  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.
