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ET-SEED: EFFICIENT TRAJECTORY-LEVEL SE(3) EQUIVARIANT DIFFUSION POLICY
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Proposes ET-SEED, a trajectory-level SE(3)-equivariant diffusion policy whose denoising uses K-1 invariant steps and one equivariant step, reducing equivariance constraints while keeping end-to-end equivariance.
Problem
Diffusion-based imitation learning for manipulation needs many demonstrations to generalize to unseen object poses; prior equivariant trajectory diffusion policies require every denoising transition to be equivariant, which is hard to train.
Approach
Extends equivariant Markov process theory to show that only one transition needs to be SE(3)-equivariant (the last step), with the preceding K-1 transitions invariant, and builds SE(3)-invariant and equivariant backbones on SE(3) Transformer with diffusion on the SE(3) manifold.
Key results
- On simulated tasks, ET-SEED reaches 67±2.74 success on Open Bottle Cap (T, 25 demos) versus 63±2.74 for EquiBot and 65±4.5 for DP3, with 74±6.52 vs 11±4.2 for DP3 on New Poses.
- Average ablation success on Open Door NP: full ET-SEED 76±2.24 vs 57±6.52 without equivariant diffusion and 24±4.48 without SE(3) backbone.
- Real-world success averages (20 demos, 10 unseen placements): ET-SEED 0.8/0.6/0.4/0.6 on Open Bottle Cap/Open Door/Calligraphy/Fold Garment versus EquiBot 0.6/0.5/0.0/0.3.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ET-SEED instead of the strongest listed baseline | simulation manipulation policies · Open Bottle Cap, Open Door, Rotate Triangle, Calligraphy, Fold Garment, and Fling Garment; 25 demos, T and NP | success rate: Open Bottle Cap NP: 63\textpm5.70 -> 74\textpm6.52; Open Door NP: 58\textpm7.58 -> 66\textpm2.74; Rotate Triangle NP: 64 | Helped |
| Use ET-SEED instead of EquiBot | real-world manipulation policies · Open Bottle Cap, Open Door, Calligraphy, and Fold Garment, unseen poses | success rate: 0.6 -> 0.8; 0.5 -> 0.6; 0.0 -> 0.4; 0.3 -> 0.6 | Helped |
| Add SE(3) invariance and equivariance to the backbone (ablation) | ET-SEED · Open Door NP | average success rate: 24\textpm4.48 -> 76\textpm2.24 | Helped |
| Add the SE(3)-equivariant diffusion process instead of non-equivariant DDIM (ablation) | ET-SEED · Open Door NP | average success rate: 57\textpm6.52 -> 76\textpm2.24 | Helped |
| Use invariant denoising for the first K-1 steps and one equivariant denoising step instead of equivariant transitions at every step | equivariant diffusion process · multi-step validation experiment | training loss convergence | Helped |
Surprising findings
- Invariant-only denoising steps plus a single equivariant step train faster than all-equivariant diffusion, with the invariant single-step network's loss converging to near zero while equivariant networks' losses did not decrease noticeably.
- DP3 with SE(3) data augmentation (DP3+Aug) does not improve over DP3 on new poses in several tasks, suggesting augmentation alone is insufficient for spatial generalization.
Limitations
- Equivariance is designed for segmented object point clouds, requiring preprocessing of scene point clouds.
- Action space is 6D end-effector poses assumed reachable via IK and controllers; not applicable to dexterous manipulation.
- Some tasks (Fold and Fling Garment) are only approximately equivariant due to deformation differences.
Experimental setup
Datasets: simulated demonstrations for 6 tasks (Open Bottle Cap, Open Door, Rotate Triangle, Calligraphy, Fold Garment, Fling Garm real-world teleoperated demonstrations (20 per task)
Benchmarks: Open Bottle Cap Open Door Rotate Triangle Calligraphy Fold Garment Fling Garment real-world Open Bottle Cap, Open Door, Calligraphy, Fold Garment
Metrics: success rate SE(3) geodesic distance
Baselines: DP3 DP3+Aug EquiBot
Builds on: Equivariant Diffusion Policy EquiBot GeoDiff SE(3) Transformer DP3
Closest papers by meaning
- Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulation (CVPR 2024 · similarity 0.90)
- Two-Steps Diffusion Policy for Robotic Manipulation via Genetic Denoising (NeurIPS 2025 · similarity 0.89)
- SE(3)-Equivariant Diffusion Policy in Spherical Fourier Space (ICML 2025 · similarity 0.89)
- Latent Diffusion Planning for Imitation Learning (ICML 2025 · similarity 0.89)
- Implicit Drifting Policy: One-Step Action Generation via Conditional Expert Geometry (NeurIPS 2026 · similarity 0.88)
- Hierarchical Equivariant Policy via Frame Transfer (ICML 2025 · similarity 0.88)
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