# Potential Based Diffusion Motion Planning

arXiv: https://arxiv.org/abs/2407.06169 · HTML: https://mlsanity.com/paper/2407.06169/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 74 references that are in the map.
- First posted on arXiv 8 Jul 2024.

## Builds on (most cited first, 30 of 47)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [Compositional Visual Generation with Composable Diffusion Models](https://mlsanity.com/paper/2206.01714/) (2022)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [Is Conditional Generative Modeling all you need for Decision-Making?](https://mlsanity.com/paper/2211.15657/) (2022)
- [Diffusion-based Generation, Optimization, and Planning in 3D Scenes](https://mlsanity.com/paper/2301.06015/) (2023)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [Offline Reinforcement Learning via High-Fidelity Generative Behavior Modeling](https://mlsanity.com/paper/2209.14548/) (2022)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [Scaling Up and Distilling Down: Language-Guided Robot Skill Acquisition](https://mlsanity.com/paper/2307.14535/) (2023)
- [Efficient Diffusion Policies for Offline Reinforcement Learning](https://mlsanity.com/paper/2305.20081/) (2023)
- [AdaptDiffuser: Diffusion Models as Adaptive Self-evolving Planners](https://mlsanity.com/paper/2302.01877/) (2023)
- [SE(3)-DiffusionFields: Learning smooth cost functions for joint grasp and motion optimization through diffusion](https://mlsanity.com/paper/2209.03855/) (2022)
- [DALL-E-Bot: Introducing Web-Scale Diffusion Models to Robotics](https://mlsanity.com/paper/2210.02438/) (2022)
- [Taming VAEs](https://mlsanity.com/paper/1810.00597/) (2018)
- [Motion Planning Networks](https://mlsanity.com/paper/1806.05767/) (2018)
- [Imitating Task and Motion Planning with Visuomotor Transformers](https://mlsanity.com/paper/2305.16309/) (2023)
- [Motion Policy Networks](https://mlsanity.com/paper/2210.12209/) (2022)
- [Path Planning using Neural A* Search](https://mlsanity.com/paper/2009.07476/) (2020)
- [Informed RRT*: Optimal Sampling-based Path Planning Focused via Direct Sampling of an Admissible Ellipsoidal Heuristic](https://mlsanity.com/paper/1404.2334/) (2014)
- [Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference](https://mlsanity.com/paper/1707.07383/) (2017)
- [EDMP: Ensemble-of-costs-guided Diffusion for Motion Planning](https://mlsanity.com/paper/2309.11414/) (2023)
- [Riemannian Motion Policies](https://mlsanity.com/paper/1801.02854/) (2018)

## Built on by (most cited first, 30 of 41)

- [Inference-time Scaling of Diffusion Models through Classical Search](https://mlsanity.com/paper/2505.23614/) (2025)
- [Generative Trajectory Stitching through Diffusion Composition](https://mlsanity.com/paper/2503.05153/) (2025)
- [Simultaneous Multi-Robot Motion Planning with Projected Diffusion Models](https://mlsanity.com/paper/2502.03607/) (2025)
- [Deep Generative Models in Robotics: A Survey on Learning from Multimodal Demonstrations](https://mlsanity.com/paper/2408.04380/) (2024)
- [Motion Planning Diffusion: Learning and Adapting Robot Motion Planning with Diffusion Models](https://mlsanity.com/paper/2412.19948/) (2024)
- [Inference-Time Enhancement of Generative Robot Policies via Predictive World Modeling](https://mlsanity.com/paper/2502.00622/) (2025)
- [Skill Expansion and Composition in Parameter Space](https://mlsanity.com/paper/2502.05932/) (2025)
- [ComDrive: Comfort-Oriented End-to-End Autonomous Driving](https://mlsanity.com/paper/2410.05051/) (2024)
- [Discrete-Guided Diffusion for Scalable and Safe Multi-Robot Motion Planning](https://mlsanity.com/paper/2508.20095/) (2025)
- [CDP: Towards Robust Autoregressive Visuomotor Policy Learning via Causal Diffusion](https://mlsanity.com/paper/2506.14769/) (2025)
- [Modality-Composable Diffusion Policy via Inference-Time Distribution-level Composition](https://mlsanity.com/paper/2503.12466/) (2025)
- [Hybrid Diffusion for Simultaneous Symbolic and Continuous Planning](https://mlsanity.com/paper/2509.21983/) (2025)
- [CHD: Coupled Hierarchical Diffusion for Long-Horizon Tasks](https://mlsanity.com/paper/2505.07261/) (2025)
- [WARPD: World model Assisted Reactive Policy Diffusion](https://mlsanity.com/paper/2410.14040/) (2024)
- [ComposableNav: Instruction-Following Navigation in Dynamic Environments via Composable Diffusion](https://mlsanity.com/paper/2509.17941/) (2025)
- [Train-Once Plan-Anywhere Kinodynamic Motion Planning via Diffusion Trees](https://mlsanity.com/paper/2508.21001/) (2025)
- [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)
- [Refining Compositional Diffusion for Reliable Long-Horizon Planning](https://mlsanity.com/paper/2605.03075/) (2026)
- [Grounding Generative Policies in Physics: Optimization-Guided Diffusion for Robot Control](https://mlsanity.com/paper/2606.24208/) (2026)
- [Robustly Invertible Nonlinear Dynamics and the BiLipREN: Contracting Neural Models with Contracting Inverses](https://mlsanity.com/paper/2505.03069/) (2025)
- [Belief-Conditioned One-Step Diffusion: Real-Time Trajectory Planning with Just-Enough Sensing](https://mlsanity.com/paper/2508.12166/) (2025)
- [Scalable Multi Agent Diffusion Policies for Coverage Control](https://mlsanity.com/paper/2509.17244/) (2025)
- [Contrastive Diffusion Guidance for Spatial Inverse Problems](https://mlsanity.com/paper/2509.26489/) (2025)
- [Flexible Locomotion Learning with Diffusion Model Predictive Control](https://mlsanity.com/paper/2510.04234/) (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)
- [Analogical Trajectory Transfer](https://mlsanity.com/paper/2605.14393/) (2026)
- [Improving Trajectory Stitching with Flow Models](https://mlsanity.com/paper/2505.07802/) (2025)
- [Real-Time Adaptive Motion Planning via Point Cloud-Guided, Energy-Based Diffusion and Potential Fields](https://mlsanity.com/paper/2507.09383/) (2025)

## Abstract (arXiv)

Effective motion planning in high dimensional spaces is a long-standing open problem in robotics. One class of traditional motion planning algorithms corresponds to potential-based motion planning. An advantage of potential based motion planning is composability -- different motion constraints can be easily combined by adding corresponding potentials. However, constructing motion paths from potentials requires solving a global optimization across configuration space potential landscape, which is often prone to local minima. We propose a new approach towards learning potential based motion planning, where we train a neural network to capture and learn an easily optimizable potentials over motion planning trajectories. We illustrate the effectiveness of such approach, significantly outperforming both classical and recent learned motion planning approaches and avoiding issues with local minima. We further illustrate its inherent composability, enabling us to generalize to a multitude of different motion constraints.