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Riemannian MeanFlow for One-Step Generation on Manifolds
Zichen Zhong · 2026-05-21 · via cs.LG updates on arXiv.org

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Abstract: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 into two terms and apply conflict-aware multi-task learning to mitigate gradient interference. RMF also supports conditional generation via classifier-free guidance. Experiments on spheres, tori, SO(3), and SE(3) demonstrate competitive one-step sampling with improved quality-efficiency trade-offs and substantially reduced sampling cost.
Comments: International Conference on Machine Learning
Subjects: Machine Learning (cs.LG)
Cite as: arXiv:2603.10718 [cs.LG]
  (or arXiv:2603.10718v2 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2603.10718

arXiv-issued DOI via DataCite

Submission history

From: Haoliang Sun [view email]
[v1] Wed, 11 Mar 2026 12:41:46 UTC (9,853 KB)
[v2] Wed, 20 May 2026 13:20:02 UTC (10,129 KB)