提出一种在流形上高效生成新样本的模型，推理只需一次前向传播。
Riemannian MeanFlow
- 直接在流形上学习流映射，实现单次前向传播生成。
- 在DNA与蛋白质生成任务中，质量相当但计算量减少10倍。
- 支持快速奖励引导设计，中间步骤即可预测最终结果。
扩散与流模型已成为流形上生成建模的主流方法，在蛋白质主链生成和DNA序列设计中取得成功。然而这些方法在推理时需数十至数百次神经网络评估，成为大规模科学采样中的计算瓶颈。本文提出黎曼平均流（Riemannian MeanFlow, RMF），直接在流形上学习流映射，实现高质量生成仅需一次前向传播。我们推导了流形平均速度的三种等价表征（欧拉、拉格朗日与半群恒等式），并分析参数化与稳定化技术以提升高维流形上的训练效果。在启动子DNA设计与蛋白质主链生成任务中，RMF在生成质量上媲美现有方法，同时减少高达10倍的函数评估次数。此外，少步流映射可实现高效的奖励引导设计，通过奖励前瞻，仅以极低额外成本从中间步骤预测终端状态。
原文摘要 · Abstract (English)
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.
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