# COMET Flows: Towards Generative Modeling of Multivariate Extremes and Tail Dependence

arXiv: https://arxiv.org/abs/2205.01224 · HTML: https://mlsanity.com/paper/2205.01224/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 32 references that are in the map.
- First posted on arXiv 2 May 2022.

## Builds on (most cited first, 20 of 20)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [Flows for simultaneous manifold learning and density estimation](https://mlsanity.com/paper/2003.13913/) (2020)
- [SoftFlow: Probabilistic Framework for Normalizing Flow on Manifolds](https://mlsanity.com/paper/2006.04604/) (2020)
- [Discretize-Optimize vs. Optimize-Discretize for Time-Series Regression and Continuous Normalizing Flows](https://mlsanity.com/paper/2005.13420/) (2020)
- [Copula Flows for Synthetic Data Generation](https://mlsanity.com/paper/2101.00598/) (2021)
- [Deep Archimedean Copulas](https://mlsanity.com/paper/2012.03137/) (2020)
- [Copulas as High-Dimensional Generative Models: Vine Copula Autoencoders](https://mlsanity.com/paper/1906.05423/) (2019)
- [Normalizing Flows Across Dimensions](https://mlsanity.com/paper/2006.13070/) (2020)
- [Copula & Marginal Flows: Disentangling the Marginal from its Joint](https://mlsanity.com/paper/1907.03361/) (2019)
- [Density estimation on low-dimensional manifolds: an inflation-deflation approach](https://mlsanity.com/paper/2105.12152/) (2021)
- [DeepClimGAN: A High-Resolution Climate Data Generator](https://mlsanity.com/paper/2011.11705/) (2020)
- [Generative modeling of spatio-temporal weather patterns with extreme event conditioning](https://mlsanity.com/paper/2104.12469/) (2021)
- [Copula-Based Normalizing Flows](https://mlsanity.com/paper/2107.07352/) (2021)
- [Loosely Conditioned Emulation of Global Climate Models With Generative Adversarial Networks](https://mlsanity.com/paper/2105.06386/) (2021)

## Built on by (most cited first, 8 of 8)

- [Marginal Tail-Adaptive Normalizing Flows](https://mlsanity.com/paper/2206.10311/) (2022)
- [Flexible Tails for Normalizing Flows](https://mlsanity.com/paper/2406.16971/) (2024)
- [Neural Bayes estimators for censored inference with peaks-over-threshold models](https://mlsanity.com/paper/2306.15642/) (2023)
- [GPDFlow: Generative Multivariate Threshold Exceedance Modeling via Normalizing Flows](https://mlsanity.com/paper/2503.11822/) (2025)
- [Generative Machine Learning for Multivariate Angular Simulation](https://mlsanity.com/paper/2504.21505/) (2025)
- [Flexible Tails for Normalising Flows, with Application to the Modelling of Financial Return Data](https://mlsanity.com/paper/2311.00580/) (2023)
- [Extrapolation in Statistical Learning with Extreme Value Theory](https://mlsanity.com/paper/2605.01909/) (2026)
- [Summary Statistics of Large-scale Model Outputs for Observation-corrected Outputs](https://mlsanity.com/paper/2506.15845/) (2025)

## Abstract (arXiv)

Normalizing flows, a popular class of deep generative models, often fail to represent extreme phenomena observed in real-world processes. In particular, existing normalizing flow architectures struggle to model multivariate extremes, characterized by heavy-tailed marginal distributions and asymmetric tail dependence among variables. In light of this shortcoming, we propose COMET (COpula Multivariate ExTreme) Flows, which decompose the process of modeling a joint distribution into two parts: (i) modeling its marginal distributions, and (ii) modeling its copula distribution. COMET Flows capture heavy-tailed marginal distributions by combining a parametric tail belief at extreme quantiles of the marginals with an empirical kernel density function at mid-quantiles. In addition, COMET Flows capture asymmetric tail dependence among multivariate extremes by viewing such dependence as inducing a low-dimensional manifold structure in feature space. Experimental results on both synthetic and real-world datasets demonstrate the effectiveness of COMET Flows in capturing both heavy-tailed marginals and asymmetric tail dependence compared to other state-of-the-art baseline architectures. All code is available on GitHub at https://github.com/andrewmcdonald27/COMETFlows.