GraspMeanFlow: SE(3)-Equivariant MeanFlow for Few-Step 6-DoF Grasp Generation

2026-08-04

AI Summary

This work addresses the limitation of existing flow-based 6-DoF grasp generation methods, which rely on multi-step iterative sampling and thus struggle to meet real-time requirements. The authors propose GraspMeanFlow, a novel framework that introduces time-ordered exponential maps into grasp synthesis for the first time. By learning an average velocity field over a finite time interval, the method generates SE(3)-equivariant grasp poses in a single or few function evaluations. GraspMeanFlow incorporates a time-conditioning mechanism that requires no modification to the backbone network and is trained with point cloud conditioning, flow-matching boundary terms, and a semigroup consistency loss. On the ACRONYM dataset, a single evaluation achieves the Earth Mover’s Distance (EMD) performance of conventional methods requiring five iterative steps, improves grasp success rates by up to 24.3 percentage points, and strictly preserves rigid-body transformation equivariance in the generated distribution.

Abstract

Recent data-driven methods for synthesizing 6-DoF grasp poses use generative models to learn complex grasp pose distributions and generate diverse candidate poses. In particular, SE(3)-equivariant flow-based models generate grasp poses that transform consistently with object rotations and translations. However, these methods sample by iterative numerical integration, requiring tens of function evaluations per grasp and limiting their use in real-time manipulation. We propose GraspMeanFlow, an SE(3)-equivariant MeanFlow framework for few-step 6-DoF grasp generation. Our method learns the average velocity over a finite time interval, defined through the time-ordered exponential so that it reproduces exactly the rigid-body displacement accumulated over that interval. We prove that a point-cloud-conditioned distribution transported by an equivariant average-velocity flow map remains invariant, so equivariance is retained under few-step sampling, and we condition the field on a pair of times by lifting both to equivariant vectors, leaving the backbone otherwise unchanged. For stable training, we pair a flow-matching boundary term with either of two consistency terms: the differential MeanFlow identity, whose target requires a Jacobian-vector product, or an equivalent semigroup loss that avoids it. Experiments on ACRONYM show that a single function evaluation of GraspMeanFlow reaches the EMD that an iterative SE(3) flow model needs five steps to approach, that a second instantiation of the same framework improves grasp success by up to 24.3 points in the few-step regime, and that both generate grasp distributions transforming exactly with the object.

Problem

• 6-DoF grasp generation
• SE(3)-equivariance
• real-time manipulation
• iterative sampling
• grasp pose distribution

Innovation

• SE(3)-equivariance
• MeanFlow
• few-step generation
• 6-DoF grasp
• flow matching