Diffusion-Based Planning

Diffusion models operate in a reflexive System 1 mode, constrained by a fixed, content-agnostic sampling schedule. This rigidity arises from the curse of state dimensionality, where the combinatorial explosion of possible states in the high-dimensional noise manifold renders explicit trajectory planning intractable and leads to systematic computational misallocation. To address this, we introduce Chain-of-Trajectories (CoTj), a train-free framework enabling System 2 deliberative planning. Central to CoTj is Diffusion DNA, a low-dimensional signature that quantifies per-stage denoising difficulty and serves as a proxy for the high-dimensional state space, allowing us to reformulate sampling as graph planning on a directed acyclic graph. Through a Predict-Plan-Execute paradigm, CoTj dynamically allocates computational effort to the most challenging generative phases. Experiments across multiple generative models demonstrate that CoTj discovers context-aware trajectories, improving output quality and stability while reducing redundant computation. This work establishes a new foundation for resource-aware, planning-based diffusion modeling. The code is available at https://github.com/UnicomAI/CoTj.

Diffusion-based trajectory planners can synthesize rich, multimodal action sequences for offline reinforcement learning, but their iterative denoising incurs substantial inference-time cost, making closed-loop planning slow under tight compute budgets. We study the problem of achieving diffusion-like trajectory planning behavior with one-step inference, while retaining the ability to sample diverse candidate plans and condition on the current state in a receding-horizon control loop. Our key observation is that conditional trajectory generation fails under naïve distribution-matching objectives when the similarity measure used to align generated trajectories with the dataset is dominated by unconstrained future dimensions. In practice, this causes attraction toward average trajectories, collapses action diversity, and yields near-static behavior. Our key insight is that conditional generative planning requires a conditioning-aware notion of neighborhood: trajectory updates should be computed using distances in a compact key space that reflects the condition, while still applying updates in the full trajectory space. Building on this, we introduce Keyed Drifting Policies (KDP), a one-step trajectory generator trained with a drift-field objective that attracts generated trajectories toward condition-matched dataset windows and repels them from nearby generated samples, using a stop-gradient drifted target to amortize iterative refinement into training. At inference, the resulting policy produces a full trajectory window in a single forward pass. Across standard RL benchmarks and real-time hardware deployments, KDP achieves strong performance with one-step inference and substantially lower planning latency than diffusion sampling. Project website, code and videos: https://keyed-drifting.github.io/

Diffusion-based models have recently shown strong performance in trajectory planning, as they are capable of capturing diverse, multimodal distributions of complex behaviors. A key limitation of these models is their slow inference speed, which results from the iterative denoising process. This makes them less suitable for real-time applications such as closed-loop model predictive control (MPC), where plans must be generated quickly and adapted continuously to a changing environment. In this paper, we investigate Implicit Maximum Likelihood Estimation (IMLE) as an alternative generative modeling approach for planning. IMLE offers strong mode coverage while enabling inference that is two orders of magnitude faster, making it particularly well suited for real-time MPC tasks. Our results demonstrate that IMLE achieves competitive performance on standard offline reinforcement learning benchmarks compared to the standard diffusion-based planner, while substantially improving planning speed in both open-loop and closed-loop settings. We further validate IMLE in a closed-loop human navigation scenario, operating in real-time, demonstrating how it enables rapid and adaptive plan generation in dynamic environments. Real-world videos and code are available at https://gmpc-imle.github.io/.

Recent advancements in Language Models (LMs) have demonstrated strong semantic reasoning capabilities, enabling their application in high-level decision-making for autonomous driving (AD). However, LMs operate over discrete token spaces and lack the ability to generate continuous, physically feasible trajectories required for motion planning. Meanwhile, diffusion models have proven effective at generating reliable and dynamically consistent trajectories, but often lack semantic interpretability and alignment with scene-level understanding. To address these limitations, we propose KnowDiffuser, a knowledge-guided motion planning framework that tightly integrates the semantic understanding of language models with the generative power of diffusion models. The framework employs a language model to infer context-aware meta-actions from structured scene representations, which are then mapped to prior trajectories that anchor the subsequent denoising process. A two-stage truncated denoising mechanism refines these trajectories efficiently, preserving both semantic alignment and physical feasibility. Experiments on the nuPlan benchmark demonstrate that KnowDiffuser significantly outperforms existing planners in both open-loop and closed-loop evaluations, establishing a robust and interpretable framework that effectively bridges the semantic-to-physical gap in AD systems.

Autonomous driving in complex traffic requires planners that generalize beyond hand-crafted rules, motivating data-driven approaches that learn behavior from expert demonstrations. Diffusion-based trajectory planners have recently shown strong closed-loop performance by iteratively denoising a full-horizon plan, but they remain difficult to certify and can fail catastrophically in rare or out-of-distribution scenarios. To address this challenge, we present PC-Diffuser, a safety augmentation framework that embeds a certifiable, path-consistent barrier-function structure directly into the denoising loop of diffusion planning. The key idea is to make safety an intrinsic part of trajectory generation rather than a post-hoc fix: we enforce forward invariance along the rollout while preserving the diffusion model's intended path geometry. Specifically, PC-Diffuser (i) evaluates collision risk using a capsule-distance barrier function that better reflects vehicle geometry and reduces unnecessary conservativeness, (ii) converts denoised waypoints into dynamically feasible motion under a kinematic bicycle model, and (iii) applies a path-consistent safety filter that eliminates residual constraint violations without geometric distortion, so the corrected plan remains close to the learned distribution. By injecting these safety-consistent corrections at every denoising step and feeding the refined trajectory back into the diffusion process, PC-Diffuser enables iterative, context-aware safeguarding instead of post-hoc repair...

Safe swarm navigation in cluttered indoor environment requires long-horizon planning, reactive obstacle avoidance, and adaptive compliance. We propose ImpedanceDiffusion, a hierarchical framework that leverages image-conditioned diffusion-based global path planning with Artificial Potential Field (APF) tracking and semantic-aware variable impedance control for aerial drone swarms. The diffusion model generates geometric global trajectories directly from RGB images without explicit map construction. These trajectories are tracked by an APF-based reactive layer, while a VLM-RAG module performs semantic obstacle classification with 90% retrieval accuracy to adapt impedance parameters for mixed obstacle environments during execution. Two diffusion planners are evaluated: (i) a top-view long-horizon planner using single-pass inference and (ii) a first-person-view (FPV) short-horizon planner deployed via a two-stage inference pipeline. Both planners achieve a 100% trajectory generation rate across twenty static and dynamic experimental configurations and are validated via zero-shot sim-to-real deployment on Crazyflie 2.1 drones through the hierarchical APF-impedance control stack. The top-view planner produces smoother trajectories that yield conservative tracking speeds of 1.0-1.2 m/s near hard obstacles and 0.6-1.0 m/s near soft obstacles. In contrast, the FPV planner generates trajectories with greater local clearance and typically higher speeds, reaching 1.4-2.0 m/s near hard obstacles and up to 1.6 m/s near soft obstacles. Across 20 experimental configurations (100 total runs), the framework achieved a 92% success rate while maintaining stable impedance-based formation control with bounded oscillations and no in-flight collisions, demonstrating reliable and adaptive swarm navigation in cluttered indoor environments.

Diffusion planners are a strong approach for offline reinforcement learning, but they can fail when value-guided selection favours trajectories that score well yet are locally inconsistent with the environment dynamics, resulting in brittle execution. We propose Self-supervised Action Gating with Energies (SAGE), an inference-time re-ranking method that penalises dynamically inconsistent plans using a latent consistency signal. SAGE trains a Joint-Embedding Predictive Architecture (JEPA) encoder on offline state sequences and an action-conditioned latent predictor for short horizon transitions. At test time, SAGE assigns each sampled candidate an energy given by its latent prediction error and combines this feasibility score with value estimates to select actions. SAGE can integrate into existing diffusion planning pipelines that can sample trajectories and select actions via value scoring; it requires no environment rollouts and no policy re-training. Across locomotion, navigation, and manipulation benchmarks, SAGE improves the performance and robustness of diffusion planners.

Diffusion models excel at short-horizon robot planning, yet scaling them to long-horizon tasks remains challenging due to computational constraints and limited training data. Existing compositional approaches stitch together short segments by separately denoising each component and averaging overlapping regions. However, this suffers from instability as the factorization assumption breaks down in noisy data space, leading to inconsistent global plans. We propose that the key to stable compositional generation lies in enforcing boundary agreement on the estimated clean data (Tweedie estimates) rather than on noisy intermediate states. Our method formulates long-horizon planning as inference over a chain-structured factor graph of overlapping video chunks, where pretrained short-horizon video diffusion models provide local priors. At inference time, we enforce boundary agreement through a novel combination of synchronous and asynchronous message passing that operates on Tweedie estimates, producing globally consistent guidance without requiring additional training. Our training-free framework demonstrates significant improvements over existing baselines, effectively generalizing to unseen start-goal combinations that were not present in the original training data. Project website: https://comp-visual-planning.github.io/

While multimodal large language models (MLLMs) provide advanced reasoning for autonomous driving, translating their discrete semantic knowledge into continuous trajectories remains a fundamental challenge. Existing methods often rely on unimodal planning heads that inherently limit their ability to represent multimodal driving behavior. Furthermore, most generative approaches frequently condition on one-hot encoded actions, discarding the nuanced navigational uncertainty critical for complex scenarios. To resolve these limitations, we introduce LAD-Drive, a generative framework that structurally disentangles high-level intention from low-level spatial planning. LAD-Drive employs an action decoder to infer a probabilistic meta-action distribution, establishing an explicit belief state that preserves the nuanced intent typically lost by one-hot encodings. This distribution, fused with the vehicle's kinematic state, conditions an action-aware diffusion decoder that utilizes a truncated denoising process to refine learned motion anchors into safe, kinematically feasible trajectories. Extensive evaluations on the LangAuto benchmark demonstrate that LAD-Drive achieves state-of-the-art results, outperforming competitive baselines by up to 59% in Driving Score while significantly reducing route deviations and collisions. We will publicly release the code and models on https://github.com/iis-esslingen/lad-drive.

Diffusion-based motion planners have achieved state-of-the-art results on benchmarks such as nuPlan, yet their evaluation within closed-loop production autonomous driving stacks remains largely unexplored. Existing evaluations abstract away ROS 2 communication latency and real-time scheduling constraints, while monolithic ONNX deployment freezes all solver parameters at export time. We present an open-source modular benchmark that addresses both gaps: using ONNX GraphSurgeon, we decompose a monolithic 18,398 node diffusion planner into three independently executable modules and reimplement the DPM-Solver++ denoising loop in native C++. Integrated as a ROS 2 node within Autoware, the open-source AD stack deployed on real vehicles worldwide, the system enables runtime-configurable solver parameters without model recompilation and per-step observability of the denoising process, breaking the black box of monolithic deployment. Unlike evaluations in standalone simulators such as CARLA, our benchmark operates within a production-grade stack and is validated through AWSIM closed-loop simulation. Through systematic comparison of DPM-Solver++ (first- and second-order) and DDIM across six step-count configurations (N in {3, 5, 7, 10, 15, 20}), we show that encoder caching yields a 3.2x latency reduction, and that second-order solving reduces FDE by 41% at N=3 compared to first-order. The complete codebase will be released as open-source, providing a direct path from simulation benchmarks to real-vehicle deployment.

Trajectory generation for mobile robots in unstructured environments faces a critical dilemma: balancing kinematic smoothness for safe execution with terminal precision for fine-grained tasks. Existing generative planners often struggle with this trade-off, yielding either smooth but imprecise paths or geometrically accurate but erratic motions. To address the aforementioned shortcomings, this article proposes DRIFT (Diffusion-based Rule-Inferred for Trajectories), a conditional diffusion framework designed to generate high-fidelity reference trajectories by integrating two complementary inductive biases. First, a Relational Inductive Bias, realized via a GNN-based Structured Scene Perception (SSP) module, encodes global topological constraints to ensure holistic smoothness. Second, a Temporal Attention Bias, implemented through a novel Graph-Conditioned Time-Aware GRU (GTGRU), dynamically attends to sparse obstacles and targets for precise local maneuvering. In the end, quantitative results demonstrate that DRIFT reconciles these conflicting objectives, achieving centimeter-level imitation fidelity (0.041m FDE) and competitive smoothness (27.19 Jerk). This balance yields highly executable reference plans for downstream control.

Diffusion models have become a popular choice for decision-making tasks in robotics, and more recently, are also being considered for solving autonomous driving tasks. However, their applications and evaluations in autonomous driving remain limited to simulation-based or laboratory settings. The full strength of diffusion models for large-scale, complex real-world settings, such as End-to-End Autonomous Driving (E2E AD), remains underexplored. In this study, we conducted a systematic and large-scale investigation to unleash the potential of the diffusion models as planners for E2E AD, based on a tremendous amount of real-vehicle data and road testing. Through comprehensive and carefully controlled studies, we identify key insights into the diffusion loss space, trajectory representation, and data scaling that significantly impact E2E planning performance. Moreover, we also provide an effective reinforcement learning post-training strategy to further enhance the safety and robustness of the learned planner. The resulting diffusion-based learning framework, Hyper Diffusion Planner (HDP), is deployed on a real-vehicle platform and evaluated across 6 urban driving scenarios and 200 km of real-world testing, achieving a notable 10x performance improvement over the base model. Our work demonstrates that diffusion models, when properly designed and trained, can serve as effective and scalable E2E AD planners for complex, real-world autonomous driving tasks.

Large Language Models (LLMs) and Vision-Language Models (VLMs) have emerged as promising candidates for end-to-end autonomous driving. However, these models typically face challenges in inference latency, action precision, and explainability. Existing autoregressive approaches struggle with slow token-by-token generation, while prior diffusion-based planners often rely on verbose, general-purpose language tokens that lack explicit geometric structure. In this work, we propose Masked Vision-Language-Action Diffusion for Autonomous Driving (MVLAD-AD), a novel framework designed to bridge the gap between efficient planning and semantic explainability via a masked vision-language-action diffusion model. Unlike methods that force actions into the language space, we introduce a discrete action tokenization strategy that constructs a compact codebook of kinematically feasible waypoints from real-world driving distributions. Moreover, we propose geometry-aware embedding learning to ensure that embeddings in the latent space approximate physical geometric metrics. Finally, an action-priority decoding strategy is introduced to prioritize trajectory generation. Extensive experiments on nuScenes and derived benchmarks demonstrate that MVLAD-AD achieves superior efficiency and outperforms state-of-the-art autoregressive and diffusion baselines in planning precision, while providing high-fidelity and explainable reasoning.

Diffusion models have shown promising capabilities in trajectory generation for planning in offline reinforcement learning (RL). However, conventional diffusion-based planning methods often fail to account for the fact that generating trajectories in RL requires unique consistency between transitions to ensure coherence in real environments. This oversight can result in considerable discrepancies between the generated trajectories and the underlying mechanisms of a real environment. To address this problem, we propose a novel diffusion-based planning method, termed as Diffusion Modulation via Environment Mechanism Modeling (DMEMM). DMEMM modulates diffusion model training by incorporating key RL environment mechanisms, particularly transition dynamics and reward functions. Experimental results demonstrate that DMEMM achieves state-of-the-art performance for planning with offline reinforcement learning.

Active search for recovering objects of interest through online, adaptive decision making with autonomous agents requires trading off exploration of unknown environments with exploitation of prior observations in the search space. Prior work has proposed information gain and Thompson sampling based myopic, greedy approaches for agents to actively decide query or search locations when the number of targets is unknown. Decision making algorithms in such partially observable environments have also shown that agents capable of lookahead over a finite horizon outperform myopic policies for active search. Unfortunately, lookahead algorithms typically rely on building a computationally expensive search tree that is simulated and updated based on the agent's observations and a model of the environment dynamics. Instead, in this work, we leverage the sequence modeling abilities of diffusion models to sample lookahead action sequences that balance the exploration-exploitation trade-off for active search without building an exhaustive search tree. We identify the optimism bias in prior diffusion based reinforcement learning approaches when applied to the active search setting and propose mitigating solutions for efficient cost-aware decision making with both single and multi-agent teams. Our proposed algorithm outperforms standard baselines in offline reinforcement learning in terms of full recovery rate and is computationally more efficient than tree search in cost-aware active decision making.

Path planning in complex environments is one of the key problems of artificial intelligence because it requires simultaneous understanding of the geometry of space and the global structure of the problem. In this paper, we explore the potential of using generative models as planning and reasoning mechanisms. We propose GenPlanner, an approach based on diffusion models and flow matching, along with two variants: DiffPlanner and FlowPlanner. We demonstrate the application of generative models to find and generate correct paths in mazes. A multi-channel condition describing the structure of the environment, including an obstacle map and information about the starting and destination points, is used to condition trajectory generation. Unlike standard methods, our models generate trajectories iteratively, starting with random noise and gradually transforming it into a correct solution. Experiments conducted show that the proposed approach significantly outperforms the baseline CNN model. In particular, FlowPlanner demonstrates high performance even with a limited number of generation steps.

Vision-Language-Action (VLA) models for autonomous driving increasingly adopt generative planners trained with imitation learning followed by reinforcement learning. Diffusion-based planners suffer from modality alignment difficulties, low training efficiency, and limited generalization. Token-based planners are plagued by cumulative causal errors and irreversible decoding. In summary, the two dominant paradigms exhibit complementary strengths and weaknesses. In this paper, we propose DriveFine, a masked diffusion VLA model that combines flexible decoding with self-correction capabilities. In particular, we design a novel plug-and-play block-MoE, which seamlessly injects a refinement expert on top of the generation expert. By enabling explicit expert selection during inference and gradient blocking during training, the two experts are fully decoupled, preserving the foundational capabilities and generic patterns of the pretrained weights, which highlights the flexibility and extensibility of the block-MoE design. Furthermore, we design a hybrid reinforcement learning strategy that encourages effective exploration of refinement expert while maintaining training stability. Extensive experiments on NAVSIM v1, v2, and Navhard benchmarks demonstrate that DriveFine exhibits strong efficacy and robustness. The code will be released at https://github.com/MSunDYY/DriveFine.

Visual traversability estimation is central to autonomous navigation, yet most approaches either rely on prompt-driven Vision-Language Model (VLM) or decouple traversability from trajectory planning, requiring separate planners with heavy mapping, manual tuning, and extended deployment time. We propose EmbodiedDiffusion, a diffusion-based framework that simultaneously predicts traversability maps and generates feasible trajectories from RGB images using planner-free synthetic supervision and embodiment conditioning for cross-platform transfer. The framework distills category-level traversability semantics from a VLM teacher into a lightweight student model during training, enabling prompt-free, real-time inference at deployment. A modular FiLM-based conditioning mechanism isolates embodiment-specific reasoning into a compact trainable subset of the network, allowing rapid adaptation to new robot platforms without retraining the visual backbone or the trajectory diffusion model. Across indoor environments with quadruped and aerial robots, EmbodiedDiffusion achieves 80-100% navigation success in the full-data regime with real-time inference (90 ms) and adapts to new platforms using only 10 min of visual data collection, demonstrating scalable, unified traversability reasoning and trajectory generation for heterogeneous robots.

Personalized autonomous driving requires understanding the driving needs implicit in user requests. This is challenging when driving demonstrations lack style annotations and behavioral adaptation risks degrading planning quality. We propose M-Diffusion Planner with a dual-decoupling design: separating intent understanding from trajectory planning, and general planning capability learning from strategy alignment. A large language model infers driving needs and selects a strategy, which is executed by the corresponding head of a shared diffusion planner. Following imitation pretraining, strategy-specific rewards specialize individual heads without style annotations. We innovatively adapt Group Relative Policy Optimization using surrogate policy-ratio estimation and constrained head-specific updates to mitigate degradation of pretrained planning capabilities. Open-loop and closed-loop evaluations on nuPlan demonstrate distinct strategy-aligned behaviors and competitive planning performance. Further experiments assess intent-to-strategy mapping and collision risk, and analyze the effects of reward design and optimization on strategy alignment and planning quality.

Most end-to-end autonomous driving methods rely on imitation learning from single expert demonstrations, often leading to conservative and homogeneous behaviors that limit generalization in complex real-world scenarios. In this work, we propose DIVER, an end-to-end driving framework that integrates reinforcement learning with diffusion-based generation to produce diverse and feasible trajectories. At the core of DIVER lies a reinforced diffusion-based generation mechanism. First, the model conditions on map elements and surrounding agents to generate multiple reference trajectories from a single ground-truth trajectory, alleviating the limitations of imitation learning that arise from relying solely on single expert demonstrations. Second, reinforcement learning is employed to guide the diffusion process, where reward-based supervision enforces safety and diversity constraints on the generated trajectories, thereby enhancing their practicality and generalization capability. Furthermore, to address the limitations of L2-based open-loop metrics in capturing trajectory diversity, we propose a novel Diversity metric to evaluate the diversity of multi-mode predictions.Extensive experiments on the closed-loop NAVSIM and Bench2Drive benchmarks, as well as the open-loop nuScenes dataset, demonstrate that DIVER significantly improves trajectory diversity, effectively addressing the mode collapse problem inherent in imitation learning.

This work presents an optimization method for generating kinodynamically feasible and collision-free multi-robot trajectories that exploits an incremental denoising scheme in diffusion models. Our key insight is that high-quality trajectories can be discovered merely by denoising noisy trajectories sampled from a distribution. This approach has no learning component, relying instead on only two ingredients: a dynamical model of the robots to obtain feasible trajectories via rollout, and a fitness function to guide denoising with Monte Carlo gradient approximation. The proposed framework iteratively optimizes a deformation for the previous trajectory with the current denoising process, allows anytime refinement as time permits, supports different dynamics, and benefits from GPU acceleration. Our evaluations for differential-drive and holonomic teams with up to 16 robots in 2D and 3D worlds show its ability to discover high-quality solutions faster than other black-box optimization methods such as MPPI. In a 2D holonomic case with 16 robots, it is almost twice as fast. As evidence for feasibility, we demonstrate zero-shot deployment of the planned trajectories on eight multirotors. Code and video: https://github.com/proroklab/d4orm