Life, Death and Miracles of Diffusion Models
Beatrice Achilli (Bocconi)
Seminar of the Series MLP@P (Machine Learning Physics @ Plateau), joint with LISN and IPhT.
Where: IPhT, Salle Itzykson *change of place!*
In recent years, generative diffusion models have emerged as powerful tools in unsupervised learning, achieving impressive results in image, text, and data generation. In this presentation I will analyze from a geometric and statistical physics perspective how these models learn, generalize, and eventually memorize data. In particular, I will highlight how the intrinsic structure of manifold data impacts the dynamics of the diffusion process. Our analysis reveals the existence of distinct phases during the generative process, in particular a manifold coverage phase where the diffusion process fits the distribution internal to the manifold, and a consolidation phase where the score becomes orthogonal to the manifold. By mapping diffusion models driven by the empirical score function onto the Random Energy Model (REM), we are able to characterize memorization and generalization timescales. These insights clarify the role of data structure in mitigating the curse of dimensionality and contribute to a deeper understanding of how diffusion models capture complex data distributions.