Efficient Hybrid SE(3)-Equivariant Visuomotor Flow Policy via Spherical Harmonics for Robot Manipulation

TL;DR

E3Flow is a novel spherical harmonic-based framework for robot manipulation that improves efficiency, stability, and multi-modal learning, achieving higher success rates and faster inference compared to previous methods.

Contribution

The paper introduces E3Flow, a new SO(3)-equivariant diffusion policy framework that unifies efficient rectified flow with multi-modal visual fusion using spherical harmonics.

Findings

Achieves 3.12% higher success rate than Spherical Diffusion Policy

Provides a 7x faster inference speed

Successfully validates effectiveness in 8 simulation and 4 real-world tasks

Abstract

While existing equivariant methods enhance data efficiency, they suffer from high computational intensity, reliance on single-modality inputs, and instability when combined with fast-sampling methods. In this work, we propose E3Flow, a novel framework that addresses the critical limitations of equivariant diffusion policies. E3Flow overcomes these challenges, successfully unifying efficient rectified flow with stable, multi-modal equivariant learning for the first time. Our framework is built upon spherical harmonic representations to ensure rigorous SO(3) equivariance. We introduce a novel invariant Feature Enhancement Module (FEM) that dynamically fuses hybrid visual modalities (point clouds and images), injecting rich visual cues into the spherical harmonic features. We evaluate E3Flow on 8 manipulation tasks from the MimicGen and further conduct 4 real-world experiments to validate its effectiveness in physical environments. Simulation results show that E3Flow achieves a 3.12% improvement in average success rate over the state-of-the-art Spherical Diffusion Policy (SDP) while simultaneously delivering a 7x inference speedup. E3Flow thus demonstrates a new and highly effective trade-off between performance, efficiency, and data efficiency for robotic policy learning. Code: https://github.com/zql-kk/E3Flow.