# ET-SEED: Efficient Trajectory-Level SE(3) Equivariant Diffusion Policy

arXiv: https://arxiv.org/abs/2411.03990 · HTML: https://mlsanity.com/paper/2411.03990/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion and flow policies for robotics, one of 14 directions in Diffusion models.
- Builds on 31 of its 37 references that are in the map.
- First posted on arXiv 6 Nov 2024.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)
- Offline RL and imitation learning from data / [Robot manipulation imitation learning](https://mlsanity.com/offlinerl/robot-manipulation-imitation-learning/)

## Builds on (most cited first, 30 of 31)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [SAM 2: Segment Anything in Images and Videos](https://mlsanity.com/paper/2408.00714/) (2024)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [LIBERO: Benchmarking Knowledge Transfer for Lifelong Robot Learning](https://mlsanity.com/paper/2306.03310/) (2023)
- [What Matters in Learning from Offline Human Demonstrations for Robot Manipulation](https://mlsanity.com/paper/2108.03298/) (2021)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Mobile ALOHA: Learning Bimanual Mobile Manipulation with Low-Cost Whole-Body Teleoperation](https://mlsanity.com/paper/2401.02117/) (2024)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Structure-based Drug Design with Equivariant Diffusion Models](https://mlsanity.com/paper/2210.13695/) (2022)
- [Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulation](https://mlsanity.com/paper/2112.05124/) (2021)
- [Scaling Robot Learning with Semantically Imagined Experience](https://mlsanity.com/paper/2302.11550/) (2023)
- [3D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Prediction](https://mlsanity.com/paper/2303.03543/) (2023)
- [VIOLA: Imitation Learning for Vision-Based Manipulation with Object Proposal Priors](https://mlsanity.com/paper/2210.11339/) (2022)
- [SE(3)-DiffusionFields: Learning smooth cost functions for joint grasp and motion optimization through diffusion](https://mlsanity.com/paper/2209.03855/) (2022)
- [EquiBot: SIM(3)-Equivariant Diffusion Policy for Generalizable and Data Efficient Learning](https://mlsanity.com/paper/2407.01479/) (2024)
- [Diffusion-EDFs: Bi-equivariant Denoising Generative Modeling on SE(3) for Visual Robotic Manipulation](https://mlsanity.com/paper/2309.02685/) (2023)
- [EquivAct: SIM(3)-Equivariant Visuomotor Policies beyond Rigid Object Manipulation](https://mlsanity.com/paper/2310.16050/) (2023)
- [SE(3) Diffusion Model-based Point Cloud Registration for Robust 6D Object Pose Estimation](https://mlsanity.com/paper/2310.17359/) (2023)
- [DiffAssemble: A Unified Graph-Diffusion Model for 2D and 3D Reassembly](https://mlsanity.com/paper/2402.19302/) (2024)
- [Leveraging SE(3) Equivariance for Learning 3D Geometric Shape Assembly](https://mlsanity.com/paper/2309.06810/) (2023)
- [USEEK: Unsupervised SE(3)-Equivariant 3D Keypoints for Generalizable Manipulation](https://mlsanity.com/paper/2209.13864/) (2022)
- [UniGarmentManip: A Unified Framework for Category-Level Garment Manipulation via Dense Visual Correspondence](https://mlsanity.com/paper/2405.06903/) (2024)
- [GarmentLab: A Unified Simulation and Benchmark for Garment Manipulation](https://mlsanity.com/paper/2411.01200/) (2024)
- [OrbitGrasp: SE(3)-Equivariant Grasp Learning](https://mlsanity.com/paper/2407.03531/) (2024)
- [Contrastive Imitation Learning for Language-guided Multi-Task Robotic Manipulation](https://mlsanity.com/paper/2406.09738/) (2024)
- [RiEMann: Near Real-Time SE(3)-Equivariant Robot Manipulation without Point Cloud Segmentation](https://mlsanity.com/paper/2403.19460/) (2024)

## Built on by (most cited first, 26 of 26)

- [OAT: Ordered Action Tokenization](https://mlsanity.com/paper/2602.04215/) (2026)
- [AdaManip: Adaptive Articulated Object Manipulation Environments and Policy Learning](https://mlsanity.com/paper/2502.11124/) (2025)
- [AffordanceVLA: A Vision-Language-Action Model Empowering Action Generation through Affordance-Aware Understanding](https://mlsanity.com/paper/2606.06155/) (2026)
- [VGGT-DP: Generalizable Robot Control via Vision Foundation Models](https://mlsanity.com/paper/2509.18778/) (2025)
- [SE(3)-Equivariant Robot Learning and Control: A Tutorial Survey](https://mlsanity.com/paper/2503.09829/) (2025)
- [SE(3)-Equivariant Diffusion Policy in Spherical Fourier Space](https://mlsanity.com/paper/2507.01723/) (2025)
- [A Practical Guide for Incorporating Symmetry in Diffusion Policy](https://mlsanity.com/paper/2505.13431/) (2025)
- [3D Equivariant Visuomotor Policy Learning via Spherical Projection](https://mlsanity.com/paper/2505.16969/) (2025)
- [Learning Part-Aware Dense 3D Feature Field for Generalizable Articulated Object Manipulation](https://mlsanity.com/paper/2602.14193/) (2026)
- [Partially Equivariant Reinforcement Learning in Symmetry-Breaking Environments](https://mlsanity.com/paper/2512.00915/) (2025)
- [A3D: Adaptive Affordance Assembly with Dual-Arm Manipulation](https://mlsanity.com/paper/2601.11076/) (2026)
- [Eq.Bot: Enhance Robotic Manipulation Learning via Group Equivariant Canonicalization](https://mlsanity.com/paper/2511.15194/) (2025)
- [Efficient Hybrid SE(3)-Equivariant Visuomotor Flow Policy via Spherical Harmonics for Robot Manipulation](https://mlsanity.com/paper/2603.23227/) (2026)
- [EquiVLA: A General Framework for Rotationally Equivariant Vision-Language-Action Models](https://mlsanity.com/paper/2606.19784/) (2026)
- [SAVLA: Symmetry-Aware Vision-Language-Action Models for Robotic Manipulation](https://mlsanity.com/paper/2609.16641/) (2026)
- [ReSeFlow: Rectifying SE(3)-Equivariant Policy Learning Flows](https://mlsanity.com/paper/2509.22695/) (2025)
- [GraspLDP: Towards Generalizable Grasping Policy via Latent Diffusion](https://mlsanity.com/paper/2602.22862/) (2026)
- [Morphologically Equivariant Flow Matching for Bimanual Mobile Manipulation](https://mlsanity.com/paper/2605.12228/) (2026)
- [The Lie We Tell: Correcting the Euclidean Fallacy in Vision Language Action Policies via Score Matching on Tangent Space](https://mlsanity.com/paper/2606.01847/) (2026)
- [Factor-Aware Mixture-of-Experts with Pretrained Encoder for Combinatorial Generalization](https://mlsanity.com/paper/2606.21100/) (2026)
- [BridgeFlow: Fast and Robust SE(2)-Equivariant Motion Planning with Flow Matching](https://mlsanity.com/paper/2607.14725/) (2026)
- [Terminal Symmetry as a Carrier of Asymmetric Process Knowledge: Statewise Refinement for Anytime Verified Construction](https://mlsanity.com/paper/2608.11318/) (2026)
- [LieSpline-DP: Lie-Group B-Spline Diffusion Policy for Smooth Robot Manipulation](https://mlsanity.com/paper/2609.15162/) (2026)
- [Manifold-Stable Flow Matching](https://mlsanity.com/paper/2609.35454/) (2026)
- [Equivariant Visual-Tactile Diffusion Policy for Contact-Rich Manipulation](https://mlsanity.com/paper/2610.03333/) (2026)
- [Phase-Conditioned Affordance Fields for SE(3)-Equivariant Visuomotor Policies](https://mlsanity.com/paper/2610.17281/) (2026)

## Abstract (arXiv)

Imitation learning, e.g., diffusion policy, has been proven effective in various robotic manipulation tasks. However, extensive demonstrations are required for policy robustness and generalization. To reduce the demonstration reliance, we leverage spatial symmetry and propose ET-SEED, an efficient trajectory-level SE(3) equivariant diffusion model for generating action sequences in complex robot manipulation tasks. Further, previous equivariant diffusion models require the per-step equivariance in the Markov process, making it difficult to learn policy under such strong constraints. We theoretically extend equivariant Markov kernels and simplify the condition of equivariant diffusion process, thereby significantly improving training efficiency for trajectory-level SE(3) equivariant diffusion policy in an end-to-end manner. We evaluate ET-SEED on representative robotic manipulation tasks, involving rigid body, articulated and deformable object. Experiments demonstrate superior data efficiency and manipulation proficiency of our proposed method, as well as its ability to generalize to unseen configurations with only a few demonstrations. Website: https://et-seed.github.io/