<p>The acquisition times of imaging modalities like computerized tomography (CT) or Magnetic Resonance Imaging (MRI) pose a persistent challenge as the studied object may change in the meantime, e.g. in medical applications due to involuntary patient movement or physiological processes such as respiration and cardiac activity. These dynamics violate the common stationary assumption in the image reconstruction step, resulting in motion-induced artefacts and degrading image quality. To address this issue, retrospective motion correction techniques have emerged as a valuable solution, operating directly on motion-affected data without altering the acquisition process. These techniques include compressed sensing (CS), generative adversarial networks (GANs), and explicit motion estimation methods, each coming with its own advantages and disadvantages. In this article, we propose an iterative approach that leverages blind motion estimates from GANs as a prior for motion estimation. By estimating deformation fields, our method enables data-consistent reconstructions that enhance both image quality and reliability. The motion estimation is realized through neural networks, enabling fast convergence and broad applicability across various imaging modalities without requiring temporal redundancy. We evaluate our supervised network approach on motion-corrupted CT data, accelerated MRI scans of the brain and knee as well as HASTE MRI data of the abdomen. For the latter, we especially demonstrate the ability of our method to estimate non-rigid respiratory motion from data that show no temporal redundancies.</p>