# AlignFlow: Cycle Consistent Learning from Multiple Domains via Normalizing Flows

## TL;DR

AlignFlow introduces a flexible generative framework using normalizing flows for multi-domain modeling, ensuring cycle consistency and superior performance in image translation and domain adaptation tasks.

## Contribution

It presents a novel normalizing flow-based approach that guarantees cycle consistency and supports multiple learning objectives for multi-domain data modeling.

## Key findings

- Outperforms relevant baselines in image-to-image translation
- Achieves exact cycle consistency in domain mappings
- Enables interpolation across multiple domains

## Abstract

Given datasets from multiple domains, a key challenge is to efficiently exploit these data sources for modeling a target domain. Variants of this problem have been studied in many contexts, such as cross-domain translation and domain adaptation. We propose AlignFlow, a generative modeling framework that models each domain via a normalizing flow. The use of normalizing flows allows for a) flexibility in specifying learning objectives via adversarial training, maximum likelihood estimation, or a hybrid of the two methods; and b) learning and exact inference of a shared representation in the latent space of the generative model. We derive a uniform set of conditions under which AlignFlow is marginally-consistent for the different learning objectives. Furthermore, we show that AlignFlow guarantees exact cycle consistency in mapping datapoints from a source domain to target and back to the source domain. Empirically, AlignFlow outperforms relevant baselines on image-to-image translation and unsupervised domain adaptation and can be used to simultaneously interpolate across the various domains using the learned representation.