Extracting the maximum amount of cosmological and astrophysical information from upcoming large-scale surveys remains a challenge. This includes evaluating the exact likelihood, parameter inference and generating new diverse synthetic examples of the incoming high-dimensional data sets. In this work, we propose the use of normalizing flows as a generative model of the neutral hydrogen (HI) maps from the CAMELS project. Normalizing flows have been very successful at parameter inference and generating new, realistic examples. Our model utilizes the spatial structure of the HI maps in order to faithfully follow the statistics of the data, allowing for high-fidelity sample generation and efficient parameter inference.