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

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.

FlowPolicy: Enabling Fast and Robust 3D Flow-based Policy via Consistency Flow Matching for Robot Manipulation

Robots can acquire complex manipulation skills by learning policies from expert demonstrations, which is often known as vision-based imitation learning. Generating policies based on diffusion and flow matching models has been shown to be effective, particularly in robotics manipulation tasks. However, recursion-based approaches are often inference inefficient in working from noise distributions to policy distributions, posing a challenging trade-off between efficiency and quality. This motivates us to propose FlowPolicy, a novel framework for fast policy generation based on consistency flow matching and 3D vision. Our approach refines the flow dynamics by normalizing the self-consistency of the velocity field, enabling the model to derive task execution policies in a single inference step. Specifically, FlowPolicy conditions on the observed 3D point cloud, where consistency flow matching directly defines straight-line flows from different time states to the same action space, while simultaneously constraining their velocity values, that is, we approximate the trajectories from noise to robot actions by normalizing the self-consistency of the velocity field within the action space, thus improving the inference efficiency. We validate the effectiveness of FlowPolicy on Adroit and Metaworld, demonstrating a 7$\times$ increase in inference speed while maintaining competitive average success rates compared to state-of-the-art policy models. Codes will be made publicly available.