# DiffPuter: Empowering Diffusion Models for Missing Data Imputation

arXiv: https://arxiv.org/abs/2405.20690 · HTML: https://mlsanity.com/paper/2405.20690/

## Key facts

- Cited by 19 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 26 of its 42 references that are in the map.
- First posted on arXiv 31 May 2024.

## 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, 26 of 26)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [RePaint: Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2201.09865/) (2022)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [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)
- [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)
- [Handling Missing Data with Graph Representation Learning](https://mlsanity.com/paper/2010.16418/) (2020)
- [Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares](https://mlsanity.com/paper/1410.2596/) (2014)
- [Missing Data Imputation using Optimal Transport](https://mlsanity.com/paper/2002.03860/) (2020)
- [EDDI: Efficient Dynamic Discovery of High-Value Information with Partial VAE](https://mlsanity.com/paper/1809.11142/) (2018)
- [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)
- [VAEM: a Deep Generative Model for Heterogeneous Mixed Type Data](https://mlsanity.com/paper/2006.11941/) (2020)
- [Generating and Imputing Tabular Data via Diffusion and Flow-based Gradient-Boosted Trees](https://mlsanity.com/paper/2309.09968/) (2023)
- [MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanisms](https://mlsanity.com/paper/2111.03187/) (2021)
- [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)
- [Transformed Distribution Matching for Missing Value Imputation](https://mlsanity.com/paper/2302.10363/) (2023)
- [Missing Data Imputation and Acquisition with Deep Hierarchical Models and Hamiltonian Monte Carlo](https://mlsanity.com/paper/2202.04599/) (2022)
- [Data Imputation with Iterative Graph Reconstruction](https://mlsanity.com/paper/2212.02810/) (2022)

## Built on by (most cited first, 19 of 19)

- [Beyond Log-Concavity and Score Regularity: Improved Convergence Bounds for Score-Based Generative Models in W2-distance](https://mlsanity.com/paper/2501.02298/) (2025)
- [Diffusion-nested Auto-Regressive Synthesis of Heterogeneous Tabular Data](https://mlsanity.com/paper/2410.21523/) (2024)
- [One Pipeline, Many Transformers: Pattern-Specific Imputation Specialists for Tabular Missing Data](https://mlsanity.com/paper/2510.02625/) (2025)
- [Incomplete Data, Complete Dynamics: A Diffusion Approach](https://mlsanity.com/paper/2509.20098/) (2025)
- [Interpretable Generative and Discriminative Learning for Multimodal and Incomplete Clinical Data](https://mlsanity.com/paper/2510.09513/) (2025)
- [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)
- [CoreFlow: Low-Rank Matrix Generative Models](https://mlsanity.com/paper/2604.24959/) (2026)
- [IMAGIC-500: IMputation benchmark on A Generative Imaginary Country (500k samples)](https://mlsanity.com/paper/2506.08844/) (2025)
- [An Interdisciplinary and Cross-Task Review on Missing Data Imputation](https://mlsanity.com/paper/2511.01196/) (2025)
- [Nearly Optimal Bayesian Inference for Structural Missingness](https://mlsanity.com/paper/2601.18500/) (2026)
- [Order-Agnostic Autoregressive Modelling with Missing Data](https://mlsanity.com/paper/2605.06355/) (2026)
- [Missing Pattern Recognized Diffusion Imputation Model for Missing Not At Random](https://mlsanity.com/paper/2605.25439/) (2026)
- [Latent Diffusion for Missing Data](https://mlsanity.com/paper/2605.28427/) (2026)
- [Learning What Not to Impute: An Uncertainty-Aware Diffusion Framework for Meaningful Missingness](https://mlsanity.com/paper/2606.05073/) (2026)
- [TabSODA: Tabular Diffusion based Imputation with Skip Pattern Detection and Ordinal Awareness](https://mlsanity.com/paper/2606.05361/) (2026)
- [Imputation Meets Clustering: Exploiting Latent Subgroup Structure for Missing Data Recovery](https://mlsanity.com/paper/2607.06930/) (2026)
- [Learning Field Reconstruction from Incomplete Data by Globally Correcting Local Estimates](https://mlsanity.com/paper/2610.05375/) (2026)
- [TabMosaic: Unified In-Context Diffusion for Tabular Generative Tasks](https://mlsanity.com/paper/2610.15699/) (2026)

## Abstract (arXiv)

Generative models play an important role in missing data imputation in that they aim to learn the joint distribution of full data. However, applying advanced deep generative models (such as Diffusion models) to missing data imputation is challenging due to 1) the inherent incompleteness of the training data and 2) the difficulty in performing conditional inference from unconditional generative models. To deal with these challenges, this paper introduces DiffPuter, a tailored diffusion model combined with the Expectation-Maximization (EM) algorithm for missing data imputation. DiffPuter iteratively trains a diffusion model to learn the joint distribution of missing and observed data and performs an accurate conditional sampling to update the missing values using a tailored reversed sampling strategy. Our theoretical analysis shows that DiffPuter's training step corresponds to the maximum likelihood estimation of data density (M-step), and its sampling step represents the Expected A Posteriori estimation of missing values (E-step). Extensive experiments across ten diverse datasets and comparisons with 17 different imputation methods demonstrate DiffPuter's superior performance. Notably, DiffPuter achieves an average improvement of 6.94% in MAE and 4.78% in RMSE compared to the most competitive existing method.