# Copulas as High-Dimensional Generative Models: Vine Copula Autoencoders

arXiv: https://arxiv.org/abs/1906.05423 · HTML: https://mlsanity.com/paper/1906.05423/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2019.

## Built on by (most cited first, 20 of 20)

- [TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Series](https://mlsanity.com/paper/2310.01327/) (2023)
- [Implicit Generative Copulas](https://mlsanity.com/paper/2109.14567/) (2021)
- [Copula Density Neural Estimation](https://mlsanity.com/paper/2211.15353/) (2022)
- [Generative Archimedean Copulas](https://mlsanity.com/paper/2102.11351/) (2021)
- [COMET Flows: Towards Generative Modeling of Multivariate Extremes and Tail Dependence](https://mlsanity.com/paper/2205.01224/) (2022)
- [Your copula is a classifier in disguise: classification-based copula density estimation](https://mlsanity.com/paper/2411.03014/) (2024)
- [Retrospective Uncertainties for Deep Models using Vine Copulas](https://mlsanity.com/paper/2302.12606/) (2023)
- [Diffusion and Flow-based Copulas: Forgetting and Remembering Dependencies](https://mlsanity.com/paper/2509.19707/) (2025)
- [Inference and Sampling for Archimax Copulas](https://mlsanity.com/paper/2205.14025/) (2022)
- [Causally Disentangled Generative Variational AutoEncoder](https://mlsanity.com/paper/2302.11737/) (2023)
- [Vine Copulas as Differentiable Computational Graphs](https://mlsanity.com/paper/2506.13318/) (2025)
- [Throwing Vines at the Wall: Structure Learning via Random Search](https://mlsanity.com/paper/2510.20035/) (2025)
- [A Scalable Inter-edge Correlation Modeling in CopulaGNN for Link Sign Prediction](https://mlsanity.com/paper/2601.19175/) (2026)
- [Amortized Vine Copulas for High-Dimensional Density and Information Estimation](https://mlsanity.com/paper/2604.20568/) (2026)
- [Learning Nonparametric High-Dimensional Generative Models: The Empirical-Beta-Copula Autoencoder](https://mlsanity.com/paper/2309.09916/) (2023)
- [A Copula-Guided Temporal Dependency Method for Multitemporal Hyperspectral Images Unmixing](https://mlsanity.com/paper/2509.11096/) (2025)
- [Cross-Modal Alignment via Variational Copula Modelling](https://mlsanity.com/paper/2511.03196/) (2025)
- [Stepwise Variational Inference with Vine Copulas](https://mlsanity.com/paper/2603.22959/) (2026)
- [Dynamic Vine Copulas: Detecting and Quantifying Time-Varying Higher-Order Interactions](https://mlsanity.com/paper/2605.03061/) (2026)
- [MIND: Marginal-Invariant Neural Dependency Diffusion for Mixed-Type Tabular Generation](https://mlsanity.com/paper/2609.39628/) (2026)

## Abstract (arXiv)

We introduce the vine copula autoencoder (VCAE), a flexible generative model for high-dimensional distributions built in a straightforward three-step procedure. First, an autoencoder (AE) compresses the data into a lower dimensional representation. Second, the multivariate distribution of the encoded data is estimated with vine copulas. Third, a generative model is obtained by combining the estimated distribution with the decoder part of the AE. As such, the proposed approach can transform any already trained AE into a flexible generative model at a low computational cost. This is an advantage over existing generative models such as adversarial networks and variational AEs which can be difficult to train and can impose strong assumptions on the latent space. Experiments on MNIST, Street View House Numbers and Large-Scale CelebFaces Attributes datasets show that VCAEs can achieve competitive results to standard baselines.