HIFlow: Generating Diverse HI Maps Conditioned on Cosmology using
  Normalizing Flow
  A wealth of cosmological and astrophysical information is expected from many
ongoing and upcoming large-scale surveys. It is crucial to prepare for these
surveys now and develop tools that can efficiently extract the maximum amount
of information. We present HIFlow: a fast emulator that is able to generate
neutral hydrogen (HI) maps conditioned only on cosmology ($\Omega_{m}$ and
$\sigma_{8}$), after training on the state-of-the-art simulations from the
Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) project.
HIFlow is designed using a class of normalizing flow models, the Masked
Autoregressive Flow (MAF), which we demonstrate are capable of generating
realistic maps without explicitly using the 2D structure or accounting for any
symmetries. HIFlow is able to generate new diverse HI maps in the column
density range $N_{\rm HI} \sim 10^{14} - 10^{21} {\rm cm^{-2}}$ at $z\sim 6$,
and naturally mimic the cosmic variance effects. Remarkably, HIFlow is able to
reproduce the CAMELS average and standard deviation HI power spectrum (Pk)
within a factor of $\lesssim$ 2, scoring a very high $R^{2} > 90\%$. HIFlow
will enable the testing of Pk pipelines for HI surveys, and assist in computing
other statistical properties beyond Pk that require generating new diverse
samples of high dimensional datasets, such as the covariance matrix. This new
tool represents a first step towards enabling rapid parameter inference at the
field level, maximizing the scientific return of future HI surveys, and opening
a new avenue to minimize the loss of information due to data compression.
