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A wealth of cosmological and astrophysical information is expected from manyongoing and upcoming large-scale surveys. It is crucial to prepare for thesesurveys now and develop tools that can efficiently extract most information. Wepresent HIFlow: a fast generative model of the neutral hydrogen (HI) maps thatis conditioned only on cosmology ($\Omega_{m}$ and $\sigma_{8}$) and designedusing a class of normalizing flow models, the Masked Autoregressive Flow (MAF).HIFlow is trained on the state-of-the-art simulations from the Cosmology andAstrophysics with MachinE Learning Simulations (CAMELS) project. HIFlow has theability to generate realistic diverse maps without explicitly incorporating theexpected 2D maps structure into the flow as an inductive bias. We find thatHIFlow is able to reproduce the CAMELS average and standard deviation HI powerspectrum (Pk) within a factor of $\lesssim$ 2, scoring a very high $R^{2} >90\%$. By inverting the flow, HIFlow provides a tractable high-dimensionallikelihood for efficient parameter inference. We show that the conditionalHIFlow on cosmology is successfully able to marginalize over astrophysics atthe field level, regardless of the stellar and AGN feedback strengths. This newtool represents a first step toward a more powerful parameter inference,maximizing the scientific return of future HI surveys, and opening a new avenueto minimize the loss of complex information due to data compression down tosummary statistics.

HIFlow: Generating Diverse HI Maps and Inferring Cosmology while Marginalizing over Astrophysics using Normalizing Flows