# Impute-MACFM: Imputation based on Mask-Aware Flow Matching

arXiv: https://arxiv.org/abs/2509.23126 · HTML: https://mlsanity.com/paper/2509.23126/

## Key facts

- Cited by 2 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 32 of its 45 references that are in the map.
- First posted on arXiv 27 Sep 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, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Glow: Generative Flow with Invertible 1x1 Convolutions](https://mlsanity.com/paper/1807.03039/) (2018)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [TabTransformer: Tabular Data Modeling Using Contextual Embeddings](https://mlsanity.com/paper/2012.06678/) (2020)
- [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)
- [SAINT: Improved Neural Networks for Tabular Data via Row Attention and Contrastive Pre-Training](https://mlsanity.com/paper/2106.01342/) (2021)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (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)
- [TransTab: Learning Transferable Tabular Transformers Across Tables](https://mlsanity.com/paper/2205.09328/) (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)
- [not-MIWAE: Deep Generative Modelling with Missing not at Random Data](https://mlsanity.com/paper/2006.12871/) (2020)
- [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)

## Built on by (most cited first, 2 of 2)

- [Observation-Aligned Mask Priors for Learning Physical Fields from Authentic Occlusions](https://mlsanity.com/paper/2605.16818/) (2026)
- [MissPath-FM: Flow Matching with Structured Priors for Partially Observed Time Series](https://mlsanity.com/paper/2610.17715/) (2026)

## Abstract (arXiv)

Tabular data are central to many applications, especially longitudinal data in healthcare, where missing values are common, undermining model fidelity and reliability. Prior imputation methods either impose restrictive assumptions or struggle with complex cross-feature structure, while recent generative approaches suffer from instability and costly inference. We propose Impute-MACFM, a mask-aware conditional flow matching framework for tabular imputation that addresses missingness mechanisms, missing completely at random, missing at random, and missing not at random. Its mask-aware objective builds trajectories only on missing entries while constraining predicted velocity to remain near zero on observed entries, using flexible nonlinear schedules. Impute-MACFM combines: (i) stability penalties on observed positions, (ii) consistency regularization enforcing local invariance, and (iii) time-decayed noise injection for numeric features. Inference uses constraint-preserving ordinary differential equation integration with per-step projection to fix observed values, optionally aggregating multiple trajectories for robustness. Across diverse benchmarks, Impute-MACFM achieves state-of-the-art results while delivering more robust, efficient, and higher-quality imputation than competing approaches, establishing flow matching as a promising direction for tabular missing-data problems, including longitudinal data.