Sampling multimodal distributions by denoising

Generative models parameterize flexible families of distributions capable of fitting complex datasets such as images or text. These models can generate independent samples from intricate high-dimensional distributions at a negligible cost. In contrast, sampling exactly from a given target distribution—such as the Boltzmann distribution of a physical system—is often a major challenge due to high dimensionality, multimodality, ill-conditioning, or a combination of these factors. This raises the question: How can generative models be leveraged to assist in the sampling task? A key difficulty in this setting is the lack of an extensive dataset to learn from upfront. In this talk, I will focus in particular on sampling from multimodal distributions and present recent attempts inspired by diffusion models to sample using a denoising process. The talk is mainly based on works with Louis Grenioux, Maxence Noble and Alain Oliviero Durmus.