# C2VAE: Gaussian Copula-based VAE Differing Disentangled from Coupled Representations with Contrastive Posterior

arXiv: https://arxiv.org/abs/2309.13303 · HTML: https://mlsanity.com/paper/2309.13303/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 52 references that are in the map.
- First posted on arXiv 23 Sep 2023.

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

- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Importance Weighted Autoencoders](https://mlsanity.com/paper/1509.00519/) (2015)
- [Ladder Variational Autoencoders](https://mlsanity.com/paper/1602.02282/) (2016)
- [Variational Inference of Disentangled Latent Concepts from Unlabeled Observations](https://mlsanity.com/paper/1711.00848/) (2017)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [DIVA: Domain Invariant Variational Autoencoders](https://mlsanity.com/paper/1905.10427/) (2019)
- [Measuring Disentanglement: A Review of Metrics](https://mlsanity.com/paper/2012.09276/) (2020)
- [Structured Disentangled Representations](https://mlsanity.com/paper/1804.02086/) (2018)
- [Progressive Learning and Disentanglement of Hierarchical Representations](https://mlsanity.com/paper/2002.10549/) (2020)
- [Contrastive Variational Autoencoder Enhances Salient Features](https://mlsanity.com/paper/1902.04601/) (2019)
- [Adversarial and Contrastive Variational Autoencoder for Sequential Recommendation](https://mlsanity.com/paper/2103.10693/) (2021)
- [ContrastVAE: Contrastive Variational AutoEncoder for Sequential Recommendation](https://mlsanity.com/paper/2209.00456/) (2022)
- [Deep Generative Quantile-Copula Models for Probabilistic Forecasting](https://mlsanity.com/paper/1907.10697/) (2019)
- [Auto-Encoding Total Correlation Explanation](https://mlsanity.com/paper/1802.05822/) (2018)
- [Deep Generative model with Hierarchical Latent Factors for Time Series Anomaly Detection](https://mlsanity.com/paper/2202.07586/) (2022)
- [Robust Variational Autoencoder for Tabular Data with Beta Divergence](https://mlsanity.com/paper/2006.08204/) (2020)
- [Continual Variational Autoencoder Learning via Online Cooperative Memorization](https://mlsanity.com/paper/2207.10131/) (2022)
- [Generative Oversampling for Imbalanced Data via Majority-Guided VAE](https://mlsanity.com/paper/2302.10910/) (2023)
- [Neural Gaussian Copula for Variational Autoencoder](https://mlsanity.com/paper/1909.03569/) (2019)
- [Robust outlier detection by de-biasing VAE likelihoods](https://mlsanity.com/paper/2108.08760/) (2021)
- [eVAE: Evolutionary Variational Autoencoder](https://mlsanity.com/paper/2301.00011/) (2023)
- [Multiband VAE: Latent Space Alignment for Knowledge Consolidation in Continual Learning](https://mlsanity.com/paper/2106.12196/) (2021)
- [Disentangling Learning Representations with Density Estimation](https://mlsanity.com/paper/2302.04362/) (2023)
- [Copula Variational LSTM for High-dimensional Cross-market Multivariate Dependence Modeling](https://mlsanity.com/paper/2305.08778/) (2023)

## Built on by (most cited first, 2 of 2)

- [SCoT: Unifying Consistency Models and Rectified Flows via Straight-Consistent Trajectories](https://mlsanity.com/paper/2502.16972/) (2025)
- [Weakly Augmented Variational Autoencoder in Time Series Anomaly Detection](https://mlsanity.com/paper/2401.03341/) (2024)

## Abstract (arXiv)

We present a self-supervised variational autoencoder (VAE) to jointly learn disentangled and dependent hidden factors and then enhance disentangled representation learning by a self-supervised classifier to eliminate coupled representations in a contrastive manner. To this end, a Contrastive Copula VAE (C2VAE) is introduced without relying on prior knowledge about data in the probabilistic principle and involving strong modeling assumptions on the posterior in the neural architecture. C2VAE simultaneously factorizes the posterior (evidence lower bound, ELBO) with total correlation (TC)-driven decomposition for learning factorized disentangled representations and extracts the dependencies between hidden features by a neural Gaussian copula for copula coupled representations. Then, a self-supervised contrastive classifier differentiates the disentangled representations from the coupled representations, where a contrastive loss regularizes this contrastive classification together with the TC loss for eliminating entangled factors and strengthening disentangled representations. C2VAE demonstrates a strong effect in enhancing disentangled representation learning. C2VAE further contributes to improved optimization addressing the TC-based VAE instability and the trade-off between reconstruction and representation.