  Galaxies are biased tracers of the underlying cosmic web, which is dominated
by dark matter components that cannot be directly observed. The relationship
between dark matter density fields and galaxy distributions can be sensitive to
assumptions in cosmology and astrophysical processes embedded in the galaxy
formation models, that remain uncertain in many aspects. Based on
state-of-the-art galaxy formation simulation suites with varied cosmological
parameters and sub-grid astrophysics, we develop a diffusion generative model
to predict the unbiased posterior distribution of the underlying dark matter
fields from the given stellar mass fields, while being able to marginalize over
the uncertainties in cosmology and galaxy formation.
