A PDE Perspective on Generative Diffusion Models

arXiv:2511.05940v2 Announce Type: replace-cross Abstract: Score-based diffusion models have emerged as a powerful class of generative methods, achieving state-of-the-art performance across diverse domains. Despite their empirical success, the mathematical foundations of those models remain only partially understood, particularly regarding the stability and consistency of the underlying stochastic and partial differential equations governing their dynamics. In this work, we develop a rigorous par