# Sliced-Wasserstein Autoencoder: An Embarrassingly Simple Generative Model

arXiv: https://arxiv.org/abs/1804.01947 · HTML: https://mlsanity.com/paper/1804.01947/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Apr 2018.

## Built on by (most cited first, 30 of 35)

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- [Learning with Differentially Private (Sliced) Wasserstein Gradients](https://mlsanity.com/paper/2502.01701/) (2025)
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- [Hierarchical Reinforcement Learning with Optimal Level Synchronization Based on Flow-Based Deep Generative Model](https://mlsanity.com/paper/2107.08183/) (2021)
- [Efficient estimates of optimal transport via low-dimensional embeddings](https://mlsanity.com/paper/2111.04838/) (2021)
- [Comparison of Representation Learning Techniques for Tracking in time resolved 3D Ultrasound](https://mlsanity.com/paper/2201.03319/) (2022)
- [Auto-Encoding Goodness of Fit](https://mlsanity.com/paper/2210.06546/) (2022)
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- [Cloud Model Characteristic Function Auto-Encoder: Integrating Cloud Model Theory with MMD Regularization for Enhanced Generative Modeling](https://mlsanity.com/paper/2508.04447/) (2025)
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## Abstract (arXiv)

In this paper we study generative modeling via autoencoders while using the elegant geometric properties of the optimal transport (OT) problem and the Wasserstein distances. We introduce Sliced-Wasserstein Autoencoders (SWAE), which are generative models that enable one to shape the distribution of the latent space into any samplable probability distribution without the need for training an adversarial network or defining a closed-form for the distribution. In short, we regularize the autoencoder loss with the sliced-Wasserstein distance between the distribution of the encoded training samples and a predefined samplable distribution. We show that the proposed formulation has an efficient numerical solution that provides similar capabilities to Wasserstein Autoencoders (WAE) and Variational Autoencoders (VAE), while benefiting from an embarrassingly simple implementation.