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.
Heat flow, log-concavity, and lipschitz transport maps.arXiv preprint arXiv:2404.15205
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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.
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Structured drift design for denoising diffusion models
A variance-aware anisotropic OU drift keeps multimodal and correlated structure longer in diffusion, and bounds reverse initialization error by local cluster variance rather than global variance.