Modeling halo and central galaxy orientations on the SO(3) manifold with score-based generative models

Upcoming cosmological weak lensing surveys are expected to constrain cosmo-logical parameters with unprecedented precision. In preparation for these surveys,large simulations with realistic galaxy populations are required to test and validateanalysis pipelines. However, these simulations are computationally very costly –and at the volumes and resolutions demanded by upcoming cosmological surveys,they are computationally infeasible. Here, we propose a Deep Generative Modelingapproach to address the specific problem of emulating realistic 3D galaxy orien-tations in synthetic catalogs. For this purpose, we develop a novel Score-BasedDiffusion Model specifically for the SO(3) manifold. The model accurately learnsand reproduces correlated orientations of galaxies and dark matter halos that arestatistically consistent with those of a reference high-resolution hydrodynamicalsimulation.