# TabSODA: Tabular Diffusion based Imputation with Skip Pattern Detection and Ordinal Awareness

arXiv: https://arxiv.org/abs/2606.05361 · HTML: https://mlsanity.com/paper/2606.05361/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 41 references that are in the map.
- First posted on arXiv 3 Jun 2026.

## Builds on (most cited first, 18 of 18)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Analog Bits: Generating Discrete Data using Diffusion Models with Self-Conditioning](https://mlsanity.com/paper/2208.04202/) (2022)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Mixed-Type Tabular Data Synthesis with Score-based Diffusion in Latent Space](https://mlsanity.com/paper/2310.09656/) (2023)
- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [Rank consistent ordinal regression for neural networks with application to age estimation](https://mlsanity.com/paper/1901.07884/) (2019)
- [Handling Missing Data with Graph Representation Learning](https://mlsanity.com/paper/2010.16418/) (2020)
- [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)
- [TabDiff: a Mixed-type Diffusion Model for Tabular Data Generation](https://mlsanity.com/paper/2410.20626/) (2024)
- [MissDiff: Training Diffusion Models on Tabular Data with Missing Values](https://mlsanity.com/paper/2307.00467/) (2023)
- [MCFlow: Monte Carlo Flow Models for Data Imputation](https://mlsanity.com/paper/2003.12628/) (2020)
- [ReMasker: Imputing Tabular Data with Masked Autoencoding](https://mlsanity.com/paper/2309.13793/) (2023)
- [DiffPuter: Empowering Diffusion Models for Missing Data Imputation](https://mlsanity.com/paper/2405.20690/) (2024)
- [Using the Softplus Function to Construct Alternative Link Functions in Generalized Linear Models and Beyond](https://mlsanity.com/paper/2111.14207/) (2021)

## Abstract (arXiv)

Missing data imputation in large-scale surveys faces two challenges that are not well handled by current tabular diffusion methods. First, structural skips, cells made inapplicable by questionnaire design, should not be imputed but are often conflated with item nonresponse. Second, ordinal responses encode ordered categories, yet most pipelines treat them as nominal levels through one-hot or analog-bit encodings. We introduce TabSODA (Tabular diffusion with Skip pattern detection and Ordinal Awareness), an Expectation-Maximization (EM)-based diffusion imputer built on the Elucidated Diffusion Model (EDM) framework. TabSODA propagates structural skips through the denoising loss and reverse-time sampler, and represents ordinal variables with cumulative-probit scalar latents while retaining analog-bit encodings for nominal variables. When a codebook skip mask is available, TabSODA uses it directly; otherwise, the TabSODA+SKIP variant estimates the mask from raw responses and questionnaire order using a CART-based skip-pattern miner. On Population Assessment of Tobacco and Health (PATH) study and the National Survey on Drug Use and Health (NSDUH), two nationally representative U.S. surveys, TabSODA reduces ordinal MACE by up to 23.7% and improves categorical accuracy by up to 9% over the strongest baseline across MCAR, MAR, and MNAR masking. The skip miner achieves near-perfect precision on both datasets, allowing TabSODA+SKIP to closely track the codebook-mask variant.