Diffusion models are recent state-of-the-art methods for image generation and likelihood
estimation. In this work, we generalize continuous-time diffusion models to arbitrary …

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 …

Many variants of the Wasserstein distance have been introduced to reduce its original
computational burden. In particular the Sliced-Wasserstein distance (SW), which leverages …

Explicit, momentum-based dynamics for optimizing functions defined on Lie groups was
recently constructed, based on techniques such as variational optimization and left …

We study the Riemannian Langevin Algorithm for the problem of sampling from a distribution
with density $\nu $ with respect to the natural measure on a manifold with metric $ g $. We …

Comparing spherical probability distributions is of great interest in various fields, including
geology, medical domains, computer vision, and deep representation learning. The utility of …

Langevin algorithms are gradient descent methods with additive noise. They have been
used for decades in Markov Chain Monte Carlo (MCMC) sampling, optimization, and …

Sampling methods, as important inference and learning techniques, are typically designed
for unconstrained domains. However, constraints are ubiquitous in machine learning …

We study the task of efficiently sampling from a Gibbs distribution $ d\pi^*= e^{-h} d {\text
{vol}} _g $ over a Riemannian manifold $ M $ via (geometric) Langevin MCMC; this …

We introduce a suite of new particle-based algorithms for sampling in constrained domains
which are entirely learning rate free. Our approach leverages coin betting ideas from convex …