Convergence of Denoising Diffusion Models Under the Manifold Hypothesis

Explore the theoretical foundations of denoising diffusion models in this 46-minute lecture by Valentin de Bortoli from CNRS, France. Delve into the convergence analysis of these state-of-the-art generative models for image and audio synthesis, focusing on scenarios where the target distribution is supported on a lower-dimensional manifold or given by an empirical distribution. Examine quantitative bounds on the Wasserstein distance between the target data distribution and the generative distribution of diffusion models. Gain insights into the theoretical underpinnings of these models, addressing limitations in current approaches that assume target density admits a density with respect to the Lebesgue measure.