# Cooperative Distribution Alignment via JSD Upper Bound

arXiv: https://arxiv.org/abs/2207.02286 · HTML: https://mlsanity.com/paper/2207.02286/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 38 references that are in the map.
- First posted on arXiv 5 Jul 2022.

## Builds on (most cited first, 24 of 24)

- [Domain-Adversarial Training of Neural Networks](https://mlsanity.com/paper/1505.07818/) (2015)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [StarGAN: Unified Generative Adversarial Networks for Multi-Domain Image-to-Image Translation](https://mlsanity.com/paper/1711.09020/) (2017)
- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Are GANs Created Equal? A Large-Scale Study](https://mlsanity.com/paper/1711.10337/) (2017)
- [Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design](https://mlsanity.com/paper/1902.00275/) (2019)
- [Residual Flows for Invertible Generative Modeling](https://mlsanity.com/paper/1906.02735/) (2019)
- [Pros and Cons of GAN Evaluation Measures](https://mlsanity.com/paper/1802.03446/) (2018)
- [On Aliased Resizing and Surprising Subtleties in GAN Evaluation](https://mlsanity.com/paper/2104.11222/) (2021)
- [Sliced Iterative Normalizing Flows](https://mlsanity.com/paper/2007.00674/) (2020)
- [AlignFlow: Cycle Consistent Learning from Multiple Domains via Normalizing Flows](https://mlsanity.com/paper/1905.12892/) (2019)
- [A Large-Scale Study on Regularization and Normalization in GANs](https://mlsanity.com/paper/1807.04720/) (2018)
- [Improving GAN Training with Probability Ratio Clipping and Sample Reweighting](https://mlsanity.com/paper/2006.06900/) (2020)
- [Log-Likelihood Ratio Minimizing Flows: Towards Robust and Quantifiable Neural Distribution Alignment](https://mlsanity.com/paper/2003.12170/) (2020)
- [Iterative Alignment Flows](https://mlsanity.com/paper/2104.07232/) (2021)

## Built on by (most cited first, 4 of 4)

- [Rethinking Multi-domain Generalization with A General Learning Objective](https://mlsanity.com/paper/2402.18853/) (2024)
- [Towards a Universal 3D Medical Multi-modality Generalization via Learning Personalized Invariant Representation](https://mlsanity.com/paper/2411.06106/) (2024)
- [Towards Practical Non-Adversarial Distribution Matching](https://mlsanity.com/paper/2310.19690/) (2023)
- [Expressive Score-Based Priors for Distribution Matching with Geometry-Preserving Regularization](https://mlsanity.com/paper/2506.14607/) (2025)

## Abstract (arXiv)

Unsupervised distribution alignment estimates a transformation that maps two or more source distributions to a shared aligned distribution given only samples from each distribution. This task has many applications including generative modeling, unsupervised domain adaptation, and socially aware learning. Most prior works use adversarial learning (i.e., min-max optimization), which can be challenging to optimize and evaluate. A few recent works explore non-adversarial flow-based (i.e., invertible) approaches, but they lack a unified perspective and are limited in efficiently aligning multiple distributions. Therefore, we propose to unify and generalize previous flow-based approaches under a single non-adversarial framework, which we prove is equivalent to minimizing an upper bound on the Jensen-Shannon Divergence (JSD). Importantly, our problem reduces to a min-min, i.e., cooperative, problem and can provide a natural evaluation metric for unsupervised distribution alignment. We show empirical results on both simulated and real-world datasets to demonstrate the benefits of our approach. Code is available at https://github.com/inouye-lab/alignment-upper-bound.