(Maths-IA) A Precise Examination of Diffusion Models via Their Application to Gaussian Distributions

After a brief introduction to diffusion models, I will present their application to Gaussian data distributions. Although this setting is of limited practical interest, it provides a simplified framework that allows for a precise characterization of the errors involved, which is essential for studying the convergence of diffusion models. First, I will explain how these errors can be quantified in the continuous formulation of diffusion models under the Gaussian assumption. Then, time permitting, I will discuss the discrete formulation of diffusion models and analyze their convergence, particularly in the context of deblurring problems, still assuming Gaussian distributions.