Related papers: Wasserstein Convergence of Critically Damped Langevin Diffusions

Wasserstein Convergence of Critically Damped Langevin Diffusions

URL: http://arxiv.org/abs/2511.02419v1
Date: Tue, 04 Nov 2025 09:49:07 GMT
Title: Wasserstein Convergence of Critically Damped Langevin Diffusions
Authors: Stanislas Strasman, Sobihan Surendran, Claire Boyer, Sylvain Le Corff, Vincent Lemaire, Antonio Ocello,
Abstract summary: Critically-damped Langevin Diffusions (CLDs) have been shown to outperform standard diffusion-based samplers numerically.<n>We derive a novel upper bound on the sampling error of CLD-based generative models in the Wasserstein metric.
Score: 9.063081094420044
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Score-based Generative Models (SGMs) have achieved impressive performance in data generation across a wide range of applications and benefit from strong theoretical guarantees. Recently, methods inspired by statistical mechanics, in particular, Hamiltonian dynamics, have introduced Critically-damped Langevin Diffusions (CLDs), which define diffusion processes on extended spaces by coupling the data with auxiliary variables. These approaches, along with their associated score-matching and sampling procedures, have been shown to outperform standard diffusion-based samplers numerically. In this paper, we analyze a generalized dynamic that extends classical CLDs by introducing an additional hyperparameter controlling the noise applied to the data coordinate, thereby better exploiting the extended space. We further derive a novel upper bound on the sampling error of CLD-based generative models in the Wasserstein metric. This additional hyperparameter influences the smoothness of sample paths, and our discretization error analysis provides practical guidance for its tuning, leading to improved sampling performance.

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