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We conduct ann-ablation across multiple (d,D) pairs to probe both predictions directly

provides a controlled setting to test two predictions of Theorem 2: (i) the convergence rate W std 1,slice ∝n −γ depends on the intrinsic dimensiond, (ii) fixingd, the rate is independent of the ambient dimensionD · 2048

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Flow Matching is Adaptive to Manifold Structures

stat.ML · 2026-02-25 · unverdicted · novelty 6.0

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.

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  • Flow Matching is Adaptive to Manifold Structures stat.ML · 2026-02-25 · unverdicted · none · ref 10

    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.