Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for compressing and decompressing data. In one aspect, a method comprises: processing data using an encoder neural network to generate a latent representation of the data; processing the latent representation of the data using a hyper-encoder neural network to generate a latent representation of an entropy model; generating an entropy encoded representation of the latent representation of the entropy model; generating an entropy encoded representation of the latent representation of the data using the latent representation of the entropy model; and determining a compressed representation of the data from the entropy encoded representations of: (i) the latent representation of the data and (ii) the latent representation of the entropy model used to entropy encode the latent representation of the data.