On Forgetting and Stability of Score-based Generative models
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866917232573939712 |
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| author | Strasman, Stanislas Cardoso, Gabriel Corff, Sylvain Le Lemaire, Vincent Ocello, Antonio |
| author_facet | Strasman, Stanislas Cardoso, Gabriel Corff, Sylvain Le Lemaire, Vincent Ocello, Antonio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21868 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Forgetting and Stability of Score-based Generative models Strasman, Stanislas Cardoso, Gabriel Corff, Sylvain Le Lemaire, Vincent Ocello, Antonio Machine Learning 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. |
| title | On Forgetting and Stability of Score-based Generative models |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2601.21868 |