# Motion Planning Diffusion: Learning and Adapting Robot Motion Planning with Diffusion Models

arXiv: https://arxiv.org/abs/2412.19948 · HTML: https://mlsanity.com/paper/2412.19948/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 65 of its 119 references that are in the map.
- First posted on arXiv 27 Dec 2024.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 30 of 65)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [Understanding Diffusion Models: A Unified Perspective](https://mlsanity.com/paper/2208.11970/) (2022)
- [The Vendi Score: A Diversity Evaluation Metric for Machine Learning](https://mlsanity.com/paper/2210.02410/) (2022)
- [3D Diffuser Actor: Policy Diffusion with 3D Scene Representations](https://mlsanity.com/paper/2402.10885/) (2024)
- [Diffusion-based Generation, Optimization, and Planning in 3D Scenes](https://mlsanity.com/paper/2301.06015/) (2023)
- [Goal-Conditioned Imitation Learning using Score-based Diffusion Policies](https://mlsanity.com/paper/2304.02532/) (2023)
- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [Guided Conditional Diffusion for Controllable Traffic Simulation](https://mlsanity.com/paper/2210.17366/) (2022)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [SE(3)-DiffusionFields: Learning smooth cost functions for joint grasp and motion optimization through diffusion](https://mlsanity.com/paper/2209.03855/) (2022)
- [A micro Lie theory for state estimation in robotics](https://mlsanity.com/paper/1812.01537/) (2018)
- [Motion Planning for Autonomous Driving: The State of the Art and Future Perspectives](https://mlsanity.com/paper/2303.09824/) (2023)
- [DALL-E-Bot: Introducing Web-Scale Diffusion Models to Robotics](https://mlsanity.com/paper/2210.02438/) (2022)
- [Constrained Synthesis with Projected Diffusion Models](https://mlsanity.com/paper/2402.03559/) (2024)
- [SafeDiffuser: Safe Planning with Diffusion Probabilistic Models](https://mlsanity.com/paper/2306.00148/) (2023)

## Built on by (most cited first, 30 of 33)

- [Simultaneous Multi-Robot Motion Planning with Projected Diffusion Models](https://mlsanity.com/paper/2502.03607/) (2025)
- [Training-Free Constrained Generation With Stable Diffusion Models](https://mlsanity.com/paper/2502.05625/) (2025)
- [FlowMP: Learning Motion Fields for Robot Planning with Conditional Flow Matching](https://mlsanity.com/paper/2503.06135/) (2025)
- [HardFlow: Hard-Constrained Sampling for Flow-Matching Models via Trajectory Optimization](https://mlsanity.com/paper/2511.08425/) (2025)
- [OmniGuide: Universal Guidance Fields for Enhancing Generalist Robot Policies](https://mlsanity.com/paper/2603.10052/) (2026)
- [A Knowledge-Driven Diffusion Policy for End-to-End Autonomous Driving Based on Expert Routing](https://mlsanity.com/paper/2509.04853/) (2025)
- [From Demonstrations to Safe Deployment: Path-Consistent Safety Filtering for Diffusion Policies](https://mlsanity.com/paper/2511.06385/) (2025)
- [How VLAs (Really) Work In Open-World Environments](https://mlsanity.com/paper/2604.21192/) (2026)
- [FLASH: Efficient Visuomotor Policy via Sparse Sampling](https://mlsanity.com/paper/2605.15492/) (2026)
- [Simulation-Informed Diffusion for Decentralized Multi-robot Motion Planning](https://mlsanity.com/paper/2605.27697/) (2026)
- [Compositional Visual Planning via Inference-Time Diffusion Scaling](https://mlsanity.com/paper/2603.02646/) (2026)
- [Inference-Time Attribute Distribution Alignment for Unconditional Diffusion](https://mlsanity.com/paper/2605.07456/) (2026)
- [FRMD: Fast Robot Motion Diffusion with Consistency-Distilled Movement Primitives for Smooth Action Generation](https://mlsanity.com/paper/2503.02048/) (2025)
- [3D-CovDiffusion: 3D-Aware Diffusion Policy for Coverage Path Planning](https://mlsanity.com/paper/2510.03011/) (2025)
- [CAPE: Context-Aware Diffusion Policy Via Proximal Mode Expansion for Collision Avoidance](https://mlsanity.com/paper/2511.22773/) (2025)
- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)
- [Flow Motion Policy: Manipulator Motion Planning with Flow Matching Models](https://mlsanity.com/paper/2604.07084/) (2026)
- [Model Tensor Planning](https://mlsanity.com/paper/2505.01059/) (2025)
- [FlatLands: Generative Floormap Completion From a Single Egocentric View](https://mlsanity.com/paper/2603.16016/) (2026)
- [FODMP: Fast One-Step Diffusion of Movement Primitives Generation for Time-Dependent Robot Actions](https://mlsanity.com/paper/2603.24806/) (2026)
- [Primitive-based Truncated Diffusion for Efficient Trajectory Generation of Differential Drive Mobile Manipulators](https://mlsanity.com/paper/2604.04166/) (2026)
- [Referring-Aware Visuomotor Policy Learning for Closed-Loop Manipulation](https://mlsanity.com/paper/2604.05544/) (2026)
- [ARIA: Adaptive Region-Based Importance Allocation for Conditional Diffusion Distillation](https://mlsanity.com/paper/2606.23898/) (2026)
- [D-SafeMPC: Diffusion-Driven Safe Model Predictive Control with Discrete-Time Control Barrier Functions](https://mlsanity.com/paper/2607.10842/) (2026)
- [BridgeFlow: Fast and Robust SE(2)-Equivariant Motion Planning with Flow Matching](https://mlsanity.com/paper/2607.14725/) (2026)
- [NeurRAFT: Robot Motion Planning via Anchor-Level Flow Matching with Clearance-Aware Preference Tuning](https://mlsanity.com/paper/2608.24026/) (2026)
- [Denoising as Projection: Constrained Optimization with Gradient-Guided Diffusion](https://mlsanity.com/paper/2608.29507/) (2026)
- [LieSpline-DP: Lie-Group B-Spline Diffusion Policy for Smooth Robot Manipulation](https://mlsanity.com/paper/2609.15162/) (2026)
- [Zero-Shot Reactive Obstacle Avoidance for Generative Robot Policies](https://mlsanity.com/paper/2609.35231/) (2026)
- [Trajectory-Level Mode Guidance for Controllable Diffusion-Based Multi-Robot Motion Planning](https://mlsanity.com/paper/2609.36530/) (2026)

## Abstract (arXiv)

The performance of optimization-based robot motion planning algorithms is highly dependent on the initial solutions, commonly obtained by running a sampling-based planner to obtain a collision-free path. However, these methods can be slow in high-dimensional and complex scenes and produce non-smooth solutions. Given previously solved path-planning problems, it is highly desirable to learn their distribution and use it as a prior for new similar problems. Several works propose utilizing this prior to bootstrap the motion planning problem, either by sampling initial solutions from it, or using its distribution in a maximum-a-posterior formulation for trajectory optimization. In this work, we introduce Motion Planning Diffusion (MPD), an algorithm that learns trajectory distribution priors with diffusion models. These generative models have shown increasing success in encoding multimodal data and have desirable properties for gradient-based motion planning, such as cost guidance. Given a motion planning problem, we construct a cost function and sample from the posterior distribution using the learned prior combined with the cost function gradients during the denoising process. Instead of learning the prior on all trajectory waypoints, we propose learning a lower-dimensional representation of a trajectory using linear motion primitives, particularly B-spline curves. This parametrization guarantees that the generated trajectory is smooth, can be interpolated at higher frequencies, and needs fewer parameters than a dense waypoint representation. We demonstrate the results of our method ranging from simple 2D to more complex tasks using a 7-dof robot arm manipulator. In addition to learning from simulated data, we also use human demonstrations on a real-world pick-and-place task.