The solution of inverse problems is of fundamental interest in medical and astronomical
imaging, geophysics as well as engineering and life sciences. Recent advances were made …

Over recent years, deep learning methods have become an increasingly popular choice for
solving tasks from the field of inverse problems. Many of these new data-driven methods …

To overcome topological constraints and improve the expressiveness of normalizing flow
architectures, Wu, Köhler, and Noé introduced stochastic normalizing flows which combine …

Bayesian inference for high-dimensional inverse problems is computationally costly and
requires selecting a suitable prior distribution. Amortized variational inference addresses …

Normalizing flows, diffusion normalizing flows and variational autoencoders are powerful
generative models. This Element provides a unified framework to handle these approaches …

In order to sample from an unnormalized probability density function, we propose to
combine continuous normalizing flows (CNFs) with rejection-resampling steps based on …

Conditional generative models became a very powerful tool to sample from Bayesian
inverse problem posteriors. It is well-known in classical Bayesian literature that posterior …

Exploiting image patches instead of whole images has proved to be a powerful approach to
tackling various problems in image processing. Recently, Wasserstein patch priors (WPPs) …

Most commonly used $ f $-divergences of measures, eg, the Kullback-Leibler divergence,
are subject to limitations regarding the support of the involved measures. A remedy consists …

We propose a novel modular inference approach combining two different generative models—
generative adversarial networks (GAN) and normalizing flows—to approximate the posterior …