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SE(3)-Equivariant Diffusion Policy in Spherical Fourier Space
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Proposes Spherical Diffusion Policy (SDP), an SE(3)-equivariant diffusion policy that embeds states, actions, and denoising in spherical Fourier space, evaluated on 20 MimicGen simulation tasks and 5 physical bi-manual/single-arm tasks.
Problem
Diffusion policies learned from human demonstrations generalize poorly to novel 3D object arrangements (SE(3) poses), requiring costly additional demonstrations.
Approach
Embed states, actions and the denoising process in spherical Fourier space so that rotations act continuously via Wigner D-matrices, combined with spherical FiLM conditioning, a spherical denoising temporal U-Net, and relative (gripper-frame) action formulation for translation invariance.
Key results
- On four MimicGen tasks with 15° tilt, SDP averages 49% success vs 20% for EquiDiff (voxel) and 9% for DiffPo-C (RGB) in the tilted-table setting (Table 1 at 15°).
- Across 12 MimicGen SE(2) tasks, SDP averages 76% success rate versus 64% for the best EquiDiff variant (voxel, absolute control).
- On five physical tasks SDP achieves 78% average success vs 17% for EquiDiff and 7% for DiffPo-C.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use SDP instead of EquiDiff | MimicGen policy · SE(3) initialization, average at 15° | success rate: 20 -> 49 | Helped |
| use SDP instead of EquiDiff | MimicGen policy · SE(3) initialization, average at 30° | success rate: 13 -> 35 | Helped |
| use SDP instead of EquiDiff with voxel observations | MimicGen policy · SE(2) initialization, 12 tasks | average success rate: 64 -> 76 | Helped |
| use SDP instead of EquiDiff | physical robot policy · 5 physical tasks | average success rate: 17 -> 78 | Helped |
| use SDP instead of DiffPo-C | physical robot policy · 5 physical tasks | average success rate: 7 -> 78 | Helped |
| replace continuous SDTU equivariance with Octahedron-discretized denoising (ablation) | SDP · MimicGen ablation tasks at 15° (average) | success rate: 49 -> 35 | Hurt |
| use absolute instead of relative actions (ablation) | SDP · MimicGen ablation tasks at 15° (average) | success rate: 49 -> 26 | Hurt |
| replace spherical features with canonicalized DP3 features (ablation) | SDP · MimicGen ablation tasks at 15° (average) | success rate: 49 -> 15 | Hurt |
| replace spherical Fourier features with EquiBot while retaining relative actions (ablation) | SDP · MimicGen ablation tasks at 15° (average) | success rate: 49 -> 8 | Hurt |
| remove relative actions and spherical Fourier features (ablation) | SDP · MimicGen ablation tasks at 15° (average) | success rate: 49 -> 6 | Hurt |
| replace spherical Fourier features with EquiBot and use absolute actions (ablation) | SDP · MimicGen ablation tasks at 15° (average) | success rate: 49 -> 2 | Hurt |
| increase spherical Fourier degree from l=1 to l=2 (ablation) | SDP · MimicGen degree study at 15° (average) | success rate: 26 -> 49 | Helped |
Surprising findings
- Discrete C8 equivariance (EquiDiff) underperforms continuous SO(3) spherical features, and removing spherical representation (EquiBot Rel.) causes larger drops than removing relative actions.
Limitations
- Position control only; ignores contact forces, causing protective stops in Flip_Book.
- Low-resolution point cloud encoder struggles with fine details (e.g., Push_Eraser, Coffee tasks).
- Performance saturates beyond ~300 demonstrations in simulation and declines under large tilt ranges due to occlusion and gravity instability.
Experimental setup
Datasets: MimicGen generated demonstrations physical human demonstrations collected with GELLO
Benchmarks: MimicGen (SE(3)-initialization tasks and SE(2)-initialization 12 tasks) 5 physical robot tasks
Metrics: success rate
Baselines: EquiDiff DiffPo EquiBot DP3 ACT BC-RNN ET-SEED
Builds on: Diffusion Policy Equiformer EquiformerV2 EquiDiff Diffuser
Closest papers by meaning
- 3D Equivariant Visuomotor Policy Learning via Spherical Projection (NeurIPS 2025 · similarity 0.91)
- ET-SEED: EFFICIENT TRAJECTORY-LEVEL SE(3) EQUIVARIANT DIFFUSION POLICY (ICLR 2025 · similarity 0.89)
- Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulation (CVPR 2024 · similarity 0.87)
- Two-Steps Diffusion Policy for Robotic Manipulation via Genetic Denoising (NeurIPS 2025 · similarity 0.86)
- Prediction with Action: Visual Policy Learning via Joint Denoising Process (NeurIPS 2024 · similarity 0.86)
- Fourier Transporter: Bi-Equivariant Robotic Manipulation in 3D (ICLR 2024 · similarity 0.86)
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