# MissDiff: Training Diffusion Models on Tabular Data with Missing Values

arXiv: https://arxiv.org/abs/2307.00467 · HTML: https://mlsanity.com/paper/2307.00467/

## Key facts

- Cited by 39 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 37 of its 73 references that are in the map.
- First posted on arXiv 2 Jul 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 37)

- [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)
- [Diffusion Probabilistic Models for 3D Point Cloud Generation](https://mlsanity.com/paper/2103.01458/) (2021)
- [Modeling Tabular data using Conditional GAN](https://mlsanity.com/paper/1907.00503/) (2019)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Sliced Score Matching: A Scalable Approach to Density and Score Estimation](https://mlsanity.com/paper/1905.07088/) (2019)
- [TabDDPM: Modelling Tabular Data with Diffusion Models](https://mlsanity.com/paper/2209.15421/) (2022)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Synthetic Data from Diffusion Models Improves ImageNet Classification](https://mlsanity.com/paper/2304.08466/) (2023)
- [Improving Robustness using Generated Data](https://mlsanity.com/paper/2110.09468/) (2021)
- [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)
- [Score-based Continuous-time Discrete Diffusion Models](https://mlsanity.com/paper/2211.16750/) (2022)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [Concrete Score Matching: Generalized Score Matching for Discrete Data](https://mlsanity.com/paper/2211.00802/) (2022)
- [Robust Learning Meets Generative Models: Can Proxy Distributions Improve Adversarial Robustness?](https://mlsanity.com/paper/2104.09425/) (2021)
- [Ambient Diffusion: Learning Clean Distributions from Corrupted Data](https://mlsanity.com/paper/2305.19256/) (2023)
- [Missing Data Imputation using Optimal Transport](https://mlsanity.com/paper/2002.03860/) (2020)
- [STaSy: Score-based Tabular data Synthesis](https://mlsanity.com/paper/2210.04018/) (2022)
- [HyperImpute: Generalized Iterative Imputation with Automatic Model Selection](https://mlsanity.com/paper/2206.07769/) (2022)
- [Diffusion models for missing value imputation in tabular data](https://mlsanity.com/paper/2210.17128/) (2022)
- [MisGAN: Learning from Incomplete Data with Generative Adversarial Networks](https://mlsanity.com/paper/1902.09599/) (2019)
- [VAEM: a Deep Generative Model for Heterogeneous Mixed Type Data](https://mlsanity.com/paper/2006.11941/) (2020)
- [not-MIWAE: Deep Generative Modelling with Missing not at Random Data](https://mlsanity.com/paper/2006.12871/) (2020)
- [Improved Techniques for Maximum Likelihood Estimation for Diffusion ODEs](https://mlsanity.com/paper/2305.03935/) (2023)
- [Learning from Irregularly-Sampled Time Series: A Missing Data Perspective](https://mlsanity.com/paper/2008.07599/) (2020)

## Built on by (most cited first, 30 of 39)

- [An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization](https://mlsanity.com/paper/2404.07771/) (2024)
- [A Survey on Diffusion Models for Time Series and Spatio-Temporal Data](https://mlsanity.com/paper/2404.18886/) (2024)
- [Generating and Imputing Tabular Data via Diffusion and Flow-based Gradient-Boosted Trees](https://mlsanity.com/paper/2309.09968/) (2023)
- [FinDiff: Diffusion Models for Financial Tabular Data Generation](https://mlsanity.com/paper/2309.01472/) (2023)
- [A Comprehensive Survey of Synthetic Tabular Data Generation](https://mlsanity.com/paper/2504.16506/) (2025)
- [A Survey on Statistical Theory of Deep Learning: Approximation, Training Dynamics, and Generative Models](https://mlsanity.com/paper/2401.07187/) (2024)
- [DiffPuter: Empowering Diffusion Models for Missing Data Imputation](https://mlsanity.com/paper/2405.20690/) (2024)
- [Self-Supervision Improves Diffusion Models for Tabular Data Imputation](https://mlsanity.com/paper/2407.18013/) (2024)
- [Diffusion and Flow Matching Models for Tabular Data: A Survey](https://mlsanity.com/paper/2502.17119/) (2025)
- [Score Matching With Missing Data](https://mlsanity.com/paper/2506.00557/) (2025)
- [Anomaly Detection and Generation with Diffusion Models: A Survey](https://mlsanity.com/paper/2506.09368/) (2025)
- [DiffImpute: Tabular Data Imputation With Denoising Diffusion Probabilistic Model](https://mlsanity.com/paper/2403.13863/) (2024)
- [Missing Data Imputation by Reducing Mutual Information with Rectified Flows](https://mlsanity.com/paper/2505.11749/) (2025)
- [Rethinking the Diffusion Models for Numerical Tabular Data Imputation from the Perspective of Wasserstein Gradient Flow](https://mlsanity.com/paper/2406.15762/) (2024)
- [Incomplete Data, Complete Dynamics: A Diffusion Approach](https://mlsanity.com/paper/2509.20098/) (2025)
- [A diffusion-based generative model for financial time series via geometric Brownian motion](https://mlsanity.com/paper/2507.19003/) (2025)
- [Impute-MACFM: Imputation based on Mask-Aware Flow Matching](https://mlsanity.com/paper/2509.23126/) (2025)
- [Risk-Sensitive Diffusion: Robustly Optimizing Diffusion Models with Noisy Samples](https://mlsanity.com/paper/2402.02081/) (2024)
- [DeepIFSAC: Deep Imputation of Missing Values Using Feature and Sample Attention within Contrastive Framework](https://mlsanity.com/paper/2501.10910/) (2025)
- [Imputation-free Learning of Tabular Data with Missing Values using Incremental Feature Partitions in Transformer](https://mlsanity.com/paper/2504.14610/) (2025)
- [How Far Are We from Generating Missing Modalities with Foundation Models?](https://mlsanity.com/paper/2506.03530/) (2025)
- [CoreFlow: Low-Rank Matrix Generative Models](https://mlsanity.com/paper/2604.24959/) (2026)
- [AugMask: Training Diffusion Models on Incomplete Tabular Data via Stochastic Augmentation and Masking](https://mlsanity.com/paper/2606.03347/) (2026)
- [Watermarking Generative Categorical Data](https://mlsanity.com/paper/2411.10898/) (2024)
- [Kriging and Gaussian Process Interpolation for Georeferenced Data Augmentation](https://mlsanity.com/paper/2501.07183/) (2025)
- [Interpolation pour l'augmentation de donnees : Application `a la gestion des adventices de la canne a sucre a la Reunion](https://mlsanity.com/paper/2501.12400/) (2025)
- [Diffusion Transformers for Imputation: Statistical Efficiency and Uncertainty Quantification](https://mlsanity.com/paper/2510.02216/) (2025)
- [Learning Robust Diffusion Models from Imprecise Supervision](https://mlsanity.com/paper/2510.03016/) (2025)
- [An Interdisciplinary and Cross-Task Review on Missing Data Imputation](https://mlsanity.com/paper/2511.01196/) (2025)
- [Boosting Predictive Performance on Tabular Data through Data Augmentation with Latent-Space Flow-Based Diffusion](https://mlsanity.com/paper/2511.16571/) (2025)

## Abstract (arXiv)

The diffusion model has shown remarkable performance in modeling data distributions and synthesizing data. However, the vanilla diffusion model requires complete or fully observed data for training. Incomplete data is a common issue in various real-world applications, including healthcare and finance, particularly when dealing with tabular datasets. This work presents a unified and principled diffusion-based framework for learning from data with missing values under various missing mechanisms. We first observe that the widely adopted "impute-then-generate" pipeline may lead to a biased learning objective. Then we propose to mask the regression loss of Denoising Score Matching in the training phase. We prove the proposed method is consistent in learning the score of data distributions, and the proposed training objective serves as an upper bound for the negative likelihood in certain cases. The proposed framework is evaluated on multiple tabular datasets using realistic and efficacious metrics and is demonstrated to outperform state-of-the-art diffusion model on tabular data with "impute-then-generate" pipeline by a large margin.