# Graph-Conditional Flow Matching for Relational Data Generation

arXiv: https://arxiv.org/abs/2505.15668 · HTML: https://mlsanity.com/paper/2505.15668/

## Key facts

- Cited by 3 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 33 of its 51 references that are in the map.
- First posted on arXiv 21 May 2025.

## 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, 30 of 33)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [How Attentive are Graph Attention Networks?](https://mlsanity.com/paper/2105.14491/) (2021)
- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [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)
- [TabDDPM: Modelling Tabular Data with Diffusion Models](https://mlsanity.com/paper/2209.15421/) (2022)
- [Mixed-Type Tabular Data Synthesis with Score-based Diffusion in Latent Space](https://mlsanity.com/paper/2310.09656/) (2023)
- [Data Synthesis based on Generative Adversarial Networks](https://mlsanity.com/paper/1806.03384/) (2018)
- [REaLTabFormer: Generating Realistic Relational and Tabular Data using Transformers](https://mlsanity.com/paper/2302.02041/) (2023)
- [Synthesizing Tabular Data using Generative Adversarial Networks](https://mlsanity.com/paper/1811.11264/) (2018)
- [Variational Flow Matching for Graph Generation](https://mlsanity.com/paper/2406.04843/) (2024)
- [Graphical-model based estimation and inference for differential privacy](https://mlsanity.com/paper/1901.09136/) (2019)
- [A Survey on Deep Graph Generation: Methods and Applications](https://mlsanity.com/paper/2203.06714/) (2022)
- [TabDiff: a Mixed-type Diffusion Model for Tabular Data Generation](https://mlsanity.com/paper/2410.20626/) (2024)
- [Generating and Imputing Tabular Data via Diffusion and Flow-based Gradient-Boosted Trees](https://mlsanity.com/paper/2309.09968/) (2023)
- [TabMT: Generating tabular data with masked transformers](https://mlsanity.com/paper/2312.06089/) (2023)
- [ClavaDDPM: Multi-relational Data Synthesis with Cluster-guided Diffusion Models](https://mlsanity.com/paper/2405.17724/) (2024)
- [Row Conditional-TGAN for generating synthetic relational databases](https://mlsanity.com/paper/2211.07588/) (2022)
- [DP-TBART: A Transformer-based Autoregressive Model for Differentially Private Tabular Data Generation](https://mlsanity.com/paper/2307.10430/) (2023)
- [Generating Realistic Synthetic Relational Data through Graph Variational Autoencoders](https://mlsanity.com/paper/2211.16889/) (2022)
- [Synthetic Data Privacy Metrics](https://mlsanity.com/paper/2501.03941/) (2025)

## Built on by (most cited first, 3 of 3)

- [PluRel: Synthetic Data unlocks Scaling Laws for Relational Foundation Models](https://mlsanity.com/paper/2602.04029/) (2026)
- [Graph Flow Matching: Enhancing Image Generation with Neighbor-Aware Flow Fields](https://mlsanity.com/paper/2505.24434/) (2025)
- [Interventional Flow Matching: Prospective Dose-Response Forecasting with Velocity-Field Jacobian Regularization](https://mlsanity.com/paper/2606.29386/) (2026)

## Abstract (arXiv)

Data synthesis is gaining momentum as a privacy-enhancing technology. While single-table tabular data generation has seen considerable progress, current methods for multi-table data often lack the flexibility and expressiveness needed to capture complex relational structures. In particular, they struggle with long-range dependencies and complex foreign-key relationships, such as tables with multiple parent tables or multiple types of links between the same pair of tables. We propose a generative model for relational data that generates the content of a relational dataset given the graph formed by the foreign-key relationships. We do this by learning a deep generative model of the content of the whole relational database by flow matching, where the neural network trained to denoise records leverages a graph neural network to obtain information from connected records. Our method is flexible, as it can support relational datasets with complex structures, and expressive, as the generation of each record can be influenced by any other record within the same connected component. We evaluate our method on several benchmark datasets and show that it achieves state-of-the-art performance in terms of synthetic data fidelity.