3 citations · 7 across the 10 of their papers we have counts for
12 papers
Convergence rates for generative drifting flows: fixed-scale obstructions and multihead acceleration
Arthur Stéphanovitch, Eddie Aamari
Drifting models offer a promising route to faster generative AI: they perform gradual transport during training, while generating new samples in a single step. This paper asks whet…
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 $β…
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…
Integral Probability Metrics on submanifolds: interpolation inequalities and optimal inference
Arthur Stéphanovitch
We study interpolation inequalities between Hölder Integral Probability Metrics (IPMs) in the case where the measures have densities on closed submanifolds. Precisely, it is shown…
Wasserstein GANs are Minimax Optimal Distribution Estimators
Arthur Stéphanovitch, Eddie Aamari, Clément Levrard
We provide non asymptotic rates of convergence of the Wasserstein Generative Adversarial networks (WGAN) estimator. We build neural networks classes representing the generators and…
Monge-Kantorovich Optimal Transport Through Constrictions and Flow-rate Constraints
Anqi Dong, Arthur Stephanovitch, Tryphon T. Georgiou
We consider the problem to transport resources/mass while abiding by constraints on the flow through constrictions along their path between specified terminal distributions. Constr…
Optimal transport through a toll
Arthur Stephanovitch, Anqi Dong, Tryphon T. Georgiou
We address the problem of optimal transport with a quadratic cost functional and a constraint on the flux through a constriction along the path. The constriction, conceptually repr…
Optimal 1-Wasserstein Distance for WGANs
Arthur Stéphanovitch, Ugo Tanielian, Benoît Cadre +2
The mathematical forces at work behind Generative Adversarial Networks raise challenging theoretical issues. Motivated by the important question of characterizing the geometrical p…