The paper identifies distinct failure mechanisms: excessive posterior-prior regularization erases mode information in latent policies, while smooth base-to-action maps limit mode coverage in generative policies.
Lipschitz regularity in Flow Matching and Diffusion Models: sharp sampling rates and functional inequalities
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Under general assumptions on the target distribution $p^\star$, we establish a sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores, with optimal dependence on time and dimension. As applications, we obtain Wasserstein discretization bounds for Euler-type samplers in dimension $d$: with $N$ discretization steps, the error achieves the optimal rate $\sqrt{d}/N$ up to logarithmic factors. Moreover, the constants do not deteriorate exponentially with the spatial extent of $p^\star$. We also show that the one-sided Lipschitz control yields a globally Lipschitz transport map from the standard Gaussian to $p^\star$, which implies Poincar\'e and log-Sobolev inequalities for a broad class of probability measures.
years
2026 4representative citing papers
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