FLAIR x AI Center Seminar - AI Fundamentals series - Prof. Eric Vanden-Eijnden

The talk is jointly organized by the EPFL Foundations of Learning and AI Research (FLAIR) group and the EPFL AI Center.

Hosting professor: Prof. Florent Krzakala

Title
Generative modeling with flows and diffusions

Abstract
Dynamical transport-based generative models have revolutionized unsupervised learning, offering powerful frameworks for mapping between probability distributions. These models, which construct transformations that convert samples from a simple distribution into samples from a complex target distribution, have evolved beyond their original image generation applications to address fundamental challenges in computational science. By leveraging these approaches, researchers can now tackle problems previously considered intractable due to the curse of dimensionality. This talk presents recent mathematical advances in flow-based and diffusion-based generative models, demonstrating how deeper theoretical understanding leads to more effective architecture design. I will introduce novel techniques for structuring transport mechanisms that efficiently capture complex target distributions while maintaining computational tractability during both training and inference. Applications in probabilistic forecasting, Monte Carlo sampling, and non-equilibrium statistical mechanics showcase how these innovations unlock new capabilities in scientific computing.

Bio
My research focuses on the mathematical and computational aspects of statistical mechanics, with applications to complex dynamical systems arising in molecular dynamics, materials science, atmosphere-ocean science, fluids dynamics, and neural networks. More recently I have become interested in the mathematical foundations of machine learning (ML) and started to explore the exciting new prospects ML offer for scientific computing. My work combines tools from probability theory, mathematical physics, numerical analysis, and optimization to uncover governing principles in complex systems and design efficient algorithms for their simulation.