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Distribution alignment has many applications in deep learning, includingdomain adaptation and unsupervised image-to-image translation. Most prior workon unsupervised distribution alignment relies either on minimizing simplenon-parametric statistical distances such as maximum mean discrepancy or onadversarial alignment. However, the former fails to capture the structure ofcomplex real-world distributions, while the latter is difficult to train anddoes not provide any universal convergence guarantees or automatic quantitativevalidation procedures. In this paper, we propose a new distribution alignmentmethod based on a log-likelihood ratio statistic and normalizing flows. We showthat, under certain assumptions, this combination yields a deep neurallikelihood-based minimization objective that attains a known lower bound uponconvergence. We experimentally verify that minimizing the resulting objectiveresults in domain alignment that preserves the local structure of inputdomains.

Log-Likelihood Ratio Minimizing Flows: Towards Robust and Quantifiable Neural Distribution Alignment