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

arXiv: https://arxiv.org/abs/2003.12170 · HTML: https://mlsanity.com/paper/2003.12170/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Mar 2020.

## Built on by (most cited first, 10 of 10)

- [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)
- [Gradual Domain Adaptation via Normalizing Flows](https://mlsanity.com/paper/2206.11492/) (2022)
- [Harmonizing Flows: Unsupervised MR harmonization based on normalizing flows](https://mlsanity.com/paper/2301.11551/) (2023)
- [BlindHarmony: "Blind" Harmonization for MR Images via Flow model](https://mlsanity.com/paper/2305.10732/) (2023)
- [Iterative Alignment Flows](https://mlsanity.com/paper/2104.07232/) (2021)
- [Cooperative Distribution Alignment via JSD Upper Bound](https://mlsanity.com/paper/2207.02286/) (2022)
- [Harmonizing Flows: Leveraging normalizing flows for unsupervised and source-free MRI harmonization](https://mlsanity.com/paper/2407.15717/) (2024)
- [Towards Practical Non-Adversarial Distribution Matching](https://mlsanity.com/paper/2310.19690/) (2023)
- [Zero Flux: Flow-Based Comparison of High-Dimensional Discrete Distributions](https://mlsanity.com/paper/2610.01472/) (2026)

## Abstract (arXiv)

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.