Rencontres statistiques

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Intervenant : OCELLO Antonio (Polytechnique)
Titre :
Theoretical Advances in Score-Based Generative Models: Convergence Bounds and Noise Schedule Optimization

Le : 31/03/2025 de : 13:30 à : 14:30
Score-based generative models (SGMs) have emerged as a state-of-the-art framework for sampling from complex data distributions, leveraging the estimation of score functions through noise-perturbed samples. A central challenge in understanding SGMs lies in quantifying their convergence to the target distribution. Various works have analyzed this convergence using Kullback-Leibler (KL) divergence and Wasserstein distances, often under restrictive assumptions.In this talk, I will present an overview of existing convergence bounds for SGMs and introduce two recent contributions that provide a refined theoretical understanding of their performance. First, I will discuss our work on the impact of the noise schedule on generative performance, where we establish explicit upper bounds for the KL divergence and Wasserstein-2 distance under mild assumptions. This result not only improves upon prior state-of-the-art bounds but also provides practical insights into hyperparameter selection. Building on this framework, I will then present recent advances in Wasserstein-2 convergence analysis. By leveraging the regularization properties of the Ornstein–Uhlenbeck (OU) process, we relax the traditional assumptions of log-concavity and score regularity. Our approach reveals that weakly log-concave distributions evolve towards log-concavity, and we establish a novel characterization of the dynamics of score function contraction and non-contraction. This enables more general and widely applicable convergence results, particularly for complex distributions such as Gaussian mixtures. This talk is based on joint work with Stanislas Strasman, Claire Boyer, Sylvain Le Corff, and Vincent Lemaire, recently accepted to Transactions on Machine Learning Research (https://openreview.net/forum?id=BlYIPa0Fx1), as well as a recent preprint in collaboration with Marta Gentiloni-Silveri (https://arxiv.org/abs/2501.02298).
Salle : A711