On Forgetting and Stability of Score-based Generative models
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.
Cite
@article{arxiv.2601.21868,
title = {On Forgetting and Stability of Score-based Generative models},
author = {Stanislas Strasman and Gabriel Cardoso and Sylvain Le Corff and Vincent Lemaire and Antonio Ocello},
journal= {arXiv preprint arXiv:2601.21868},
year = {2026}
}