Sharp Lipschitz regularity for flow-matching vector fields and diffusion scores, with optimal time/dimension dependence, gives √d/N Wasserstein discretization error for Euler samplers and globally Lipschitz Gaussian-to-target transport maps implying Poincaré and log-Sobolev inequalities.
Smooth transport map via diffusion process.arXiv preprint arXiv:2411.10235
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Lipschitz regularity in Flow Matching and Diffusion Models: sharp sampling rates and functional inequalities
Sharp Lipschitz regularity for flow-matching vector fields and diffusion scores, with optimal time/dimension dependence, gives √d/N Wasserstein discretization error for Euler samplers and globally Lipschitz Gaussian-to-target transport maps implying Poincaré and log-Sobolev inequalities.