# Missing Data Imputation by Reducing Mutual Information with Rectified Flows

arXiv: https://arxiv.org/abs/2505.11749 · HTML: https://mlsanity.com/paper/2505.11749/

## Key facts

- Cited by 6 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 21 of its 43 references that are in the map.
- First posted on arXiv 16 May 2025.

## 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, 21 of 21)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [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)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [MINE: Mutual Information Neural Estimation](https://mlsanity.com/paper/1801.04062/) (2018)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [Missing Data Imputation using Optimal Transport](https://mlsanity.com/paper/2002.03860/) (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)
- [MisGAN: Learning from Incomplete Data with Generative Adversarial Networks](https://mlsanity.com/paper/1902.09599/) (2019)
- [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)
- [Transformed Distribution Matching for Missing Value Imputation](https://mlsanity.com/paper/2302.10363/) (2023)
- [Minimizing f-Divergences by Interpolating Velocity Fields](https://mlsanity.com/paper/2305.15577/) (2023)
- [Imputation estimators for unnormalized models with missing data](https://mlsanity.com/paper/1903.03630/) (2019)

## Built on by (most cited first, 6 of 6)

- [Zero-Flow Two-Sample Tests](https://mlsanity.com/paper/2607.21542/) (2026)
- [Analyzing and Improving Diffusion Models for Time-Series Data Imputation: A Proximal Recursion Perspective](https://mlsanity.com/paper/2602.01182/) (2026)
- [Generative Modeling under Non-Monotone MAR Missingness via Approximate Wasserstein Gradient Flows](https://mlsanity.com/paper/2604.04567/) (2026)
- [Observation-Aligned Mask Priors for Learning Physical Fields from Authentic Occlusions](https://mlsanity.com/paper/2605.16818/) (2026)
- [PAMF: Prior-Aware Multimodal Fusion for Incomplete Time Series Data](https://mlsanity.com/paper/2606.06328/) (2026)
- [Impute-EM: Native Mixed-State Diffusion Models for Heterogeneous Data Imputation](https://mlsanity.com/paper/2609.15284/) (2026)

## Abstract (arXiv)

This paper introduces a novel iterative method for missing data imputation that sequentially reduces the mutual information between data and the corresponding missingness mask. Inspired by GAN-based approaches that train generators to decrease the predictability of missingness patterns, our method explicitly targets this reduction in mutual information. Specifically, our algorithm iteratively minimizes the KL divergence between the joint distribution of the imputed data and missingness mask, and the product of their marginals from the previous iteration. We show that the optimal imputation under this framework can be achieved by solving an ODE whose velocity field minimizes a rectified flow training objective. We further illustrate that some existing imputation techniques can be interpreted as approximate special cases of our mutual-information-reducing framework. Comprehensive experiments on synthetic and real-world datasets validate the efficacy of our proposed approach, demonstrating its superior imputation performance. Our implementation is available at https://github.com/yujhml/MIRI-Imputation.