  Data-driven approaches recently achieved remarkable success in magnetic
resonance imaging (MRI) reconstruction, but integration into clinical routine
remains challenging due to a lack of generalizability and interpretability. In
this paper, we address these challenges in a unified framework based on
generative image priors. We propose a novel deep neural network based
regularizer which is trained in a generative setting on reference magnitude
images only. After training, the regularizer encodes higher-level domain
statistics which we demonstrate by synthesizing images without data. Embedding
the trained model in a classical variational approach yields high-quality
reconstructions irrespective of the sub-sampling pattern. In addition, the
model shows stable behavior when confronted with out-of-distribution data in
the form of contrast variation. Furthermore, a probabilistic interpretation
provides a distribution of reconstructions and hence allows uncertainty
quantification. To reconstruct parallel MRI, we propose a fast algorithm to
jointly estimate the image and the sensitivity maps. The results demonstrate
competitive performance, on par with state-of-the-art end-to-end deep learning
methods, while preserving the flexibility with respect to sub-sampling patterns
and allowing for uncertainty quantification.
