Abstract: Generative modeling aims to produce new random examples from an unknown target distribution, given access to a finite collection of examples. Among the leading approaches, denoising diffusion probabilistic models (DDPMs) construct such examples by mapping a Brownian motion via a diffusion process driven by an estimated score function. In this work, we first provide empirical evidence that DDPMs are robust to constant-variance noise in the score evaluations. We then establish finite-sample guarantees in Wasserstein-2 distance that exhibit two key features: (i) they characterize and quantify the robustness of DDPMs to noisy score estimates, and (ii) they achieve faster convergence rates than previously known results. Furthermore, we observe that the obtained rates match those known in the Gaussian case, implying their optimality. (Joint work with V. Arsenyan and E. Vardanyan)

Bio: Arnak Dalalyan is a full professor of Statistics at ENSAE Paris. He obtained his PhD (2001) from Le Mans University on Statistics for Random Processes. He was a postdoctoral fellow (2002–03) at the Humboldt University of Berlin, an assistant professor (2003–08) at Paris 6 University and a research professor at ENPC (2008–2011). Arnak’s research focuses on high dimensional statistics, statistics of diffusion processes and statistical learning theory. Presently, he is an associate editor of the Annals of Statistics, Bernoulli, Statistical Inference for Stochastic Processes and Journal of the Japan Statistical Society. Arnak is also regularly serving in the programme committees (either as area chair or as reviewer) of machine learning conferences COLT, ALT, ICML and NeurIPS. He was a member of the Bernoulli Society council (2017-2021). Between 2014 and 2021, Arnak Dalalyan was the head of the ENSAE graduate programme on Statistics and Machine Learning, whereas between 2020 and 2026 he was the director of the Center of Research in Economics and Statistics (CREST).