Riemannian MeanFlow

TL;DR

Riemannian MeanFlow (RMF) is a novel framework for efficient flow-based generative modeling on manifolds, requiring fewer neural network evaluations while maintaining high sample quality, with applications in biological sequence design.

Contribution

RMF introduces a manifold-aware flow model with theoretical characterizations and stabilization techniques, enabling high-quality generation with significantly fewer evaluations.

Findings

RMF achieves comparable sample quality to prior methods.

RMF requires up to 10× fewer function evaluations.

Few-step flow maps facilitate reward-guided design with minimal additional cost.

Abstract

Diffusion and flow models have become the dominant paradigm for generative modeling on Riemannian manifolds, with successful applications in protein backbone generation and DNA sequence design. However, these methods require tens to hundreds of neural network evaluations at inference time, which can become a computational bottleneck in large-scale scientific sampling workflows. We introduce Riemannian MeanFlow~(RMF), a framework for learning flow maps directly on manifolds, enabling high-quality generations with as few as one forward pass. We derive three equivalent characterizations of the manifold average velocity (Eulerian, Lagrangian, and semigroup identities), and analyze parameterizations and stabilization techniques to improve training on high-dimensional manifolds. In promoter DNA design and protein backbone generation settings, RMF achieves comparable sample quality to prior methods while requiring up to 10$\times$ fewer function evaluations. Finally, we show that few-step flow maps enable efficient reward-guided design through reward look-ahead, where terminal states can be predicted from intermediate steps at minimal additional cost.