Riemannian MeanFlow
This work addresses the computational bottleneck of diffusion and flow models for generative modeling on manifolds, which is critical for large-scale scientific sampling workflows.
Riemannian MeanFlow (RMF) learns flow maps on Riemannian manifolds, enabling high-quality generative sampling with as few as one forward pass, achieving comparable sample quality to prior methods while requiring up to 10× fewer function evaluations in DNA and protein design tasks.
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.