  We introduce the thermodynamic variational objective (TVO) for learning in
both continuous and discrete deep generative models. The TVO arises from a key
connection between variational inference and thermodynamic integration that
results in a tighter lower bound to the log marginal likelihood than the
standard variational variational evidence lower bound (ELBO) while remaining as
broadly applicable. We provide a computationally efficient gradient estimator
for the TVO that applies to continuous, discrete, and non-reparameterizable
distributions and show that the objective functions used in variational
inference, variational autoencoders, wake sleep, and inference compilation are
all special cases of the TVO. We use the TVO to learn both discrete and
continuous deep generative models and empirically demonstrate state of the art
model and inference network learning.
