Conditional sampling within generative diffusion models

TL;DR

This paper reviews methods for extending generative diffusion models to perform conditional sampling, addressing a key challenge in applying these models to tasks like Bayesian inverse problems.

Contribution

It provides a comprehensive overview of existing approaches for conditional sampling in diffusion models, highlighting key methodologies and their underlying principles.

Findings

Summarizes techniques using joint distributions for conditional sampling.

Highlights methods relying on marginal distributions with explicit likelihoods.

Identifies open challenges and future directions in the field.

Abstract

Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their success in these domains, an important open challenge remains: extending these techniques to sample from conditional distributions, as required in, for example, Bayesian inverse problems. In this paper, we present a comprehensive review of existing computational approaches to conditional sampling within generative diffusion models. Specifically, we highlight key methodologies that either utilise the joint distribution, or rely on (pre-trained) marginal distributions with explicit likelihoods, to construct conditional generative samplers.