Using a large sample of galaxies taken from the Cosmology and Astrophysics with MachinE Learning Simulations (CAMELS) project, a suite of hydrodynamic simulations varying both cosmological and astrophysical parameters, we train a normalizing flow (NF) to map the probability of various galaxy and halo properties conditioned on astrophysical and cosmological parameters. By leveraging the learnt conditional relationships we can explore a wide range of interesting questions, whilst enabling simple marginalization over nuisance parameters. We demonstrate how the model can be used as a generative model for arbitrary values of our conditional parameters; we generate halo masses and matched galaxy properties, and produce realizations of the halo mass function as well as a number of galaxy scaling relations and distribution functions. The model represents a unique and flexible approach to modelling the galaxy-halo relationship.