Flow matching achieves near-minimax optimal statistical consistency for manifold-supported distributions, with convergence rates governed by intrinsic dimension and smoothness rather than ambient dimension.
(c) Projected Gaussian onS d: finiteM V by Proposition 2 for moderate∥γ∥
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Flow Matching is Adaptive to Manifold Structures
Flow matching achieves near-minimax optimal statistical consistency for manifold-supported distributions, with convergence rates governed by intrinsic dimension and smoothness rather than ambient dimension.