  The Energy-Based Model (EBM) framework is a very general approach to
generative modeling that tries to learn and exploit probability distributions
only defined though unnormalized scores. It has risen in popularity recently
thanks to the impressive results obtained in image generation by parameterizing
the distribution with Convolutional Neural Networks (CNN). However, the
motivation and theoretical foundations behind modern EBMs are often absent from
recent papers and this sometimes results in some confusion. In particular, the
theoretical justifications behind the popular MCMC-based learning algorithm
Contrastive Divergence (CD) are often glossed over and we find that this leads
to theoretical errors in recent influential papers (Du & Mordatch, 2019; Du et
al., 2020). After offering a first-principles introduction of MCMC-based
training, we argue that the learning algorithm they use can in fact not be
described as CD and reinterpret theirs methods in light of a new
interpretation. Finally, we discuss the implications of our new interpretation
and provide some illustrative experiments.
