Machine learning models that leverage a latent space with a structure similar to the underlying data distribution have been shown to be highly successful. However, when the data is produced by a quantum process, classical computers are expected to struggle to generate a matching latent space. Here, we show that using a quantum processor to produce the latent space used by a generator in a generative adversarial network (GAN) leads to improved performance on a small-scale quantum dataset. We also demonstrate that this approach is scalable to large-scale data. These results constitute a promising first step towards building real-world generative models with an inductive bias for data with quantum statistics.