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arXiv · 2601.21868

On Forgetting and Stability of Score-based Generative models

Stanislas Strasman·Gabriel Cardoso·Sylvain Le Corff·Vincent Lemaire·Antonio Ocello
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Abstract

Understanding the stability and long-time behavior of generative models is a fundamental problem in modern machine learning. This paper provides quantitative bounds on the sampling error of score-based generative models by leveraging stability and forgetting properties of the Markov chain associated with the reverse-time dynamics. Under weak assumptions, we provide the two structural properties to ensure the propagation of initialization and discretization errors of the backward process: a Lyapunov drift condition and a Doeblin-type minorization condition. A practical consequence is quantitative stability of the sampling procedure, as the reverse diffusion dynamics induces a contraction mechanism along the sampling trajectory. Our results clarify the role of stochastic dynamics in score-based models and provide a principled framework for analyzing propagation of errors in such approaches.

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Stanislas Strasman, Gabriel Cardoso, Sylvain Le Corff, Vincent Lemaire, Antonio Ocello. 2026-01-29. On Forgetting and Stability of Score-based Generative models. https://arxiv.org/abs/2601.21868

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