We review and formulate results concerning log-concavity and strong-log-concavity in both
discrete and continuous settings. We show how preservation of log-concavity and strongly …

The objective of molecular dynamics computations is to infer macroscopic properties of
matter from atomistic models via averages with respect to probability measures dictated by …

We provide theoretical convergence guarantees for score-based generative models (SGMs)
such as denoising diffusion probabilistic models (DDPMs), which constitute the backbone of …

While efficient distribution learning is no doubt behind the groundbreaking success of
diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the …

Progressively applying Gaussian noise transforms complex data distributions to
approximately Gaussian. Reversing this dynamic defines a generative model. When the …

Score-based generative modeling (SGM) is a highly successful approach for learning a
probability distribution from data and generating further samples. We prove the first …

Score-based generative models (SGMs) are a powerful class of generative models that
exhibit remarkable empirical performance. Score-based generative modelling (SGM) …

Abstract Along with Markov chain Monte Carlo (MCMC) methods, variational inference (VI)
has emerged as a central computational approach to large-scale Bayesian inference …

Classically, the continuous-time Langevin diffusion converges exponentially fast to its
stationary distribution π under the sole assumption that π satisfies a Poincaré inequality …

Originally released in Italian, the series now publishes textbooks in English addressed to
students in mathematics worldwide. Some of the most successful books in the series have …