Generative models and Bayesian inversion using Laplace approximation. (arXiv:2203.07755v2 [stat.ML] UPDATED)

The Bayesian approach to solving inverse problems relies on the choice of a
prior. This critical ingredient allows the formulation of expert knowledge or
physical constraints in a probabilistic fashion and plays an important role for
the success of the inference. Recently, Bayesian inverse problems were solved
using generative models as highly informative priors. Generative models are a
popular tool in machine learning to generate data whose properties closely
resemble those of a given database. Typically, the generated distribution of …

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