Conditional sampling within generative diffusion models
This is an incremental review paper that synthesizes existing methods for a specific technical problem in generative modeling.
This paper reviews computational approaches for conditional sampling in generative diffusion models, addressing the challenge of sampling from conditional distributions needed for applications like Bayesian inverse problems.
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.