Learning cosmic web environments with diffusion models

Abstract

The cosmic web, consisting of an intricate network of voids, walls, filaments, and nodes, encodes key information about structure formation and the cosmological parameters that govern it. In the era of high-precision cosmology, large ensembles of numerical simulations are required to analyse next-generation galaxy surveys, motivating the use of generative models to circumvent their high computational cost. While they have shown promise in emulating high-fidelity cosmic web simulations, their ability to capture distinct cosmic web environments remains largely unexplored. For this study, we trained a diffusion model on the Quijote N-body simulation suite to investigate the semantic information learnt by its self-attention maps. Using statistical estimators such as the Dice coefficient and cross-power spectra, we quantified the correspondence between attention maps and cosmic web environments defined by the T-Web classifier. We find that attention maps of varying spatial resolutions across different layers capture overdense and underdense structures in distinct ways, exhibiting strong positive correlations and anti-correlations with both the overall matter distribution and individual cosmic web environments. Moreover, the diffusion model predominantly encodes cosmological information at intermediate-to-large spatial scales, indicating that attention maps primarily capture globally coherent structures. Our results show that, beyond accurately reproducing two-point statistics, diffusion models learn a multi-scale representation of the cosmic web through self-attention, including non-Gaussian information.