  Upcoming cosmological weak lensing surveys are expected to constrain
cosmological parameters with unprecedented precision. In preparation for these
surveys, large simulations with realistic galaxy populations are required to
test and validate analysis 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 Modeling approach to address the specific problem of
emulating realistic 3D galaxy orientations in synthetic catalogs. For this
purpose, we develop a novel Score-Based Diffusion Model specifically for the
SO(3) manifold. The model accurately learns and reproduces correlated
orientations of galaxies and dark matter halos that are statistically
consistent with those of a reference high-resolution hydrodynamical simulation.
