On Forgetting and Stability of Score-based Generative models

• URL: http://arxiv.org/abs/2601.21868v1
• Date: Thu, 29 Jan 2026 15:37:50 GMT
• Title: On Forgetting and Stability of Score-based Generative models
• Authors: Stanislas Strasman, Gabriel Cardoso, Sylvain Le Corff, Vincent Lemaire, Antonio Ocello,
• Abstract summary: Understanding the stability and long-time behavior of generative models is a fundamental problem in modern machine learning.<n>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.
• Score: 6.259598237089842
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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