# Copula Flows for Synthetic Data Generation

arXiv: https://arxiv.org/abs/2101.00598 · HTML: https://mlsanity.com/paper/2101.00598/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 49 references that are in the map.
- First posted on arXiv 3 Jan 2021.

## Builds on (most cited first, 26 of 26)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [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)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [MADE: Masked Autoencoder for Distribution Estimation](https://mlsanity.com/paper/1502.03509/) (2015)
- [A note on the evaluation of generative models](https://mlsanity.com/paper/1511.01844/) (2015)
- [Neural Autoregressive Flows](https://mlsanity.com/paper/1804.00779/) (2018)
- [VEEGAN: Reducing Mode Collapse in GANs using Implicit Variational Learning](https://mlsanity.com/paper/1705.07761/) (2017)
- [Generating Multi-label Discrete Patient Records using Generative Adversarial Networks](https://mlsanity.com/paper/1703.06490/) (2017)
- [Data Synthesis based on Generative Adversarial Networks](https://mlsanity.com/paper/1806.03384/) (2018)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [TensorFlow Distributions](https://mlsanity.com/paper/1711.10604/) (2017)
- [Discrete Flows: Invertible Generative Models of Discrete Data](https://mlsanity.com/paper/1905.10347/) (2019)
- [Latent Normalizing Flows for Discrete Sequences](https://mlsanity.com/paper/1901.10548/) (2019)
- [Boosting Deep Learning Risk Prediction with Generative Adversarial Networks for Electronic Health Records](https://mlsanity.com/paper/1709.01648/) (2017)
- [Transformation Autoregressive Networks](https://mlsanity.com/paper/1801.09819/) (2018)
- [Autoregressive Energy Machines](https://mlsanity.com/paper/1904.05626/) (2019)
- [Generative Adversarial Networks in Computer Vision: A Survey and Taxonomy](https://mlsanity.com/paper/1906.01529/) (2019)
- [Gaussian Process Vine Copulas for Multivariate Dependence](https://mlsanity.com/paper/1302.3979/) (2013)
- [The future of statistical disclosure control](https://mlsanity.com/paper/1812.09204/) (2018)

## Built on by (most cited first, 30 of 35)

- [Deep Neural Networks and Tabular Data: A Survey](https://mlsanity.com/paper/2110.01889/) (2021)
- [Language Models are Realistic Tabular Data Generators](https://mlsanity.com/paper/2210.06280/) (2022)
- [Differentially Private Tabular Data Synthesis using Large Language Models](https://mlsanity.com/paper/2406.01457/) (2024)
- [Distributional Learning of Variational AutoEncoder: Application to Synthetic Data Generation](https://mlsanity.com/paper/2302.11294/) (2023)
- [Doubling Your Data in Minutes: Ultra-fast Tabular Data Generation via LLM-Induced Dependency Graphs](https://mlsanity.com/paper/2507.19334/) (2025)
- [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)
- [FFPDG: Fast, Fair and Private Data Generation](https://mlsanity.com/paper/2307.00161/) (2023)
- [Navigating Tabular Data Synthesis Research: Understanding User Needs and Tool Capabilities](https://mlsanity.com/paper/2405.20959/) (2024)
- [Marginal Causal Flows for Validation and Inference](https://mlsanity.com/paper/2411.01295/) (2024)
- [Your copula is a classifier in disguise: classification-based copula density estimation](https://mlsanity.com/paper/2411.03014/) (2024)
- [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)
- [An evaluation framework for synthetic data generation models](https://mlsanity.com/paper/2404.08866/) (2024)
- [Quasi-Bayes meets Vines](https://mlsanity.com/paper/2406.12764/) (2024)
- [FairGen: Fair Synthetic Data Generation](https://mlsanity.com/paper/2210.13023/) (2022)
- [P-TA: Using Proximal Policy Optimization to Enhance Tabular Data Augmentation via Large Language Models](https://mlsanity.com/paper/2406.11391/) (2024)
- [A text-to-tabular approach to generate synthetic patient data using LLMs](https://mlsanity.com/paper/2412.05153/) (2024)
- [Generative Modeling of Complex Data](https://mlsanity.com/paper/2202.02145/) (2022)
- [CasTGAN: Cascaded Generative Adversarial Network for Realistic Tabular Data Synthesis](https://mlsanity.com/paper/2307.00384/) (2023)
- [Towards a framework on tabular synthetic data generation: a minimalist approach: theory, use cases, and limitations](https://mlsanity.com/paper/2411.10982/) (2024)
- [Overcoming limited battery data challenges: A coupled neural network approach](https://mlsanity.com/paper/2111.15348/) (2021)
- [Convex space learning for tabular synthetic data generation](https://mlsanity.com/paper/2407.09789/) (2024)
- [Frugal, Flexible, Faithful: Causal Data Simulation via Frengression](https://mlsanity.com/paper/2508.01018/) (2025)
- [OOG- Optuna Optimized GAN Sampling Technique for Tabular Imbalanced Malware Data](https://mlsanity.com/paper/2212.01274/) (2022)
- [Masked Language Modeling Becomes Conditional Density Estimation for Tabular Data Synthesis](https://mlsanity.com/paper/2405.20602/) (2024)
- [LLMSynthor: Macro-Aligned Micro-Records Synthesis with Large Language Models](https://mlsanity.com/paper/2505.14752/) (2025)
- [SAGE: Sparse Adaptive Guidance for Dependency-Aware Tabular Data Generation](https://mlsanity.com/paper/2604.24368/) (2026)
- [Generating Synthetic Data with Locally Estimated Distributions for Disclosure Control](https://mlsanity.com/paper/2210.00884/) (2022)
- [IsoEx: an explainable unsupervised approach to process event logs cyber investigation](https://mlsanity.com/paper/2306.09260/) (2023)

## Abstract (arXiv)

The ability to generate high-fidelity synthetic data is crucial when available (real) data is limited or where privacy and data protection standards allow only for limited use of the given data, e.g., in medical and financial data-sets. Current state-of-the-art methods for synthetic data generation are based on generative models, such as Generative Adversarial Networks (GANs). Even though GANs have achieved remarkable results in synthetic data generation, they are often challenging to interpret.Furthermore, GAN-based methods can suffer when used with mixed real and categorical variables.Moreover, loss function (discriminator loss) design itself is problem specific, i.e., the generative model may not be useful for tasks it was not explicitly trained for. In this paper, we propose to use a probabilistic model as a synthetic data generator. Learning the probabilistic model for the data is equivalent to estimating the density of the data. Based on the copula theory, we divide the density estimation task into two parts, i.e., estimating univariate marginals and estimating the multivariate copula density over the univariate marginals. We use normalising flows to learn both the copula density and univariate marginals. We benchmark our method on both simulated and real data-sets in terms of density estimation as well as the ability to generate high-fidelity synthetic data