  We introduce a diffusion-based generative model to describe the distribution
of galaxies in our Universe directly as a collection of points in 3-D space
(coordinates) optionally with associated attributes (e.g., velocities and
masses), without resorting to binning or voxelization. The custom diffusion
model can be used both for emulation, reproducing essential summary statistics
of the galaxy distribution, as well as inference, by computing the conditional
likelihood of a galaxy field. We demonstrate a first application to massive
dark matter haloes in the Quijote simulation suite. This approach can be
extended to enable a comprehensive analysis of cosmological data, circumventing
limitations inherent to summary statistic -- as well as neural simulation-based
inference methods.
