# CFMI: Flow Matching for Missing Data Imputation

arXiv: https://arxiv.org/abs/2506.09258 · HTML: https://mlsanity.com/paper/2506.09258/

## Key facts

- Cited by 5 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 15 of its 73 references that are in the map.
- First posted on arXiv 10 Jun 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, 15 of 15)

- [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)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Discrete Flow Matching](https://mlsanity.com/paper/2407.15595/) (2024)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [Flow Matching for Scalable Simulation-Based Inference](https://mlsanity.com/paper/2305.17161/) (2023)
- [Generating and Imputing Tabular Data via Diffusion and Flow-based Gradient-Boosted Trees](https://mlsanity.com/paper/2309.09968/) (2023)
- [Learning deep kernels for exponential family densities](https://mlsanity.com/paper/1811.08357/) (2018)
- [Uncertainty-Aware Variational-Recurrent Imputation Network for Clinical Time Series](https://mlsanity.com/paper/2003.00662/) (2020)
- [Arbitrary Conditional Distributions with Energy](https://mlsanity.com/paper/2102.04426/) (2021)

## Built on by (most cited first, 5 of 5)

- [Incomplete Data, Complete Dynamics: A Diffusion Approach](https://mlsanity.com/paper/2509.20098/) (2025)
- [Overcoming Selection Bias in Statistical Studies With Amortized Bayesian Inference](https://mlsanity.com/paper/2604.18319/) (2026)
- [PAMF: Prior-Aware Multimodal Fusion for Incomplete Time Series Data](https://mlsanity.com/paper/2606.06328/) (2026)
- [Flow Matching with Missing Data](https://mlsanity.com/paper/2607.28698/) (2026)
- [MissPath-FM: Flow Matching with Structured Priors for Partially Observed Time Series](https://mlsanity.com/paper/2610.17715/) (2026)

## Abstract (arXiv)

We introduce conditional flow matching for imputation (CFMI), a new general-purpose method to impute missing data. The method combines continuous normalising flows, flow-matching, and shared conditional modelling to deal with intractabilities of traditional multiple imputation. Our comparison with nine classical and state-of-the-art imputation methods on 24 small to moderate-dimensional tabular data sets shows that CFMI matches or outperforms both traditional and modern techniques across a wide range of metrics. Applying the method to zero-shot imputation of time-series data, we find that it matches the accuracy of a related diffusion-based method while outperforming it in terms of computational efficiency. Overall, CFMI performs at least as well as traditional methods on lower-dimensional data while remaining scalable to high-dimensional settings, matching or exceeding the performance of other deep learning-based approaches, making it a go-to imputation method for a wide range of data types and dimensionalities.