# Towards Identifiable Unsupervised Domain Translation: A Diversified Distribution Matching Approach

arXiv: https://arxiv.org/abs/2401.09671 · HTML: https://mlsanity.com/paper/2401.09671/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 63 references that are in the map.
- First posted on arXiv 18 Jan 2024.

## Builds on (most cited first, 30 of 47)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [High-Resolution Image Synthesis and Semantic Manipulation with Conditional GANs](https://mlsanity.com/paper/1711.11585/) (2017)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Least Squares Generative Adversarial Networks](https://mlsanity.com/paper/1611.04076/) (2016)
- [Multimodal Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/1804.04732/) (2018)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [Contrastive Learning for Unpaired Image-to-Image Translation](https://mlsanity.com/paper/2007.15651/) (2020)
- [Unsupervised Image-to-Image Translation Networks](https://mlsanity.com/paper/1703.00848/) (2017)
- [Word Translation Without Parallel Data](https://mlsanity.com/paper/1710.04087/) (2017)
- [Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style](https://mlsanity.com/paper/2106.04619/) (2021)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning](https://mlsanity.com/paper/1805.08651/) (2018)
- [Learning to Discover Cross-Domain Relations with Generative Adversarial Networks](https://mlsanity.com/paper/1703.05192/) (2017)
- [Unsupervised Machine Translation Using Monolingual Corpora Only](https://mlsanity.com/paper/1711.00043/) (2017)
- [Few-Shot Unsupervised Image-to-Image Translation](https://mlsanity.com/paper/1905.01723/) (2019)
- [Contrastive Learning Inverts the Data Generating Process](https://mlsanity.com/paper/2102.08850/) (2021)
- [Coupled Generative Adversarial Networks](https://mlsanity.com/paper/1606.07536/) (2016)
- [U-GAT-IT: Unsupervised Generative Attentional Networks with Adaptive Layer-Instance Normalization for Image-to-Image Translation](https://mlsanity.com/paper/1907.10830/) (2019)
- [Unsupervised Cross-Domain Image Generation](https://mlsanity.com/paper/1611.02200/) (2016)
- [Image-to-Image Translation: Methods and Applications](https://mlsanity.com/paper/2101.08629/) (2021)
- [The Unusual Effectiveness of Averaging in GAN Training](https://mlsanity.com/paper/1806.04498/) (2018)

## Built on by (most cited first, 5 of 5)

- [Diverse Influence Component Analysis: A Geometric Approach to Nonlinear Mixture Identifiability](https://mlsanity.com/paper/2510.17040/) (2025)
- [Identifiable Shared Component Analysis of Unpaired Multimodal Mixtures](https://mlsanity.com/paper/2409.19422/) (2024)
- [Content-Style Learning from Unaligned Domains: Identifiability under Unknown Latent Dimensions](https://mlsanity.com/paper/2411.03755/) (2024)
- [Unregistered Spectral Image Fusion: Unmixing, Adversarial Learning, and Recoverability](https://mlsanity.com/paper/2603.21510/) (2026)
- [Domain Transfer Becomes Identifiable via a Single Alignment](https://mlsanity.com/paper/2605.17918/) (2026)

## Abstract (arXiv)

Unsupervised domain translation (UDT) aims to find functions that convert samples from one domain (e.g., sketches) to another domain (e.g., photos) without changing the high-level semantic meaning (also referred to as ``content''). The translation functions are often sought by probability distribution matching of the transformed source domain and target domain. CycleGAN stands as arguably the most representative approach among this line of work. However, it was noticed in the literature that CycleGAN and variants could fail to identify the desired translation functions and produce content-misaligned translations. This limitation arises due to the presence of multiple translation functions -- referred to as ``measure-preserving automorphism" (MPA) -- in the solution space of the learning criteria. Despite awareness of such identifiability issues, solutions have remained elusive. This study delves into the core identifiability inquiry and introduces an MPA elimination theory. Our analysis shows that MPA is unlikely to exist, if multiple pairs of diverse cross-domain conditional distributions are matched by the learning function. Our theory leads to a UDT learner using distribution matching over auxiliary variable-induced subsets of the domains -- other than over the entire data domains as in the classical approaches. The proposed framework is the first to rigorously establish translation identifiability under reasonable UDT settings, to our best knowledge. Experiments corroborate with our theoretical claims.