Inferring accurate posteriors for high-dimensional representations of the brightness of gravitationally-lensed sources is a major challenge, in part due to the difficulties of accurately quantifying the priors. Here, we report the use of a score-based model to encode the prior for the inference of undistorted images of background galaxies. This model is trained on a set of high-resolution images of undistorted galaxies. By adding the likelihood score to the prior score and using a reverse-time stochastic differential equation solver, we obtain samples from the posterior. Our method produces independent posterior samples and models the data almost down to the noise level. We show how the balance between the likelihood and the prior meet our expectations in an experiment with out-of-distribution data.

We present DECORAS, a deep learning based approach to detect both point and extended sources from Very Long Baseline Interferometry (VLBI) observations. Our approach is based on an encoder-decoder neural network architecture that uses a low number of convolutional layers to provide a scalable solution for source detection. In addition, DECORAS performs source characterization in terms of the position, effective radius and peak brightness of the detected sources. We have trained and tested the network with images that are based on realistic Very Long Baseline Array (VLBA) observations at 20 cm. Also, these images have not gone through any prior de-convolution step and are directly related to the visibility data via a Fourier transform. We find that the source catalog generated by DECORAS has a better overall completeness and purity, when compared to a traditional source detection algorithm. DECORAS is complete at the 7.5$\sigma$ level, and has an almost factor of two improvement in reliability at 5.5$\sigma$. We find that DECORAS can recover the position of the detected sources to within 0.61 $\pm$ 0.69 mas, and the effective radius and peak surface brightness are recovered to within 20 per cent for 98 and 94 per cent of the sources, respectively. Overall, we find that DECORAS provides a reliable source detection and characterization solution for future wide-field VLBI surveys.