Unsupervised learning is about capturing dependencies between variables and is driven by the contrast between the probable vs improbable configurations of these variables, often either via a generative model which only samples probable ones or with an energy function (unnormalized log-density) which is low for probable ones and high for improbable ones. Here we consider learning both an energy function and an efficient approximate sampling mechanism for the corresponding distribution... Whereas the critic (or discriminator) in generative adversarial networks (GANs) learns to separate data and generator samples, introducing an entropy maximization regularizer on the generator can turn the interpretation of the critic into an energy function, which separates the training distribution from everything else, and thus can be used for tasks like anomaly or novelty detection. This paper is motivated by the older idea of sampling in latent space rather than data space because running a Monte-Carlo Markov Chain (MCMC) in latent space has been found to be easier and more efficient, and because a GAN-like generator can convert latent space samples to data space samples. For this purpose, we show how a Markov chain can be run in latent space whose samples can be mapped to data space, producing better samples. These samples are also used for the negative phase gradient required to estimate the log-likelihood gradient of the data space energy function. To maximize entropy at the output of the generator, we take advantage of recently introduced neural estimators of mutual information. We find that in addition to producing a useful scoring function for anomaly detection, the resulting approach produces sharp samples (like GANs) while covering the modes well, leading to high Inception and Fréchet scores. (read more)