Mathematics Colloquium

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Statistical Physics of Generative Diffusion

Speaker: Marc Mézard, Bocconi University

Location: 60 Fifth Avenue 7th Floor

Date: Thursday, November 9, 2023, 10 a.m.

Synopsis:

Generative models, in which one trains an algorithm to generate samples ‘similar’ to those of a data base, is a major new direction developed in machine learning in the recent years. In particular, generative models based on diffusion equations have become the state of the art, notably for image generation. However, the reasons for this spectacular technological success are not well understood, and neither are its limitations.
 
After an introduction to this topic, the talk will focus on the behavior of generative diffusion in the high-dimensional limit, where data are formed by a very large number of variables.  Using methods from statistical physics, and through a detailed analysis of two well-controlled high-dimensional cases, a Gaussian model and the Curie-Weiss model, we explain the various phase transitions that take place during the dynamics of generation.