Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for providing a data sample in response to a request for a data sample. In one aspect, a method comprises: receiving a request for a new data sample; until a candidate new data sample is generated that satisfies an acceptance criterion, performing operations comprising: generating a candidate new data sample using a generator neural network; processing the candidate new data sample using a discriminator neural network to generate an imitation score; and determining, from the imitation score, whether the candidate new data sample satisfies the acceptance criterion; and providing the candidate new data sample that satisfies the acceptance criterion in response to the received request.