  We propose a novel algorithm for the support estimation of partially known
Gaussian graphical models that incorporates prior information about the
underlying graph. In contrast to classical approaches that provide a point
estimate based on a maximum likelihood or a maximum a posteriori criterion
using (simple) priors on the precision matrix, we consider a prior on the graph
and rely on annealed Langevin diffusion to generate samples from the posterior
distribution. Since the Langevin sampler requires access to the score function
of the underlying graph prior, we use graph neural networks to effectively
estimate the score from a graph dataset (either available beforehand or
generated from a known distribution). Numerical experiments demonstrate the
benefits of our approach.
