aiqbench analysis
This paper establishes quantitative bounds on sampling error for score-based generative models by leveraging stability and forgetting properties within their associated Markov chains. By identifying a Lyapunov drift condition and a Doeblin-type minorization condition, the work demonstrates how reverse diffusion dynamics naturally induce a contraction mechanism that mitigates initialization and discretization errors. These findings offer a principled theoretical framework for analyzing error propagation in stochastic dynamics, providing essential rigor for the development of robust generative AI systems.
On Forgetting and Stability of Score-based Generative models
arXiv:2601.21868v2 Announce Type: replace-cross 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.
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.
Machine Learning (stat.ML); Machine Learning (cs.LG)
arXiv:2601.21868 [stat.ML]
(or arXiv:2601.21868v2 [stat.ML] for this version)
https://doi.org/10.48550/arXiv.2601.21868 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 218 words