SE(3)-MeanFlow: Few-Step Protein Backbone Generation on Lie Groups

2026-07-29

AI Summary

This work addresses the high computational cost of existing protein backbone generation models, which rely on hundreds of ODE integration steps and hinder high-throughput design. The authors propose SE(3)-MeanFlow, an extension of the MeanFlow framework to the SE(3) Lie group, enabling few-step generation without numerical integration by directly modeling dynamics in the so(3) Lie algebra and ℝ³. Key innovations include the first closed-form mean velocity identities for rotation and translation on SE(3), an SE(3) alpha-Flow warm-up strategy, a small-t stabilization loss, and a correction mechanism to enhance few-step performance. Experiments demonstrate that the method significantly outperforms existing flow-matching baselines in backbone generation quality at equal or fewer sampling steps, with particularly pronounced advantages in ultra-few-step regimes and only minor trade-offs in diversity.

Abstract

Generative modeling of protein backbones promises the de novo design of proteins with prescribed structural and functional properties. Existing diffusion and flow-matching models produce high-quality backbones on SE(3)^N, but inference requires numerically integrating an ODE over hundreds of network evaluations, each involving a Lie group exponential map - a bottleneck for high-throughput design campaigns. We introduce SE(3)-MeanFlow, a few-step generative framework that extends MeanFlow from Euclidean space to the Lie group geometry of protein frames. Working natively in the Lie algebra so(3) and in R^3, we derive closed-form average-velocity identities for rotations and translations, giving simulation-free training targets. We further introduce an SE(3) alpha-Flow objective that removes the Jacobian-vector product from the rotation branch and serves as a warm-up stage, after which training switches to a small-t stabilized MeanFlow loss that is used for the remainder of pretraining and for rectification-based post-training. In protein backbone generation, SE(3)-MeanFlow matches or exceeds flow-matching baselines that use several times more sampling steps, and its advantage widens in the few-step regime, where rectification lets it lead at every matched budget - at a modest cost in diversity.

Problem

• protein backbone generation
• SE(3)
• few-step inference
• Lie groups
• generative modeling

Innovation

• SE(3)-MeanFlow
• Lie group generative modeling
• few-step generation
• closed-form velocity
• rectification-based training