  Learning energy-based model (EBM) requires MCMC sampling of the learned model
as an inner loop of the learning algorithm. However, MCMC sampling of EBMs in
high-dimensional data space is generally not mixing, because the energy
function, which is usually parametrized by a deep network, is highly
multi-modal in the data space. This is a serious handicap for both theory and
practice of EBMs. In this paper, we propose to learn an EBM with a flow-based
model (or in general a latent variable model) serving as a backbone, so that
the EBM is a correction or an exponential tilting of the flow-based model. We
show that the model has a particularly simple form in the space of the latent
variables of the backbone model, and MCMC sampling of the EBM in the latent
space mixes well and traverses modes in the data space. This enables proper
sampling and learning of EBMs.
