveVA achieves an impressive PDM-based planning performance of 90.9 PDM score on the NAVSIM benchmark. Extensive experiments also demonstrate the zero-shot capability and cross-domain generalization of DriveVA, which reduces average L2 error and collision rate by 78.9% and 83.3% on nuScenes and 52.5% and 52.4% on the Bench2Drive built on CARLA v2 compared with the state-of-the-art world-model-based planner.