# Conditional Sampling via Wasserstein Autoencoders and Triangular Transport

arXiv: https://arxiv.org/abs/2604.02644 · HTML: https://mlsanity.com/paper/2604.02644/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 30 references that are in the map.
- First posted on arXiv 3 Apr 2026.

## Builds on (most cited first, 15 of 15)

- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [SMAC3: A Versatile Bayesian Optimization Package for Hyperparameter Optimization](https://mlsanity.com/paper/2109.09831/) (2021)
- [Back to Basics: Unsupervised Learning of Optical Flow via Brightness Constancy and Motion Smoothness](https://mlsanity.com/paper/1608.05842/) (2016)
- [Conditional Sampling with Monotone GANs: from Generative Models to Likelihood-Free Inference](https://mlsanity.com/paper/2006.06755/) (2020)
- [Likelihood-informed dimension reduction for nonlinear inverse problems](https://mlsanity.com/paper/1403.4680/) (2014)
- [Conditional Optimal Transport on Function Spaces](https://mlsanity.com/paper/2311.05672/) (2023)
- [Nonlinear Filtering with Brenier Optimal Transport Maps](https://mlsanity.com/paper/2310.13886/) (2023)
- [A low-rank ensemble Kalman filter for elliptic observations](https://mlsanity.com/paper/2203.05120/) (2022)
- [Optimal Transportation Methods in Nonlinear Filtering: The feedback particle filter](https://mlsanity.com/paper/2102.10712/) (2021)
- [Paired Wasserstein Autoencoders for Conditional Sampling](https://mlsanity.com/paper/2412.07586/) (2024)
- [Fast filtering of non-Gaussian models using Amortized Optimal Transport Maps](https://mlsanity.com/paper/2503.12633/) (2025)
- [Data-Driven Approximation of Stationary Nonlinear Filters with Optimal Transport Maps](https://mlsanity.com/paper/2403.15630/) (2024)
- [Subspace accelerated measure transport methods for fast and scalable sequential experimental design, with application to photoacoustic imaging](https://mlsanity.com/paper/2502.20086/) (2025)
- [Error Analysis of Triangular Optimal Transport Maps for Filtering](https://mlsanity.com/paper/2510.19283/) (2025)

## Built on by (most cited first, 1 of 1)

- [Generative Priors Conditioned on Natural Language for Bayesian Inversion in PDEs](https://mlsanity.com/paper/2609.32941/) (2026)

## Abstract (arXiv)

We present Conditional Wasserstein Autoencoders (CWAEs), a framework for conditional simulation that exploits low-dimensional structure in both the conditioned and the conditioning variables. The key idea is to modify a Wasserstein autoencoder to use a (block-) triangular decoder and impose an appropriate independence assumption on the latent variables. We show that the resulting model gives an autoencoder that can exploit low-dimensional structure while simultaneously the decoder can be used for conditional simulation. We explore various theoretical properties of CWAEs, including their connections to conditional optimal transport (OT) problems. We also present alternative formulations that lead to three architectural variants forming the foundation of our algorithms. We present a series of numerical experiments that demonstrate that our different CWAE variants achieve substantial reductions in approximation error relative to the low-rank ensemble Kalman filter (LREnKF), particularly in problems where the support of the conditional measures is truly low-dimensional.