Uncertainty Quantification with Generative Models

TL;DR

This paper introduces a generative model-based framework for Bayesian inverse problems, enabling efficient data-driven priors and tractable uncertainty quantification for image reconstruction tasks.

Contribution

It presents a novel approach that leverages trained generative models for Bayesian inverse problems, addressing prior complexity and computational efficiency.

Findings

Efficient uncertainty quantification in latent and data space.

Single training on uncorrupted data enables handling various corruption types.

Framework improves Bayesian reconstruction with complex priors.

Abstract

We develop a generative model-based approach to Bayesian inverse problems, such as image reconstruction from noisy and incomplete images. Our framework addresses two common challenges of Bayesian reconstructions: 1) It makes use of complex, data-driven priors that comprise all available information about the uncorrupted data distribution. 2) It enables computationally tractable uncertainty quantification in the form of posterior analysis in latent and data space. The method is very efficient in that the generative model only has to be trained once on an uncorrupted data set, after that, the procedure can be used for arbitrary corruption types.