  This paper studies a training method to jointly estimate an energy-based
model and a flow-based model, in which the two models are iteratively updated
based on a shared adversarial value function. This joint training method has
the following traits. (1) The update of the energy-based model is based on
noise contrastive estimation, with the flow model serving as a strong noise
distribution. (2) The update of the flow model approximately minimizes the
Jensen-Shannon divergence between the flow model and the data distribution. (3)
Unlike generative adversarial networks (GAN) which estimates an implicit
probability distribution defined by a generator model, our method estimates two
explicit probabilistic distributions on the data. Using the proposed method we
demonstrate a significant improvement on the synthesis quality of the flow
model, and show the effectiveness of unsupervised feature learning by the
learned energy-based model. Furthermore, the proposed training method can be
easily adapted to semi-supervised learning. We achieve competitive results to
the state-of-the-art semi-supervised learning methods.
