Title: Stability and Forgetting Mechanisms in Score-Based Generative Models

Abstract: The stability and long-term behavior of generative models constitute a core challenge in contemporary machine learning research. This study establishes quantitative limits on the sampling error inherent in score-based generative models by exploiting the forgetting and stability characteristics of the Markov chain linked to reverse-time dynamics. Operating under minimal assumptions, we identify two key structural properties that govern the propagation of initialization and discretization errors within the backward process: specifically, a Lyapunov drift condition and a Doeblin-type minorization condition. A significant practical implication of these findings is the quantitative stability of the sampling procedure, driven by the contraction mechanism induced by reverse diffusion dynamics along the sampling path. These insights shed light on the function of stochastic dynamics in score-based frameworks and offer a rigorous methodology for examining error propagation in these systems.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC