# Continuous Diffusion for Mixed-Type Tabular Data

arXiv: https://arxiv.org/abs/2312.10431 · HTML: https://mlsanity.com/paper/2312.10431/

## Key facts

- Cited by 17 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 46 of its 66 references that are in the map.
- First posted on arXiv 16 Dec 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, 30 of 46)

- [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)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Multi-Task Learning Using Uncertainty to Weigh Losses for Scene Geometry and Semantics](https://mlsanity.com/paper/1705.07115/) (2017)
- [Variational Diffusion Models](https://mlsanity.com/paper/2107.00630/) (2021)
- [Diffusion-LM Improves Controllable Text Generation](https://mlsanity.com/paper/2205.14217/) (2022)
- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [A Continuous Time Framework for Discrete Denoising Models](https://mlsanity.com/paper/2205.14987/) (2022)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [TabDDPM: Modelling Tabular Data with Diffusion Models](https://mlsanity.com/paper/2209.15421/) (2022)
- [Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioning](https://mlsanity.com/paper/2208.04202/) (2022)
- [Understanding Diffusion Objectives as the ELBO with Simple Data Augmentation](https://mlsanity.com/paper/2303.00848/) (2023)
- [Language Models are Realistic Tabular Data Generators](https://mlsanity.com/paper/2210.06280/) (2022)
- [Continuous diffusion for categorical data](https://mlsanity.com/paper/2211.15089/) (2022)
- [Scalable Adaptive Computation for Iterative Generation](https://mlsanity.com/paper/2212.11972/) (2022)
- [On the Importance of Noise Scheduling for Diffusion Models](https://mlsanity.com/paper/2301.10972/) (2023)

## Built on by (most cited first, 17 of 17)

- [TabDiff: a Mixed-type Diffusion Model for Tabular Data Generation](https://mlsanity.com/paper/2410.20626/) (2024)
- [The DCR Delusion: Measuring the Privacy Risk of Synthetic Data](https://mlsanity.com/paper/2505.01524/) (2025)
- [Diffusion and Flow Matching Models for Tabular Data: A Survey](https://mlsanity.com/paper/2502.17119/) (2025)
- [Flow Matching for Tabular Data Synthesis](https://mlsanity.com/paper/2512.00698/) (2025)
- [TabRep: Training Tabular Diffusion Models with a Simple and Effective Continuous Representation](https://mlsanity.com/paper/2504.04798/) (2025)
- [Cascaded Flow Matching for Heterogeneous Tabular Data with Mixed-Type Features](https://mlsanity.com/paper/2601.22816/) (2026)
- [Rethinking Anonymity Claims in Synthetic Data Generation: A Model-Centric Privacy Attack Perspective](https://mlsanity.com/paper/2601.22434/) (2026)
- [TabDLM: Free-Form Tabular Data Generation via Joint Numerical-Language Diffusion](https://mlsanity.com/paper/2602.22586/) (2026)
- [A Sobering Look at Tabular Data Generation via Probabilistic Circuits](https://mlsanity.com/paper/2603.23016/) (2026)
- [Self-Reinforcing Controllable Synthesis of Rare Relational Data via Bayesian Calibration](https://mlsanity.com/paper/2604.16817/) (2026)
- [AugMask: Training Diffusion Models on Incomplete Tabular Data via Stochastic Augmentation and Masking](https://mlsanity.com/paper/2606.03347/) (2026)
- [Privacy-Preserving Tabular Synthetic Data Generation Using TabularARGN](https://mlsanity.com/paper/2508.06647/) (2025)
- [CDMT-EHR: A Continuous-Time Diffusion Framework for Generating Mixed-Type Time-Series Electronic Health Records](https://mlsanity.com/paper/2603.23719/) (2026)
- [Segment-driven Structural Induction and Semantic Alignment for Heterogeneous Tabular Representation](https://mlsanity.com/paper/2606.01890/) (2026)
- [Understanding Latent Flow Models for Tabular Data Synthesis: Targets, Paths, and Sampling](https://mlsanity.com/paper/2606.20878/) (2026)
- [FUSE: Feature-Wise Unified Specialization with Cross-Column Exchange for Mixed-Type Tabular Flow Matching](https://mlsanity.com/paper/2608.07294/) (2026)
- [Usefulness of Quantile-Aware Diffusion Modeling for Highly Imbalanced Tabular Data](https://mlsanity.com/paper/2610.05825/) (2026)

## Abstract (arXiv)

Score-based generative models, commonly referred to as diffusion models, have proven to be successful at generating text and image data. However, their adaptation to mixed-type tabular data remains underexplored. In this work, we propose CDTD, a Continuous Diffusion model for mixed-type Tabular Data. CDTD is based on a novel combination of score matching and score interpolation to enforce a unified continuous noise distribution for both continuous and categorical features. We explicitly acknowledge the necessity of homogenizing distinct data types by relying on model-specific loss calibration and initialization schemes. To further address the high heterogeneity in mixed-type tabular data, we introduce adaptive feature- or type-specific noise schedules. These ensure balanced generative performance across features and optimize the allocation of model capacity across features and diffusion time. Our experimental results show that CDTD consistently outperforms state-of-the-art benchmark models, captures feature correlations exceptionally well, and that heterogeneity in the noise schedule design boosts sample quality. Replication code is available at https://github.com/muellermarkus/cdtd.