  We propose to learn energy-based model (EBM) in the latent space of a
generator model, so that the EBM serves as a prior model that stands on the
top-down network of the generator model. Both the latent space EBM and the
top-down network can be learned jointly by maximum likelihood, which involves
short-run MCMC sampling from both the prior and posterior distributions of the
latent vector. Due to the low dimensionality of the latent space and the
expressiveness of the top-down network, a simple EBM in latent space can
capture regularities in the data effectively, and MCMC sampling in latent space
is efficient and mixes well. We show that the learned model exhibits strong
performances in terms of image and text generation and anomaly detection. The
one-page code can be found in supplementary materials.
