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Abstract 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 most information. We present HIF low : a fast generative model of the neutral hydrogen (H i ) maps that is conditioned only on cosmology (Ω m and σ 8 ) and designed using a class of normalizing flow models, the masked autoregressive flow. HIF low is trained on the state-of-the-art simulations from the Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) project. HIF low has the ability to generate realistic diverse maps without explicitly incorporating the expected two-dimensional maps structure into the flow as an inductive bias. We find that HIF low is able to reproduce the CAMELS average and standard deviation H i power spectrum within a factor of ≲2, scoring a very high R 2 > 90%. By inverting the flow, HIF low provides a tractable high-dimensional likelihood for efficient parameter inference. We show that the conditional HIF low on cosmology is successfully able to marginalize over astrophysics at the field level, regardless of the stellar and AGN feedback strengths. This new tool represents a first step toward a more powerful parameter inference, maximizing the scientific return of future H i surveys, and opening a new avenue to minimize the loss of complex information due to data compression down to summary statistics.