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

arXiv: https://arxiv.org/abs/1905.12892 · HTML: https://mlsanity.com/paper/1905.12892/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2019.

## Built on by (most cited first, 30 of 33)

- [Dual Diffusion Implicit Bridges for Image-to-Image Translation](https://mlsanity.com/paper/2203.08382/) (2022)
- [CyCLIP: Cyclic Contrastive Language-Image Pretraining](https://mlsanity.com/paper/2205.14459/) (2022)
- [Domain Invariant Representation Learning with Domain Density Transformations](https://mlsanity.com/paper/2102.05082/) (2021)
- [Fair Normalizing Flows](https://mlsanity.com/paper/2106.05937/) (2021)
- [TTTFlow: Unsupervised Test-Time Training with Normalizing Flow](https://mlsanity.com/paper/2210.11389/) (2022)
- [Debias Coarsely, Sample Conditionally: Statistical Downscaling through Optimal Transport and Probabilistic Diffusion Models](https://mlsanity.com/paper/2305.15618/) (2023)
- [General Image-to-Image Translation with One-Shot Image Guidance](https://mlsanity.com/paper/2307.14352/) (2023)
- [DeFlow: Learning Complex Image Degradations from Unpaired Data with Conditional Flows](https://mlsanity.com/paper/2101.05796/) (2021)
- [Data synthesis and adversarial networks: A review and meta-analysis in cancer imaging](https://mlsanity.com/paper/2107.09543/) (2021)
- [TrafficFlowGAN: Physics-informed Flow based Generative Adversarial Network for Uncertainty Quantification](https://mlsanity.com/paper/2206.09319/) (2022)
- [Gradual Domain Adaptation via Normalizing Flows](https://mlsanity.com/paper/2206.11492/) (2022)
- [Learning Cycle-Consistent Cooperative Networks via Alternating MCMC Teaching for Unsupervised Cross-Domain Translation](https://mlsanity.com/paper/2103.04285/) (2021)
- [10 Years of Fair Representations: Challenges and Opportunities](https://mlsanity.com/paper/2407.03834/) (2024)
- [Fair Group-Shared Representations with Normalizing Flows](https://mlsanity.com/paper/2201.06336/) (2022)
- [Harmonizing Flows: Unsupervised MR harmonization based on normalizing flows](https://mlsanity.com/paper/2301.11551/) (2023)
- [Iterative Alignment Flows](https://mlsanity.com/paper/2104.07232/) (2021)
- [CAFLOW: Conditional Autoregressive Flows](https://mlsanity.com/paper/2106.02531/) (2021)
- [CDCGen: Cross-Domain Conditional Generation via Normalizing Flows and Adversarial Training](https://mlsanity.com/paper/2108.11368/) (2021)
- [Flow-Adapter Architecture for Unsupervised Machine Translation](https://mlsanity.com/paper/2204.12225/) (2022)
- [Cooperative Distribution Alignment via JSD Upper Bound](https://mlsanity.com/paper/2207.02286/) (2022)
- [Unsupervised Domain Transfer with Conditional Invertible Neural Networks](https://mlsanity.com/paper/2303.10191/) (2023)
- [Harmonizing Flows: Leveraging normalizing flows for unsupervised and source-free MRI harmonization](https://mlsanity.com/paper/2407.15717/) (2024)
- [SerpentFlow: Generative Unpaired Domain Alignment via Shared-Structure Decomposition](https://mlsanity.com/paper/2601.01979/) (2026)
- [Fair Interpretable Representation Learning with Correction Vectors](https://mlsanity.com/paper/2202.03078/) (2022)
- [CROVIA: Seeing Drone Scenes from Car Perspective via Cross-View Adaptation](https://mlsanity.com/paper/2304.07199/) (2023)
- [Domain Translation via Latent Space Mapping](https://mlsanity.com/paper/2212.03361/) (2022)
- [Semi-supervised Learning of Pushforwards For Domain Translation & Adaptation](https://mlsanity.com/paper/2304.08673/) (2023)
- [Towards Practical Non-Adversarial Distribution Matching](https://mlsanity.com/paper/2310.19690/) (2023)
- [Constrained Density Matching and Modeling for Cross-lingual Alignment of Contextualized Representations](https://mlsanity.com/paper/2201.13429/) (2022)
- [How to Construct Energy for Images? Denoising Autoencoder Can Be Energy Based Model](https://mlsanity.com/paper/2303.03887/) (2023)

## Abstract (arXiv)

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.