Diffusion-based mass map reconstruction from weak lensing data

Diffusion models have been used in cosmological applications as a generative model for fast simulations and to reconstruct underlying cosmological fields or astrophysical images from noisy data. These two tasks are often treated as separate: diffusion models trained for one purpose do not generalize to perform the other task. In this paper, we develop a single diffusion model that can be used for both tasks. By using the diffusion posterior sampling (DPS) approach, we use a diffusion model trained to simulate weak lensing maps for the inverse problem of reconstructing mass maps from noisy weak lensing data. We find that the standard DPS method leads to biased inference but we correct this bias by down weighting the likelihood term at early sampling time steps of the diffusion. Our method gives us a way to reconstruct accurate high-resolution (subarcminute) mass maps that have the correct power spectrum and a range of non-Gaussian summary statistics. We discuss several applications enabled by the computational efficiency and accuracy of our model. These include generation of simulation quality mass maps at a fraction of the computational cost, which in turn enables applications such as covariance estimation for higher order statistics. The higher resolution of the reconstructed maps will enable finding filaments, voids, and clusters from noisy lensing shear data and cross-correlation studies with optical and Sunyaev-Zeldovich maps.