Par Tony Bonnaire (IAS)
Abstract :
Diffusion models have emerged as powerful generative tools, capable of producing highly realistic images, videos, and sounds by learning a stochastic mapping starting from a simple Gaussian distribution. Despite their empirical success, the underlying reasons for their effectiveness remain poorly understood. In this talk, we will give a brief primer on the formalism of diffusion models and then dive into the analysis of a well-defined high-dimensional data distribution-a mixture of two Gaussians-under the assumption of an optimally-trained model. In particular, this reveals the existence of a ‘memorization’ transition where the trajectories are inevitably attracted to one of the training points and reproduce it exactly. Interestingly, we will provide an explanation on why diffusion models can still generalize despite this curse thanks to an implicit regularization mechanism in their training dynamics. This creates a generalization window that grows linearly with the training set size, enabling diffusion models to generalize. These findings are supported by both analytical results on simplified models and large-scale numerical experiments on realistic models and datasets. If time permits, we will discuss ongoing applications of such generative models in physics, especially in disordered systems and cosmology.
Lieu : IAS, bât. 121, salle 4-5 (4ème étage)