We introduce a new approach to learning in hierarchical latent-variable generative models called the “distributed distributional code Helmholtz machine”, which emphasises flexibility and accuracy in the inferential process. Like the original Helmholtz machine and later variational autoencoder algorithms (but unlike adver- sarial methods) our approach learns an explicit inference or “recognition” model to approximate the posterior distribution over the latent variables. Unlike these earlier methods, it employs a posterior representation that is not limited to a narrow tractable parametrised form (nor is it represented by samples). To train the genera- tive and recognition models we develop an extended wake-sleep algorithm inspired by the original Helmholtz machine. This makes it possible to learn hierarchical latent models with both discrete and continuous variables, where an accurate poste- rior representation is essential. We demonstrate that the new algorithm outperforms current state-of-the-art methods on synthetic, natural image patch and the MNIST data sets.