Any centered 1-subgaussian random vector equals the sum of a universal number of standard Gaussians, solving Talagrand's convexity conjecture.
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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.
Establishes dimension- and step-optimal Wasserstein bounds for DDPMs under Lipschitz score conditions and broad variance schedules via Föllmer process analysis, recovering prior results and extending to log-concave targets.
citing papers explorer
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On Talagrand's Convexity Conjecture
Any centered 1-subgaussian random vector equals the sum of a universal number of standard Gaussians, solving Talagrand's convexity conjecture.
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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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Wasserstein bounds for denoising diffusion probabilistic models via the F\"ollmer process
Establishes dimension- and step-optimal Wasserstein bounds for DDPMs under Lipschitz score conditions and broad variance schedules via Föllmer process analysis, recovering prior results and extending to log-concave targets.