A PDE Perspective on Generative Diffusion Models

תקציר מקורי באנגליתarXiv:2511.05940v3 Announce Type: replace-cross Abstract: Score-based diffusion models have emerged as a powerful class of generative methods, with successful applications across diverse domains. Despite their empirical success, their mathematical foundations remain only partially understood, particularly regarding the stability and consistency of the stochastic and partial differential equations underlying their dynamics. In this work, we develop a partial differential equation (PDE) framework for score-based diffusion processes associated with the heat flow of a compactly supported data measure. After establishing weak well-posedness on positive-time intervals, we derive a sharp one-sided divergence bound for the score and use it to obtain sharp uniform $L^p$-stability estimates for the