  We formalize the problem of learning interdomain correspondences in the
absence of paired data as Bayesian inference in a latent variable model (LVM),
where one seeks the underlying hidden representations of entities from one
domain as entities from the other domain. First, we introduce implicit latent
variable models, where the prior over hidden representations can be specified
flexibly as an implicit distribution. Next, we develop a new variational
inference (VI) algorithm for this model based on minimization of the symmetric
Kullback-Leibler (KL) divergence between a variational joint and the exact
joint distribution. Lastly, we demonstrate that the state-of-the-art
cycle-consistent adversarial learning (CYCLEGAN) models can be derived as a
special case within our proposed VI framework, thus establishing its connection
to approximate Bayesian inference methods.
