8 papers
Statistical Analysis of Markovian Generative Modeling
Eddie Aamari, Arthur Stéphanovitch
These lecture notes introduce the statistical analysis of continuous-time generative models built from Markov dynamics. We begin with the stochastic-calculus foundations of score-b…
Lipschitz regularity in Flow Matching and Diffusion Models: sharp sampling rates and functional inequalities
Arthur Stéphanovitch
Under general assumptions on the target distribution , we establish a sharp Lipschitz regularity theory for flow-matching vector fields and diffusion-model scores, with op…
Generalization bounds for score-based generative models: a synthetic proof
Arthur Stéphanovitch, Eddie Aamari, Clément Levrard
We establish minimax convergence rates for score-based generative models (SGMs) under the -Wasserstein distance. Assuming the target density lies in a nonparametric $Î…
Generative model for optimal density estimation on unknown manifold
Arthur Stéphanovitch
We propose a generative model that achieves minimax-optimal convergence rates for estimating probability distributions supported on unknown low-dimensional manifolds. Building on F…
Regularity of the score function in generative models
Arthur Stéphanovitch
We study the regularity of the score function in score-based generative models and show that it naturally adapts to the smoothness of the data distribution. Under minimal assumptio…
Smooth transport map via diffusion process
Arthur Stéphanovitch
We extend the classical regularity theory of optimal transport to non-optimal transport maps generated by heat flow for perturbations of Gaussian measures. Considering probability…