# Equivariant Diffusion Policy

arXiv: https://arxiv.org/abs/2407.01812 · HTML: https://mlsanity.com/paper/2407.01812/

## Key facts

- Cited by 66 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 49 of its 59 references that are in the map.
- First posted on arXiv 1 Jul 2024.

## Placed in

- Diffusion models / [Diffusion and flow policies for robotics](https://mlsanity.com/diffusion/diffusion-and-flow-policies-for-robotics/)

## Builds on (most cited first, 30 of 49)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Learning Fine-Grained Bimanual Manipulation with Low-Cost Hardware](https://mlsanity.com/paper/2304.13705/) (2023)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [What Matters in Learning from Offline Human Demonstrations for Robot Manipulation](https://mlsanity.com/paper/2108.03298/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Diffusion Policies as an Expressive Policy Class for Offline Reinforcement Learning](https://mlsanity.com/paper/2208.06193/) (2022)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Implicit Behavioral Cloning](https://mlsanity.com/paper/2109.00137/) (2021)
- [Relay Policy Learning: Solving Long-Horizon Tasks via Imitation and Reinforcement Learning](https://mlsanity.com/paper/1910.11956/) (2019)
- [MimicGen: A Data Generation System for Scalable Robot Learning using Human Demonstrations](https://mlsanity.com/paper/2310.17596/) (2023)
- [Deep Imitation Learning for Complex Manipulation Tasks from Virtual Reality Teleoperation](https://mlsanity.com/paper/1710.04615/) (2017)
- [Imitating Human Behaviour with Diffusion Models](https://mlsanity.com/paper/2301.10677/) (2023)
- [Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulation](https://mlsanity.com/paper/2112.05124/) (2021)
- [3D Equivariant Diffusion for Target-Aware Molecule Generation and Affinity Prediction](https://mlsanity.com/paper/2303.03543/) (2023)
- [AdaptDiffuser: Diffusion Models as Adaptive Self-evolving Planners](https://mlsanity.com/paper/2302.01877/) (2023)
- [Incorporating Symmetry into Deep Dynamics Models for Improved Generalization](https://mlsanity.com/paper/2002.03061/) (2020)
- [Self-Supervised Correspondence in Visuomotor Policy Learning](https://mlsanity.com/paper/1909.06933/) (2019)
- [Vision-Based Multi-Task Manipulation for Inexpensive Robots Using End-To-End Learning from Demonstration](https://mlsanity.com/paper/1707.02920/) (2017)
- [SO(2)-Equivariant Reinforcement Learning](https://mlsanity.com/paper/2203.04439/) (2022)
- [What Matters for Adversarial Imitation Learning?](https://mlsanity.com/paper/2106.00672/) (2021)
- [Equivariant Q Learning in Spatial Action Spaces](https://mlsanity.com/paper/2110.15443/) (2021)
- [Equivariant Descriptor Fields: SE(3)-Equivariant Energy-Based Models for End-to-End Visual Robotic Manipulation Learning](https://mlsanity.com/paper/2206.08321/) (2022)
- [Strictly Batch Imitation Learning by Energy-based Distribution Matching](https://mlsanity.com/paper/2006.14154/) (2020)
- [Sample Efficient Grasp Learning Using Equivariant Models](https://mlsanity.com/paper/2202.09468/) (2022)

## Built on by (most cited first, 30 of 66)

- [Diffusion-VLA: Generalizable and Interpretable Robot Foundation Model via Self-Generated Reasoning](https://mlsanity.com/paper/2412.03293/) (2024)
- [Generalizable Humanoid Manipulation with 3D Diffusion Policies](https://mlsanity.com/paper/2410.10803/) (2024)
- [Failure Prediction at Runtime for Generative Robot Policies](https://mlsanity.com/paper/2510.09459/) (2025)
- [Motion Planning Diffusion: Learning and Adapting Robot Motion Planning with Diffusion Models](https://mlsanity.com/paper/2412.19948/) (2024)
- [Learning Long-Context Diffusion Policies via Past-Token Prediction](https://mlsanity.com/paper/2505.09561/) (2025)
- [CordViP: Correspondence-based Visuomotor Policy for Dexterous Manipulation in Real-World](https://mlsanity.com/paper/2502.08449/) (2025)
- [Curating Demonstrations using Online Experience](https://mlsanity.com/paper/2503.03707/) (2025)
- [FlowMP: Learning Motion Fields for Robot Planning with Conditional Flow Matching](https://mlsanity.com/paper/2503.06135/) (2025)
- [Diagnose, Correct, and Learn from Manipulation Failures via Visual Symbols](https://mlsanity.com/paper/2512.02787/) (2025)
- [Two by Two: Learning Multi-Task Pairwise Objects Assembly for Generalizable Robot Manipulation](https://mlsanity.com/paper/2504.06961/) (2025)
- [SE(3)-Equivariant Robot Learning and Control: A Tutorial Survey](https://mlsanity.com/paper/2503.09829/) (2025)
- [What's the Move? Hybrid Imitation Learning via Salient Points](https://mlsanity.com/paper/2412.05426/) (2024)
- [Demystifying Diffusion Policies: Action Memorization and Simple Lookup Table Alternatives](https://mlsanity.com/paper/2505.05787/) (2025)
- [Latent Theory of Mind: A Decentralized Diffusion Architecture for Cooperative Manipulation](https://mlsanity.com/paper/2505.09144/) (2025)
- [FreqPolicy: Frequency Autoregressive Visuomotor Policy with Continuous Tokens](https://mlsanity.com/paper/2506.01583/) (2025)
- [Compose Your Policies! Improving Diffusion-based or Flow-based Robot Policies via Test-time Distribution-level Composition](https://mlsanity.com/paper/2510.01068/) (2025)
- [SE(3)-Equivariant Diffusion Policy in Spherical Fourier Space](https://mlsanity.com/paper/2507.01723/) (2025)
- [4D Visual Pre-training for Robot Learning](https://mlsanity.com/paper/2508.17230/) (2025)
- [MATCH POLICY: A Simple Pipeline from Point Cloud Registration to Manipulation Policies](https://mlsanity.com/paper/2409.15517/) (2024)
- [High-Rank Irreducible Cartesian Tensor Decomposition and Bases of Equivariant Spaces](https://mlsanity.com/paper/2412.18263/) (2024)
- [Constraint-Preserving Data Generation for Visuomotor Policy Learning](https://mlsanity.com/paper/2508.03944/) (2025)
- [R2RGEN: Real-to-Real 3D Data Generation for Spatially Generalized Manipulation](https://mlsanity.com/paper/2510.08547/) (2025)
- [Morphologically Symmetric Reinforcement Learning for Ambidextrous Bimanual Manipulation](https://mlsanity.com/paper/2505.05287/) (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)
- [AnchorDP3: 3D Affordance Guided Sparse Diffusion Policy for Robotic Manipulation](https://mlsanity.com/paper/2506.19269/) (2025)
- [ADPro: a Test-time Adaptive Diffusion Policy via Manifold-constrained Denoising and Task-aware Initialization for Robotic Manipulation](https://mlsanity.com/paper/2508.06266/) (2025)
- [EfficientFlow: Efficient Equivariant Flow Policy Learning for Embodied AI](https://mlsanity.com/paper/2512.02020/) (2025)
- [OMP: One-step Meanflow Policy with Directional Alignment](https://mlsanity.com/paper/2512.19347/) (2025)
- [EquiReg: Equivariance Regularized Diffusion for Inverse Problems](https://mlsanity.com/paper/2505.22973/) (2025)

## Abstract (arXiv)

Recent work has shown diffusion models are an effective approach to learning the multimodal distributions arising from demonstration data in behavior cloning. However, a drawback of this approach is the need to learn a denoising function, which is significantly more complex than learning an explicit policy. In this work, we propose Equivariant Diffusion Policy, a novel diffusion policy learning method that leverages domain symmetries to obtain better sample efficiency and generalization in the denoising function. We theoretically analyze the SO(2) symmetry of full 6-DoF control and characterize when a diffusion model is SO(2)-equivariant. We furthermore evaluate the method empirically on a set of 12 simulation tasks in MimicGen, and show that it obtains a success rate that is, on average, 21.9% higher than the baseline Diffusion Policy. We also evaluate the method on a real-world system to show that effective policies can be learned with relatively few training samples, whereas the baseline Diffusion Policy cannot.