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 min
This research is part of ongoing efforts to deepen the theoretical understanding of generative AI models, addressing fundamental questions of their reliability and long-term behavior as they become more central to AI development.
Understanding the stability and forgetting properties of score-based generative models is crucial for their reliable deployment and scaling, especially in applications requiring high fidelity and consistency over time.
This theoretical work advances our ability to predict and control the behavior of complex generative AI systems, moving beyond empirical observations to more robust mathematical guarantees of performance.
- · AI researchers
- · Generative AI developers
- · AI model auditing firms
- · Unreliable generative AI applications
Improved theoretical foundations for generative AI models will lead to more stable and predictable systems.
Enhanced reliability and predictability will accelerate the adoption of generative AI in critical and commercial applications.
The ability to quantify and manage AI model stability could eventually impact regulatory frameworks for AI safety and trustworthy AI.
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