Riemannian MeanFlow for One-Step Generation on Manifolds
Flow Matching enables simulation-free training of generative models on Riemannian manifolds, yet sampling typically still relies on numerically integrating a probability-flow ODE. We propose Riemannian MeanFlow (RMF), extending MeanFlow to manifold-valued generation where velocities lie in location-dependent tangent spaces. RMF defines an average-velocity field via parallel transport and derives a Riemannian MeanFlow identity that links average and instantaneous velocities for intrinsic supervision. We make this identity practical in a log-map tangent representation, avoiding trajectory simulation and heavy geometric computations. For stable optimization, we decompose the RMF objective in...
| Authors | Zichen Zhong, Haoliang Sun, Yukun Zhao et al. |
|---|---|
| Primary category | cs.LG |
| Published | 11 March 2026 |
| Last updated at source | 17 June 2026 |
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