A variational autoencoder (VAE) neural network system, comprising an encoder neural network to encode an input data item to define a posterior distribution for a set of latent variables, and a decoder neural network to generate an output data item representing values of a set of latent variables sampled from the posterior distribution. The system is configured for training with an objective function including a term dependent on a difference between the posterior distribution and a prior distribution. The prior and posterior distributions are arranged so that they cannot be matched to one another. The VAE system may be used for compressing and decompressing data.