A Practical Guide for Incorporating Symmetry in Diffusion Policy

TL;DR

This paper presents practical methods to incorporate symmetry into diffusion policies, improving generalization and performance without complex equivariant architectures, by using invariant representations and symmetry-aware feature extraction.

Contribution

It introduces simple, effective approaches for integrating symmetry into diffusion policies, reducing implementation complexity compared to traditional equivariant neural networks.

Findings

Invariant representations with equivariant feature extraction enhance policy performance.

Combining eye-in-hand perception with delta actions yields SE(3)-invariance.

Proposed methods match or surpass fully equivariant architectures in performance.

Abstract

Recently, equivariant neural networks for policy learning have shown promising improvements in sample efficiency and generalization, however, their wide adoption faces substantial barriers due to implementation complexity. Equivariant architectures typically require specialized mathematical formulations and custom network design, posing significant challenges when integrating with modern policy frameworks like diffusion-based models. In this paper, we explore a number of straightforward and practical approaches to incorporate symmetry benefits into diffusion policies without the overhead of full equivariant designs. Specifically, we investigate (i) invariant representations via relative trajectory actions and eye-in-hand perception, (ii) integrating equivariant vision encoders, and (iii) symmetric feature extraction with pretrained encoders using Frame Averaging. We first prove that combining eye-in-hand perception with relative or delta action parameterization yields inherent SE(3)-invariance, thus improving policy generalization. We then perform a systematic experimental study on those design choices for integrating symmetry in diffusion policies, and conclude that an invariant representation with equivariant feature extraction significantly improves the policy performance. Our method achieves performance on par with or exceeding fully equivariant architectures while greatly simplifying implementation.