  Reconstructing the initial conditions of the universe is a key problem in
cosmology. Methods based on simulating the forward evolution of the universe
have provided a way to infer initial conditions consistent with present-day
observations. However, due to the high complexity of the inference problem,
these methods either fail to sample a distribution of possible initial density
fields or require significant approximations in the simulation model to be
tractable, potentially leading to biased results. In this work, we propose the
use of score-based generative models to sample realizations of the early
universe given present-day observations. We infer the initial density field of
full high-resolution dark matter N-body simulations from the present-day
density field and verify the quality of produced samples compared to the ground
truth based on summary statistics. The proposed method is capable of providing
plausible realizations of the early universe density field from the initial
conditions posterior distribution marginalized over cosmological parameters and
can sample orders of magnitude faster than current state-of-the-art methods.
