3D Reconstruction of Dark Matter Fields with Diffusion Models: Towards Application to Galaxy Surveys

Probabilistic diffusion models have shown great success in conditional image synthesis. In this work, we develop a high-resolution 3D diffusion model to reconstruct the dark matter density field from a galaxy distribution. We train a pixel space diffusion model at different resolutions on the CAMELS simulation and achieve good agreement in visual quality and summary statistics. However, we identify some challenges in scaling up the resolution. We then analyze the model’s ability to capture variations in simulation parameters and conclude that the model indeed captures the right change in the field when changing $\Omega_m$. Next, we train our model on a more realistic dataset where the input conditioning consists of mass thresholded galaxy catalogs from CAMELS and find excellent adaptation of diffusion models to low galaxy density inputs. Finally, we show a preliminary application to a real galaxy catalog. Our results suggest that diffusion models are a powerful method to reconstruct the 3D dark matter field from galaxies.