Apparaît dans la collection : 2025 IHES Summer School – Statistical Aspects of Nonlinear Physics

We will first present « diffusion models » which are nowadays the state of the art methods used to generate images, videos and sounds. They are very much related to ideas developed in stochastic thermodynamics, and based on time-reversing stochastic processes. The outcome of these methods is a Langevin process that generates from white noise (the initial condition) new images, videos and sounds. We will show that tools of statistical physics allow to characterise two main phenomena emerging during the Langevin generative diffusion process. The first one, that we call 'speciation’ transition, is where the gross structure of data is unraveled, through a mechanism similar to symmetry breaking in phase transitions. The second phenomenon is the generalisation-memorisation transition, which turns out to be related to the glass transition of Derrida’s random energy model. We will present analytical solutions for simple models and show numerical experiments on real datasets which validate the theoretical analysis.