  Energy-based models (EBMs) are versatile density estimation models that
directly parameterize an unnormalized log density. Although very flexible, EBMs
lack a specified normalization constant of the model, making the likelihood of
the model computationally intractable. Several approximate samplers and
variational inference techniques have been proposed to estimate the likelihood
gradients for training. These techniques have shown promising results in
generating samples, but little attention has been paid to the statistical
accuracy of the estimated density, such as determining the relative importance
of different classes in a dataset. In this work, we propose a new maximum
likelihood training algorithm for EBMs that uses a different type of generative
model, normalizing flows (NF), which have recently been proposed to facilitate
sampling. Our method fits an NF to an EBM during training so that an
NF-assisted sampling scheme provides an accurate gradient for the EBMs at all
times, ultimately leading to a fast sampler for generating new data.
