Flow Matching on General Geometries

arXiv:2302.03660v3 Announce Type: replace
Abstract: We propose Riemannian Flow Matching (RFM), a simple yet powerful framework for training continuous normalizing flows on manifolds. Existing methods for generative modeling on manifolds either require expensive simulation, are inherently unable to scale to high dimensions, or use approximations for limiting quantities that result in biased training objectives. Riemannian Flow Matching bypasses these limitations and offers several advantages over previous approaches: it is simulation-free on simple geometries, does not require divergence computation, and computes …

abstract arxiv continuous continuous normalizing flows cs.ai cs.lg dimensions flow framework general generative generative modeling modeling scale simple simulation stat.ml training type