揭示了得分生成模型采样过程的稳定性机制。
On Forgetting and Stability of Score-based Generative models
- 通过马尔可夫链的稳定与遗忘性质分析采样误差
- 在弱假设下证明误差传播受控，采样路径具收缩性
- 为生成模型误差分析提供理论框架，适合研究者参考
理解生成模型的稳定性和长期行为是现代机器学习中的基础问题。本文通过利用与反向时间动态相关的马尔可夫链的稳定性和遗忘特性，对得分生成模型的采样误差给出了量化边界。在弱假设下，我们提出了两个结构性质以确保反向过程初始值和离散化误差的传播：李亚普诺夫漂移条件和Doeblin型最小化条件。一个实际结果是采样过程的定量稳定性，因为反向扩散动态在采样轨迹上诱导了收缩机制。我们的结果阐明了随机动态在得分模型中的作用，并为这类方法中的误差传播分析提供了原则性框架。
原文摘要 · Abstract (English)
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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