# Generating and Imputing Tabular Data via Diffusion and Flow-based Gradient-Boosted Trees

arXiv: https://arxiv.org/abs/2309.09968 · HTML: https://mlsanity.com/paper/2309.09968/

## Key facts

- Cited by 62 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 147 references that are in the map.
- First posted on arXiv 18 Sep 2023.

## Builds on (most cited first, 30 of 51)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [WaveGrad: Estimating Gradients for Waveform Generation](https://mlsanity.com/paper/2009.00713/) (2020)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [Tabular Data: Deep Learning is Not All You Need](https://mlsanity.com/paper/2106.03253/) (2021)
- [Deep Neural Networks and Tabular Data: A Survey](https://mlsanity.com/paper/2110.01889/) (2021)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [TabDDPM: Modelling Tabular Data with Diffusion Models](https://mlsanity.com/paper/2209.15421/) (2022)

## Built on by (most cited first, 30 of 62)

- [Large Language Models(LLMs) on Tabular Data: Prediction, Generation, and Understanding -- A Survey](https://mlsanity.com/paper/2402.17944/) (2024)
- [A Comprehensive Survey on Data Augmentation](https://mlsanity.com/paper/2405.09591/) (2024)
- [A Comprehensive Survey of Synthetic Tabular Data Generation](https://mlsanity.com/paper/2504.16506/) (2025)
- [Training-Free Guidance Beyond Differentiability: Scalable Path Steering with Tree Search in Diffusion and Flow Models](https://mlsanity.com/paper/2502.11420/) (2025)
- [DiffPuter: Empowering Diffusion Models for Missing Data Imputation](https://mlsanity.com/paper/2405.20690/) (2024)
- [Continuous Diffusion for Mixed-Type Tabular Data](https://mlsanity.com/paper/2312.10431/) (2023)
- [Self-Supervision Improves Diffusion Models for Tabular Data Imputation](https://mlsanity.com/paper/2407.18013/) (2024)
- [Tabular Data Augmentation for Machine Learning: Progress and Prospects of Embracing Generative AI](https://mlsanity.com/paper/2407.21523/) (2024)
- [A Survey on Deep Learning Approaches for Tabular Data Generation: Utility, Alignment, Fidelity, Privacy, Diversity, and Beyond](https://mlsanity.com/paper/2503.05954/) (2025)
- [Exponential Family Variational Flow Matching for Tabular Data Generation](https://mlsanity.com/paper/2506.05940/) (2025)
- [TabularARGN: A Flexible and Efficient Auto-Regressive Framework for Generating High-Fidelity Synthetic Data](https://mlsanity.com/paper/2501.12012/) (2025)
- [Causality for Tabular Data Synthesis: A High-Order Structure Causal Benchmark Framework](https://mlsanity.com/paper/2406.08311/) (2024)
- [Synthetic Tabular Data Generation for Imbalanced Classification: The Surprising Effectiveness of an Overlap Class](https://mlsanity.com/paper/2412.15657/) (2024)
- [Diffusion and Flow Matching Models for Tabular Data: A Survey](https://mlsanity.com/paper/2502.17119/) (2025)
- [Explicit Flow Matching: On The Theory of Flow Matching Algorithms with Applications](https://mlsanity.com/paper/2402.03232/) (2024)
- [Tabular Data Synthesis with Differential Privacy: A Survey](https://mlsanity.com/paper/2411.03351/) (2024)
- [Flow Matching for Tabular Data Synthesis](https://mlsanity.com/paper/2512.00698/) (2025)
- [Do we need rebalancing strategies? A theoretical and empirical study around SMOTE and its variants](https://mlsanity.com/paper/2402.03819/) (2024)
- [Guided Discrete Diffusion for Electronic Health Record Generation](https://mlsanity.com/paper/2404.12314/) (2024)
- [Treeffuser: Probabilistic Predictions via Conditional Diffusions with Gradient-Boosted Trees](https://mlsanity.com/paper/2406.07658/) (2024)
- [Scaling Up Diffusion and Flow-based XGBoost Models](https://mlsanity.com/paper/2408.16046/) (2024)
- [TabRep: Training Tabular Diffusion Models with a Simple and Effective Continuous Representation](https://mlsanity.com/paper/2504.04798/) (2025)
- [CFMI: Flow Matching for Missing Data Imputation](https://mlsanity.com/paper/2506.09258/) (2025)
- [Unmasking Trees for Tabular Data](https://mlsanity.com/paper/2407.05593/) (2024)
- [A text-to-tabular approach to generate synthetic patient data using LLMs](https://mlsanity.com/paper/2412.05153/) (2024)
- [Tabby: A Language Model Architecture for Tabular and Structured Data Synthesis](https://mlsanity.com/paper/2503.02152/) (2025)
- [One Pipeline, Many Transformers: Pattern-Specific Imputation Specialists for Tabular Missing Data](https://mlsanity.com/paper/2510.02625/) (2025)
- [Cascaded Flow Matching for Heterogeneous Tabular Data with Mixed-Type Features](https://mlsanity.com/paper/2601.22816/) (2026)
- [BUFF: Boosted Decision Tree based Ultra-Fast Flow matching](https://mlsanity.com/paper/2404.18219/) (2024)
- [Generalization Bounds for Causal Regression: Insights, Guarantees and Sensitivity Analysis](https://mlsanity.com/paper/2405.09516/) (2024)

## Abstract (arXiv)

Tabular data is hard to acquire and is subject to missing values. This paper introduces a novel approach for generating and imputing mixed-type (continuous and categorical) tabular data utilizing score-based diffusion and conditional flow matching. In contrast to prior methods that rely on neural networks to learn the score function or the vector field, we adopt XGBoost, a widely used Gradient-Boosted Tree (GBT) technique. To test our method, we build one of the most extensive benchmarks for tabular data generation and imputation, containing 27 diverse datasets and 9 metrics. Through empirical evaluation across the benchmark, we demonstrate that our approach outperforms deep-learning generation methods in data generation tasks and remains competitive in data imputation. Notably, it can be trained in parallel using CPUs without requiring a GPU. Our Python and R code is available at https://github.com/SamsungSAILMontreal/ForestDiffusion.