We study the use of normalizing flows to represent the field-level probability density distribution of random fields in cosmology such as the matter and radiation distribution. We evaluate the performance of the real NVP flow for sampling of Gaussian and near-Gaussian random fields, and N-body simulations, and check the quality of samples with different statistics such as power spectrum and bispectrum estimators. We explore aspects of these flows that are specific to cosmology, such as flowing from a physical prior distribution and evaluating the density estimation results in the analytically tractable correlated Gaussian case.