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Local Manifold Approximation and Projection for Manifold-Aware Diffusion Planning
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Proposes LoMAP, a training-free test-time projection that maps each guided diffusion sample onto a local low-rank PCA subspace built from nearest offline trajectories, reducing manifold deviation in diffusion planners.
Problem
Diffusion planners for offline RL often produce infeasible trajectories because inexact reward guidance pushes intermediate samples off the data manifold, limiting use in safety-critical settings.
Approach
Derives a lower bound (order sqrt(d)) on the guidance gap of MSE-trained return guidance, then at each reverse step retrieves k nearest offline trajectories to the Tweedie-denoised sample, forward-diffuses them, runs PCA to get a local basis U, and projects the sample onto span(U) (plug-and-play, no training).
Key results
- On MuJoCo locomotion, Diffuser with LoMAP averages 82.8 normalized return versus 81.2 for RGG and 77.5 for Diffuser-style baselines reported in the table.
- On AntMaze, HD with LoMAP averages 86.7 success versus 55.3 for standard HD, and Diffuser with LoMAP averages 34.2 versus 13.3 for Diffuser.
- On Maze2D single-task, Diffuser with LoMAP averages 136.3 versus 119.5 for Diffuser and 125.3 for RGG.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add LoMAP projection to Diffuser | Diffuser · Maze2D tasks (single-task and Multi2D) | return: 113.9 -> 126.0; 121.5 -> 131.0; 123.0 -> 151.9; 128.9 -> 133.1; 127.2 -> 129.1; 132.1 -> 154.7 | Mixed |
| Add LoMAP projection to Diffuser | Diffuser · MuJoCo locomotion tasks | normalized average return: 77.5 -> 82.8 | Helped |
| Add LoMAP projection to Diffuser | Diffuser · AntMaze Play Medium, Play Large, Diverse Medium, Diverse Large | normalized average return: 6.7 -> 40.7; 17.3 -> 20.7; 2.0 -> 36.0; 27.3 -> 39.3 | Helped |
| Add LoMAP projection to Hierarchical Diffuser | Hierarchical Diffuser · AntMaze Play Medium, Play Large, Diverse Medium, Diverse Large | normalized average return: 42.0 -> 92.7; 54.7 -> 74.0; 78.7 -> 98.0; 46.0 -> 82.0 | Helped |
| Add LoMAP projection to Diffuser | Diffuser · Maze2D U-Maze, Medium, Large | realism score: 1.23 -> 1.30; 1.40 -> 1.56; 1.36 -> 1.47 | Helped |
| Add LoMAP projection to Diffuser | Diffuser · Maze2D-Large, 10 plans | artifact ratio: 0.50 -> 0.35 | Helped |
| Add LoMAP projection to Diffuser | Diffuser · halfcheetah-medium | Dynamic MSE: 0.352 -> 0.285 | Helped |
| Apply projection selectively during intermediate to later reverse-diffusion stages rather than uniformly (ablation) | LoMAP · offline control planning | sampling quality | Helped |
Surprising findings
- Projection is most beneficial at intermediate-to-late diffusion steps, so applying it selectively reduces cost and can improve performance.
- Constrained gradient guidance, despite explicitly modeling maze walls, produced a higher artifact ratio than Diffuser with LoMAP.
Limitations
- Cosine-distance manifold approximation may not scale to very high-dimensional observations such as pixels.
- Keeping samples close to the offline data manifold may restrict exploration of novel behaviors.
Experimental setup
Datasets: D4RL Maze2D D4RL MuJoCo locomotion (Medium, Medium-Replay, Medium-Expert) D4RL AntMaze
Benchmarks: Maze2D Multi2D MuJoCo locomotion (D4RL) AntMaze
Metrics: normalized return success rate artifact ratio realism score dynamic MSE
Baselines: Diffuser RGG TAT Decision Diffuser Hierarchical Diffuser IQL CQL MOPO MOReL Decision Transformer Trajectory Transformer BC
Builds on: Diffuser Restoration Gap Guidance Hierarchical Diffuser Tweedie's formula Manifold-preserving guided diffusion
Closest papers by meaning
- Simple Hierarchical Planning with Diffusion (ICLR 2024 · similarity 0.88)
- Temporal Alignment Guidance: On-manifold Sampling in Diffusion Models (NeurIPS 2026 · similarity 0.88)
- Manifold Preserving Guided Diffusion (ICLR 2024 · similarity 0.88)
- Prior-Guided Diffusion Planning for Offline Reinforcement Learning (NeurIPS 2025 · similarity 0.88)
- Structural Information-based Hierarchical Diffusion for Offline Reinforcement Learning (NeurIPS 2025 · similarity 0.88)
- State-Covering Trajectory Stitching for Diffusion Planners (NeurIPS 2025 · similarity 0.87)
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