  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.
