  Distribution alignment has many applications in deep learning, including
domain adaptation and unsupervised image-to-image translation. Most prior work
on unsupervised distribution alignment relies either on minimizing simple
non-parametric statistical distances such as maximum mean discrepancy or on
adversarial alignment. However, the former fails to capture the structure of
complex real-world distributions, while the latter is difficult to train and
does not provide any universal convergence guarantees or automatic quantitative
validation procedures. In this paper, we propose a new distribution alignment
method based on a log-likelihood ratio statistic and normalizing flows. We show
that, under certain assumptions, this combination yields a deep neural
likelihood-based minimization objective that attains a known lower bound upon
convergence. We experimentally verify that minimizing the resulting objective
results in domain alignment that preserves the local structure of input
domains.
