# CoDi: Co-evolving Contrastive Diffusion Models for Mixed-type Tabular Synthesis

arXiv: https://arxiv.org/abs/2304.12654 · HTML: https://mlsanity.com/paper/2304.12654/

## Key facts

- Cited by 78 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 25 of its 57 references that are in the map.
- First posted on arXiv 25 Apr 2023.

## 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, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [FaceNet: A Unified Embedding for Face Recognition and Clustering](https://mlsanity.com/paper/1503.03832/) (2015)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Revisiting Deep Learning Models for Tabular Data](https://mlsanity.com/paper/2106.11959/) (2021)
- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [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)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (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)
- [TaBERT: Pretraining for Joint Understanding of Textual and Tabular Data](https://mlsanity.com/paper/2005.08314/) (2020)
- [Real-valued (Medical) Time Series Generation with Recurrent Conditional GANs](https://mlsanity.com/paper/1706.02633/) (2017)
- [How to train your neural ODE: the world of Jacobian and kinetic regularization](https://mlsanity.com/paper/2002.02798/) (2020)
- [VEEGAN: Reducing Mode Collapse in GANs using Implicit Variational Learning](https://mlsanity.com/paper/1705.07761/) (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)
- [STaSy: Score-based Tabular data Synthesis](https://mlsanity.com/paper/2210.04018/) (2022)
- [SOS: Score-based Oversampling for Tabular Data](https://mlsanity.com/paper/2206.08555/) (2022)
- [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)
- [Generating Synthetic but Plausible Healthcare Record Datasets](https://mlsanity.com/paper/1807.01514/) (2018)
- [An Empirical Study on the Membership Inference Attack against Tabular Data Synthesis Models](https://mlsanity.com/paper/2208.08114/) (2022)

## Built on by (most cited first, 30 of 78)

- [Mixed-Type Tabular Data Synthesis with Score-based Diffusion in Latent Space](https://mlsanity.com/paper/2310.09656/) (2023)
- [Large Language Models(LLMs) on Tabular Data: Prediction, Generation, and Understanding -- A Survey](https://mlsanity.com/paper/2402.17944/) (2024)
- [TabDiff: a Mixed-type Diffusion Model for Tabular Data Generation](https://mlsanity.com/paper/2410.20626/) (2024)
- [Enhancing Deep Reinforcement Learning: A Tutorial on Generative Diffusion Models in Network Optimization](https://mlsanity.com/paper/2308.05384/) (2023)
- [Representation Learning for Tabular Data: A Comprehensive Survey](https://mlsanity.com/paper/2504.16109/) (2025)
- [ClavaDDPM: Multi-relational Data Synthesis with Cluster-guided Diffusion Models](https://mlsanity.com/paper/2405.17724/) (2024)
- [A Comprehensive Survey of Synthetic Tabular Data Generation](https://mlsanity.com/paper/2504.16506/) (2025)
- [Language-driven Grasp Detection](https://mlsanity.com/paper/2406.09489/) (2024)
- [AutoDiff: combining Auto-encoder and Diffusion model for tabular data synthesizing](https://mlsanity.com/paper/2310.15479/) (2023)
- [Diffuse Everything: Multimodal Diffusion Models on Arbitrary State Spaces](https://mlsanity.com/paper/2506.07903/) (2025)
- [A Survey on Diffusion Models for Recommender Systems](https://mlsanity.com/paper/2409.05033/) (2024)
- [Systematic Assessment of Tabular Data Synthesis](https://mlsanity.com/paper/2402.06806/) (2024)
- [Continuous Diffusion for Mixed-Type Tabular Data](https://mlsanity.com/paper/2312.10431/) (2023)
- [DiSK: A Diffusion Model for Structured Knowledge](https://mlsanity.com/paper/2312.05253/) (2023)
- [Self-Supervision Improves Diffusion Models for Tabular Data Imputation](https://mlsanity.com/paper/2407.18013/) (2024)
- [TabEBM: A Tabular Data Augmentation Method with Distinct Class-Specific Energy-Based Models](https://mlsanity.com/paper/2409.16118/) (2024)
- [Diffusion Models for Tabular Data Imputation and Synthetic Data Generation](https://mlsanity.com/paper/2407.02549/) (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)
- [CuTS: Customizable Tabular Synthetic Data Generation](https://mlsanity.com/paper/2307.03577/) (2023)
- [A Survey on Diffusion Models for Anomaly Detection](https://mlsanity.com/paper/2501.11430/) (2025)
- [Balanced Mixed-Type Tabular Data Synthesis with Diffusion Models](https://mlsanity.com/paper/2404.08254/) (2024)
- [TabGen-ICL: Residual-Aware In-Context Example Selection for Tabular Data Generation](https://mlsanity.com/paper/2502.16414/) (2025)
- [DiffLM: Controllable Synthetic Data Generation via Diffusion Language Models](https://mlsanity.com/paper/2411.03250/) (2024)
- [LLM-TabLogic: Preserving Inter-Column Logical Relationships in Synthetic Tabular Data via Prompt-Guided Latent Diffusion](https://mlsanity.com/paper/2503.02161/) (2025)
- [A Comprehensive Survey on Generative Diffusion Models for Structured Data](https://mlsanity.com/paper/2306.04139/) (2023)
- [Causality for Tabular Data Synthesis: A High-Order Structure Causal Benchmark Framework](https://mlsanity.com/paper/2406.08311/) (2024)
- [Diffusion and Flow Matching Models for Tabular Data: A Survey](https://mlsanity.com/paper/2502.17119/) (2025)

## Abstract (arXiv)

With growing attention to tabular data these days, the attempt to apply a synthetic table to various tasks has been expanded toward various scenarios. Owing to the recent advances in generative modeling, fake data generated by tabular data synthesis models become sophisticated and realistic. However, there still exists a difficulty in modeling discrete variables (columns) of tabular data. In this work, we propose to process continuous and discrete variables separately (but being conditioned on each other) by two diffusion models. The two diffusion models are co-evolved during training by reading conditions from each other. In order to further bind the diffusion models, moreover, we introduce a contrastive learning method with a negative sampling method. In our experiments with 11 real-world tabular datasets and 8 baseline methods, we prove the efficacy of the proposed method, called CoDi.