# Gromov-Wasserstein Autoencoders

arXiv: https://arxiv.org/abs/2209.07007 · HTML: https://mlsanity.com/paper/2209.07007/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 89 references that are in the map.
- First posted on arXiv 15 Sep 2022.

## Builds on (most cited first, 30 of 50)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Deep Variational Information Bottleneck](https://mlsanity.com/paper/1612.00410/) (2016)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Self-labelling via simultaneous clustering and representation learning](https://mlsanity.com/paper/1911.05371/) (2019)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Autoencoding beyond pixels using a learned similarity metric](https://mlsanity.com/paper/1512.09300/) (2015)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Adversarial Feature Learning](https://mlsanity.com/paper/1605.09782/) (2016)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [Toward Controlled Generation of Text](https://mlsanity.com/paper/1703.00955/) (2017)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [Adversarially Learned Inference](https://mlsanity.com/paper/1606.00704/) (2016)
- [Flexibly Fair Representation Learning by Disentanglement](https://mlsanity.com/paper/1906.02589/) (2019)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [DARLA: Improving Zero-Shot Transfer in Reinforcement Learning](https://mlsanity.com/paper/1707.08475/) (2017)
- [On the Fairness of Disentangled Representations](https://mlsanity.com/paper/1905.13662/) (2019)
- [Recent Advances in Autoencoder-Based Representation Learning](https://mlsanity.com/paper/1812.05069/) (2018)
- [Information Dropout: Learning Optimal Representations Through Noisy Computation](https://mlsanity.com/paper/1611.01353/) (2016)
- [Adversarial Variational Bayes: Unifying Variational Autoencoders and Generative Adversarial Networks](https://mlsanity.com/paper/1701.04722/) (2017)
- [Measuring Disentanglement: A Review of Metrics](https://mlsanity.com/paper/2012.09276/) (2020)

## Built on by (most cited first, 7 of 7)

- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Preventing Model Collapse in Gaussian Process Latent Variable Models](https://mlsanity.com/paper/2404.01697/) (2024)
- [Monotone Generative Modeling via a Gromov-Monge Embedding](https://mlsanity.com/paper/2311.01375/) (2023)
- [Simplex Autoencoders](https://mlsanity.com/paper/2301.06489/) (2023)
- [Sparsification and Reconstruction from the Perspective of Representation Geometry](https://mlsanity.com/paper/2505.22506/) (2025)
- [Relation-Aware Slicing in Cross-Domain Alignment](https://mlsanity.com/paper/2507.13194/) (2025)
- [TRANSPORTER: Transferring Visual Semantics from VLM Manifolds](https://mlsanity.com/paper/2511.18359/) (2025)

## Abstract (arXiv)

Variational Autoencoder (VAE)-based generative models offer flexible representation learning by incorporating meta-priors, general premises considered beneficial for downstream tasks. However, the incorporated meta-priors often involve ad-hoc model deviations from the original likelihood architecture, causing undesirable changes in their training. In this paper, we propose a novel representation learning method, Gromov-Wasserstein Autoencoders (GWAE), which directly matches the latent and data distributions using the variational autoencoding scheme. Instead of likelihood-based objectives, GWAE models minimize the Gromov-Wasserstein (GW) metric between the trainable prior and given data distributions. The GW metric measures the distance structure-oriented discrepancy between distributions even with different dimensionalities, which provides a direct measure between the latent and data spaces. By restricting the prior family, we can introduce meta-priors into the latent space without changing their objective. The empirical comparisons with VAE-based models show that GWAE models work in two prominent meta-priors, disentanglement and clustering, with their GW objective unchanged.