# Wasserstein Auto-Encoders

**Authors:** Ilya Tolstikhin, Olivier Bousquet, Sylvain Gelly, Bernhard Schoelkopf  
**arXiv:** [1711.01558](https://arxiv.org/abs/1711.01558)  
**Date:** 2017-11-05  
**Summary page:** https://www.summarizepaper.com/en/paper/1711.01558v1/

## Key points

- The Wasserstein Auto-Encoder (WAE) is a novel algorithm for generative modeling of data distributions
- WAE minimizes a penalized form of the Wasserstein distance between the model distribution and the target distribution
- WAE is a generalization of adversarial auto-encoders (AAE)
- WAE outperforms Variational Auto-Encoders (VAEs) in terms of sample quality, as measured by the FID score
- WAE generates samples of better quality compared to existing methods
- The improvement in sample quality is attributed to the use of the penalized Wasserstein distance and its associated regularizer
- WAE maintains stable training and a well-defined latent manifold structure, similar to VAEs
- WAE introduces an innovative approach for generative modeling using Wasserstein Auto-Encoders

## Summary

The Wasserstein Auto-Encoder (WAE) is a novel algorithm proposed by Ilya Tolstikhin, Olivier Bousquet, Sylvain Gelly, and Bernhard Schoelkopf for building generative models of data distributions. Unlike the Variational Auto-Encoder (VAE), WAE minimizes a penalized form of the Wasserstein distance between the model distribution and the target distribution. This leads to a different regularizer that encourages the encoded training distribution to match the prior. In their study, the authors compare WAE with several other techniques and demonstrate that it is a generalization of adversarial auto-encoders (AAE). The experiments conducted show that WAE shares many properties with VAEs, such as stable training and an encoder-decoder architecture. However, WAE outperforms VAEs in terms of sample quality, as measured by the FID score. The authors highlight that WAE generates samples of better quality compared to existing methods. This improvement in sample quality is attributed to the use of the penalized Wasserstein distance and its associated regularizer. Additionally, WAE maintains desirable properties found in VAEs, such as stable training and a well-defined latent manifold structure. Overall, this research introduces an innovative approach for generative modeling using Wasserstein Auto-Encoders. The findings suggest that WAE can produce higher-quality samples compared to traditional methods like VAEs while retaining important characteristics such as stability during training and a latent manifold structure.