This tutorial provides a comprehensive survey of methods for fine-tuning diffusion models to
optimize downstream reward functions. While diffusion models are widely known to provide …

Solving transport problems, ie finding a map transporting one given distribution to another,
has numerous applications in machine learning. Novel mass transport methods motivated …

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

ABSTRACT Statisticians often use Monte Carlo methods to approximate probability
distributions, primarily with Markov chain Monte Carlo and importance sampling. Sequential …

The Schrödinger bridge problem (SBP) finds the most likely stochastic evolution between
two probability distributions given a prior stochastic evolution. As well as applications in the …

In 1931--1932, Erwin Schrödinger studied a hot gas Gedankenexperiment (an instance of
large deviations of the empirical distribution). Schrödinger's problem represents an early …

Recently, a series of papers proposed deep learning-based approaches to sample from
target distributions using controlled diffusion processes, being trained only on the …

Denoising diffusion models have recently emerged as a powerful class of generative
models. They provide state-of-the-art results, not only for unconditional simulation, but also …

More than twenty years after its introduction, Annealed Importance Sampling (AIS) remains
one of the most effective methods for marginal likelihood estimation. It relies on a sequence …

The static optimal transport $(\mathrm {OT}) $ problem between Gaussians seeks to recover
an optimal map, or more generally a coupling, to morph a Gaussian into another. It has been …