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Potential Based Diffusion Motion Planning
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Learns a diffusion-based energy function over whole motion-plan trajectories and samples plans by gradient denoising, composing separately trained potentials to generalize to more obstacles and constraint types.
Problem
Potential-based motion planning is composable but gradient optimization over configuration-space potentials gets stuck in local minima and needs implicit obstacle representations; learned planners generalize poorly to out-of-distribution obstacle configurations.
Approach
Train a trajectory-level energy-based diffusion model (energy gradient acts as denoiser) conditioned on start, goal and constraints, so motion plans are obtained by annealed stochastic gradient descent on the energy; separately learned energies are summed at test time to satisfy multiple/new constraints.
Key results
- On Dual KUKA, the method reaches about 97.7% success with 0.27 s planning time, outperforming BIT* (82.1%) and the learned MPiNet (63.9%).
- Composing two separately trained potentials generalizes to 6+6 obstacles in Maze2D with 97.0% success, while BIT* stays at 100% but MPiNet drops to 66.2%.
- Refining motion plans raises Dual KUKA success from 47.0% to 80.8% with 10 refine attempts.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the learned diffusion potential planner instead of the strongest learning-based baseline | Maze2D · Maze2D | collision checks: 178.7 -> 97.0 | Helped |
| Use the learned diffusion potential planner instead of the strongest learning-based baseline | KUKA · KUKA | success rate: 88.7 -> 99.7 | Helped |
| Use the learned diffusion potential planner instead of the strongest learning-based baseline | Dual KUKA · Dual KUKA | success rate: 63.9 -> 97.7 | Helped |
| Use the learned diffusion potential planner instead of BIT* | Maze2D — Concave · Maze2D — Concave | planning time: 0.45 -> 0.15 | Helped |
| Compose potentials trained separately on Static 1 and Static 2 | Maze2D — Static 1 + Static 2 · Maze2D — Static 1 + Static 2 | collision checks: 3486.9 -> 304.7 | Helped |
| Compose static and dynamic obstacle potentials | Maze2D — Static 1 + Dynamic · Maze2D — Static 1 + Dynamic | success rate: 70.4 -> 96.6 | Helped |
| Compose obstacle potentials at test time rather than using one uncomposed potential | Maze2D — 6 + 3 obstacles · Maze2D — 6 + 3 obstacles | success rate: 95.4 -> 99.5 | Helped |
| Compose obstacle potentials at test time rather than using one uncomposed potential | Dual KUKA — 5 + 4 obstacles · Dual KUKA — 5 + 4 obstacles | success rate: 58.1 -> 87.8 | Helped |
| Add motion refining with 3 attempts (ablation) | Ours · Maze2D | success rate: 96.3 -> 99.8 | Helped |
| Add motion refining with 5 attempts (ablation) | Ours · KUKA | success rate: 69.5 -> 94.3 | Helped |
| Add motion refining with 10 attempts (ablation) | Ours · Dual KUKA | success rate: 47.0 -> 80.8 | Helped |
| Increase motion refining attempts from 5 to 10 (ablation) | Ours · Maze2D | success rate: 99.0 -> 100.0 | No clear effect |
Surprising findings
- Learned diffusion potential planner is the only learning-based method that solved all Maze2D evaluation problems, and it beats BIT* on planning time by about 3x in concave Maze2D environments.
Limitations
- Generated trajectories are often suboptimal, with shorter paths existing.
- Composing potentials scales linearly with the number of models, increasing computation.
- Collision refinement may require resampling from pure noise when catastrophic collisions occur.
Experimental setup
Datasets: BIT*-collected motion planning datasets (Maze2D, KUKA, Dual KUKA) ETH/UCY
Benchmarks: Maze2D KUKA Dual KUKA ETH/UCY
Metrics: success rate planning time number of collision checks
Baselines: RRT* P-RRT* BIT* SIPP RMP MPNet MPiNet AMP-LS MPD GNN
Builds on: denoising diffusion probabilistic models energy-based models Motion Planning Networks (MPNet) MPD (diffusion motion planning) BIT*
Closest papers by meaning
- Model-based Diffusion for Trajectory Optimization (NeurIPS 2024 · similarity 0.86)
- Physics-informed Temporal Difference Metric Learning for Robot Motion Planning (ICLR 2025 · similarity 0.85)
- Multi-Robot Motion Planning with Diffusion Models (ICLR 2025 · similarity 0.85)
- BaB-ND: Long-Horizon Motion Planning with Branch-and-Bound and Neural Dynamics (ICLR 2025 · similarity 0.85)
- Generative Trajectory Stitching through Diffusion Composition (NeurIPS 2025 · similarity 0.84)
- Simultaneous Multi-Robot Motion Planning with Projected Diffusion Models (ICML 2025 · similarity 0.84)
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