# Paired Wasserstein Autoencoders for Conditional Sampling

arXiv: https://arxiv.org/abs/2412.07586 · HTML: https://mlsanity.com/paper/2412.07586/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 26 references that are in the map.
- First posted on arXiv 10 Dec 2024.

## Builds on (most cited first, 11 of 11)

- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Neural Optimal Transport](https://mlsanity.com/paper/2201.12220/) (2022)
- [Unpaired Image-to-Image Translation via Neural Schr"odinger Bridge](https://mlsanity.com/paper/2305.15086/) (2023)
- [Schr"odinger Bridge Flow for Unpaired Data Translation](https://mlsanity.com/paper/2409.09347/) (2024)
- [Generative Sliced MMD Flows with Riesz Kernels](https://mlsanity.com/paper/2305.11463/) (2023)
- [The Monge Gap: A Regularizer to Learn All Transport Maps](https://mlsanity.com/paper/2302.04953/) (2023)
- [Tutorial: Deriving the Standard Variational Autoencoder (VAE) Loss Function](https://mlsanity.com/paper/1907.08956/) (2019)
- [Learning from small data sets: Patch-based regularizers in inverse problems for image reconstruction](https://mlsanity.com/paper/2312.16611/) (2023)
- [Coupled Variational Autoencoder](https://mlsanity.com/paper/2306.02565/) (2023)
- [Stacked Wasserstein Autoencoder](https://mlsanity.com/paper/1910.02560/) (2019)

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

- [Good Things Come in Pairs: Paired Autoencoders for Inverse Problems](https://mlsanity.com/paper/2505.06549/) (2025)
- [Latent Twins](https://mlsanity.com/paper/2509.20615/) (2025)
- [Conditional Sampling via Wasserstein Autoencoders and Triangular Transport](https://mlsanity.com/paper/2604.02644/) (2026)
- [Variational Sparse Paired Autoencoders (vsPAIR) for Inverse Problems and Uncertainty Quantification](https://mlsanity.com/paper/2602.02948/) (2026)
- [Graph-Informed Adversarial Modeling: Infimal Subadditivity of Interpolative Divergences](https://mlsanity.com/paper/2603.20025/) (2026)

## Abstract (arXiv)

Generative autoencoders learn compact latent representations of data distributions through jointly optimized encoder--decoder pairs. In particular, Wasserstein autoencoders (WAEs) minimize a relaxed optimal transport (OT) objective, where similarity between distributions is measured through a cost-minimizing joint distribution (OT coupling). Beyond distribution matching, neural OT methods aim to learn mappings between two data distributions induced by an OT coupling. Building on the formulation of the WAE loss, we derive a novel loss that enables sampling from OT-type couplings via two paired WAEs with shared latent space. The resulting fully parametrized joint distribution yields (i) learned cost-optimal transport maps between the two data distributions via deterministic encoders. Under cost-consistency constraints, it further enables (ii) conditional sampling from an OT-type coupling through stochastic decoders. As a proof of concept, we use synthetic data with known and visualizable marginal and conditional distributions.