# Copula & Marginal Flows: Disentangling the Marginal from its Joint

arXiv: https://arxiv.org/abs/1907.03361 · HTML: https://mlsanity.com/paper/1907.03361/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2019.

## Built on by (most cited first, 17 of 17)

- [TACTiS: Transformer-Attentional Copulas for Time Series](https://mlsanity.com/paper/2202.03528/) (2022)
- [TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Series](https://mlsanity.com/paper/2310.01327/) (2023)
- [Pareto GAN: Extending the Representational Power of GANs to Heavy-Tailed Distributions](https://mlsanity.com/paper/2101.09113/) (2021)
- [Marginal Tail-Adaptive Normalizing Flows](https://mlsanity.com/paper/2206.10311/) (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)
- [Copula-Based Normalizing Flows](https://mlsanity.com/paper/2107.07352/) (2021)
- [Quasi-Bayesian Nonparametric Density Estimation via Autoregressive Predictive Updates](https://mlsanity.com/paper/2206.06462/) (2022)
- [Generative Machine Learning for Multivariate Angular Simulation](https://mlsanity.com/paper/2504.21505/) (2025)
- [On some theoretical limitations of Generative Adversarial Networks](https://mlsanity.com/paper/2110.10915/) (2021)
- [Robust training of implicit generative models for multivariate and heavy-tailed distributions with an invariant statistical loss](https://mlsanity.com/paper/2410.22381/) (2024)
- [Graphical Transformation Models](https://mlsanity.com/paper/2503.17845/) (2025)
- [Amortized Vine Copulas for High-Dimensional Density and Information Estimation](https://mlsanity.com/paper/2604.20568/) (2026)
- [Extrapolation in Statistical Learning with Extreme Value Theory](https://mlsanity.com/paper/2605.01909/) (2026)
- [Modelling and simulating spatial extremes by combining extreme value theory with generative adversarial networks](https://mlsanity.com/paper/2111.00267/) (2021)
- [Adapting Noise to Data: Generative Flows from 1D Processes](https://mlsanity.com/paper/2510.12636/) (2025)
- [An Extreme Value Perspective on Learning Stress Laws](https://mlsanity.com/paper/2607.10700/) (2026)

## Abstract (arXiv)

Deep generative networks such as GANs and normalizing flows flourish in the context of high-dimensional tasks such as image generation. However, so far exact modeling or extrapolation of distributional properties such as the tail asymptotics generated by a generative network is not available. In this paper, we address this issue for the first time in the deep learning literature by making two novel contributions. First, we derive upper bounds for the tails that can be expressed by a generative network and demonstrate Lp-space related properties. There we show specifically that in various situations an optimal generative network does not exist. Second, we introduce and propose copula and marginal generative flows (CM flows) which allow for an exact modeling of the tail and any prior assumption on the CDF up to an approximation of the uniform distribution. Our numerical results support the use of CM flows.