Markov chain Monte Carlo (MCMC) is an essential set of tools for estimating features of
probability distributions commonly encountered in modern applications. For MCMC …

This paper surveys in detail the relations between numerical integration and the Hamiltonian
(or hybrid) Monte Carlo method (HMC). Since the computational cost of HMC mainly lies in …

Score-based generative models (SGMs) need to approximate the scores $\nabla\log p_t $ of
the intermediate distributions as well as the final distribution $ p_T $ of the forward process …

Abstract We study the Unadjusted Langevin Algorithm (ULA) for sampling from a probability
distribution $\nu= e^{-f} $ on $\R^ n $. We prove a convergence guarantee in Kullback …

We study the underdamped Langevin diffusion when the log of the target distribution is
smooth and strongly concave. We present a MCMC algorithm based on its discretization and …

We study the problem of sampling from a strongly log-concave density supported on
$\mathbb {R}^ d $, and prove a non-asymptotic upper bound on the mixing time of the …

Optimization algorithms and Monte Carlo sampling algorithms have provided the
computational foundations for the rapid growth in applications of statistical machine learning …

We introduce the Generalized Energy Based Model (GEBM) for generative modelling. These
models combine two trained components: a base distribution (generally an implicit model) …

Langevin diffusion processes and their discretizations are often used for sampling from a
target density. The most convenient framework for assessing the quality of such a sampling …

We study the problem of sampling from a distribution $ p^*(x)\propto\exp\left (-U (x)\right) $,
where the function $ U $ is $ L $-smooth everywhere and $ m $-strongly convex outside a …