# Generating Tabular Data Using Heterogeneous Sequential Feature Forest Flow Matching

arXiv: https://arxiv.org/abs/2410.15516 · HTML: https://mlsanity.com/paper/2410.15516/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 13 of its 53 references that are in the map.
- First posted on arXiv 20 Oct 2024.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 13 of 13)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [Deep Neural Networks and Tabular Data: A Survey](https://mlsanity.com/paper/2110.01889/) (2021)
- [TabDDPM: Modelling Tabular Data with Diffusion Models](https://mlsanity.com/paper/2209.15421/) (2022)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [Data Synthesis based on Generative Adversarial Networks](https://mlsanity.com/paper/1806.03384/) (2018)
- [CTAB-GAN: Effective Table Data Synthesizing](https://mlsanity.com/paper/2102.08369/) (2021)
- [Generating and Imputing Tabular Data via Diffusion and Flow-based Gradient-Boosted Trees](https://mlsanity.com/paper/2309.09968/) (2023)
- [OCT-GAN: Neural ODE-based Conditional Tabular GANs](https://mlsanity.com/paper/2105.14969/) (2021)
- [Invertible Tabular GANs: Killing Two Birds with OneStone for Tabular Data Synthesis](https://mlsanity.com/paper/2202.03636/) (2022)

## Built on by (most cited first, 1 of 1)

- [Interleaved Gibbs Diffusion: Generating Discrete-Continuous Data with Implicit Constraints](https://mlsanity.com/paper/2502.13450/) (2025)

## Abstract (arXiv)

Privacy and regulatory constraints make data generation vital to advancing machine learning without relying on real-world datasets. A leading approach for tabular data generation is the Forest Flow (FF) method, which combines Flow Matching with XGBoost. Despite its good performance, FF is slow and makes errors when treating categorical variables as one-hot continuous features. It is also highly sensitive to small changes in the initial conditions of the ordinary differential equation (ODE). To overcome these limitations, we develop Heterogeneous Sequential Feature Forest Flow (HS3F). Our method generates data sequentially (feature-by-feature), reducing the dependency on noisy initial conditions through the additional information from previously generated features. Furthermore, it generates categorical variables using multinomial sampling (from an XGBoost classifier) instead of flow matching, improving generation speed. We also use a Runge-Kutta 4th order (Rg4) ODE solver for improved performance over the Euler solver used in FF. Our experiments with 25 datasets reveal that HS3F produces higher quality and more diverse synthetic data than FF, especially for categorical variables. It also generates data 21-27 times faster for datasets with ≥20% categorical variables. HS3F further demonstrates enhanced robustness to affine transformation in flow ODE initial conditions compared to FF. This study not only validates the HS3F but also unveils promising new strategies to advance generative models.