# Momentum Contrastive Autoencoder: Using Contrastive Learning for Latent Space Distribution Matching in WAE

arXiv: https://arxiv.org/abs/2110.10303 · HTML: https://mlsanity.com/paper/2110.10303/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 42 references that are in the map.
- First posted on arXiv 19 Oct 2021.

## Builds on (most cited first, 29 of 29)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Bootstrap your own latent: A new approach to self-supervised Learning](https://mlsanity.com/paper/2006.07733/) (2020)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Understanding Contrastive Representation Learning through Alignment and Uniformity on the Hypersphere](https://mlsanity.com/paper/2005.10242/) (2020)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [Adversarial Feature Learning](https://mlsanity.com/paper/1605.09782/) (2016)
- [VAE with a VampPrior](https://mlsanity.com/paper/1705.07120/) (2017)
- [Adversarially Learned Inference](https://mlsanity.com/paper/1606.00704/) (2016)
- [Diagnosing and Enhancing VAE Models](https://mlsanity.com/paper/1903.05789/) (2019)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [Variational Lossy Autoencoder](https://mlsanity.com/paper/1611.02731/) (2016)
- [From Variational to Deterministic Autoencoders](https://mlsanity.com/paper/1903.12436/) (2019)
- [Mode Regularized Generative Adversarial Networks](https://mlsanity.com/paper/1612.02136/) (2016)
- [Generalized Denoising Auto-Encoders as Generative Models](https://mlsanity.com/paper/1305.6663/) (2013)
- [Dual Contradistinctive Generative Autoencoder](https://mlsanity.com/paper/2011.10063/) (2020)
- [Resampled Priors for Variational Autoencoders](https://mlsanity.com/paper/1810.11428/) (2018)
- [Towards Deeper Understanding of Variational Autoencoding Models](https://mlsanity.com/paper/1702.08658/) (2017)
- [From optimal transport to generative modeling: the VEGAN cookbook](https://mlsanity.com/paper/1705.07642/) (2017)
- [Cramer-Wold AutoEncoder](https://mlsanity.com/paper/1805.09235/) (2018)

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

- [Latent Zoning Network: A Unified Principle for Generative Modeling, Representation Learning, and Classification](https://mlsanity.com/paper/2509.15591/) (2025)

## Abstract (arXiv)

Wasserstein autoencoder (WAE) shows that matching two distributions is equivalent to minimizing a simple autoencoder (AE) loss under the constraint that the latent space of this AE matches a pre-specified prior distribution. This latent space distribution matching is a core component of WAE, and a challenging task. In this paper, we propose to use the contrastive learning framework that has been shown to be effective for self-supervised representation learning, as a means to resolve this problem. We do so by exploiting the fact that contrastive learning objectives optimize the latent space distribution to be uniform over the unit hyper-sphere, which can be easily sampled from. We show that using the contrastive learning framework to optimize the WAE loss achieves faster convergence and more stable optimization compared with existing popular algorithms for WAE. This is also reflected in the FID scores on CelebA and CIFAR-10 datasets, and the realistic generated image quality on the CelebA-HQ dataset.