  Optimal extraction of cosmological information from observations of the
Cosmic Microwave Background critically relies on our ability to accurately undo
the distortions caused by weak gravitational lensing. In this work, we
demonstrate the use of denoising diffusion models in performing Bayesian
lensing reconstruction. We show that score-based generative models can produce
accurate, uncorrelated samples from the CMB lensing convergence map posterior,
given noisy CMB observations. To validate our approach, we compare the samples
of our model to those obtained using established Hamiltonian Monte Carlo
methods, which assume a Gaussian lensing potential. We then go beyond this
assumption of Gaussianity, and train and validate our model on non-Gaussian
lensing data, obtained by ray-tracing N-body simulations. We demonstrate that
in this case, samples from our model have accurate non-Gaussian statistics
beyond the power spectrum. The method provides an avenue towards more efficient
and accurate lensing reconstruction, that does not rely on an approximate
analytic description of the posterior probability. The reconstructed lensing
maps can be used as an unbiased tracer of the matter distribution, and to
improve delensing of the CMB, resulting in more precise cosmological parameter
inference.
