# MCFlow: Monte Carlo Flow Models for Data Imputation

arXiv: https://arxiv.org/abs/2003.12628 · HTML: https://mlsanity.com/paper/2003.12628/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2020.

## Built on by (most cited first, 30 of 37)

- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [Ambient Diffusion: Learning Clean Distributions from Corrupted Data](https://mlsanity.com/paper/2305.19256/) (2023)
- [HyperImpute: Generalized Iterative Imputation with Automatic Model Selection](https://mlsanity.com/paper/2206.07769/) (2022)
- [MissDiff: Training Diffusion Models on Tabular Data with Missing Values](https://mlsanity.com/paper/2307.00467/) (2023)
- [Transformed Distribution Matching for Missing Value Imputation](https://mlsanity.com/paper/2302.10363/) (2023)
- [DiffPuter: Empowering Diffusion Models for Missing Data Imputation](https://mlsanity.com/paper/2405.20690/) (2024)
- [MTSCI: A Conditional Diffusion Model for Multivariate Time Series Consistent Imputation](https://mlsanity.com/paper/2408.05740/) (2024)
- [Squared Neural Families: A New Class of Tractable Density Models](https://mlsanity.com/paper/2305.13552/) (2023)
- [DAEMA: Denoising Autoencoder with Mask Attention](https://mlsanity.com/paper/2106.16057/) (2021)
- [Score Matching With Missing Data](https://mlsanity.com/paper/2506.00557/) (2025)
- [EMFlow: Data Imputation in Latent Space via EM and Deep Flow Models](https://mlsanity.com/paper/2106.04804/) (2021)
- [Optimal Transport for Structure Learning Under Missing Data](https://mlsanity.com/paper/2402.15255/) (2024)
- [Missing Data Imputation by Reducing Mutual Information with Rectified Flows](https://mlsanity.com/paper/2505.11749/) (2025)
- [A Context-Aware Approach for Enhancing Data Imputation with Pre-trained Language Models](https://mlsanity.com/paper/2405.17712/) (2024)
- [FragmGAN: Generative Adversarial Nets for Fragmentary Data Imputation and Prediction](https://mlsanity.com/paper/2203.04692/) (2022)
- [FastSTI: A Fast Conditional Pseudo Numerical Diffusion Model for Spatio-temporal Traffic Data Imputation](https://mlsanity.com/paper/2410.15248/) (2024)
- [CACTI: Leveraging Copy Masking and Contextual Information to Improve Tabular Data Imputation](https://mlsanity.com/paper/2506.02306/) (2025)
- [MagiNet: Mask-Aware Graph Imputation Network for Incomplete Traffic Data](https://mlsanity.com/paper/2406.03511/) (2024)
- [Impute-MACFM: Imputation based on Mask-Aware Flow Matching](https://mlsanity.com/paper/2509.23126/) (2025)
- [Training Deep Normalizing Flow Models in Highly Incomplete Data Scenarios with Prior Regularization](https://mlsanity.com/paper/2104.01482/) (2021)
- [Semi-supervised Learning with Missing Values Imputation](https://mlsanity.com/paper/2106.01708/) (2021)
- [Viscos Flows: Variational Schur Conditional Sampling With Normalizing Flows](https://mlsanity.com/paper/2107.02474/) (2021)
- [Missingness Augmentation: A General Approach for Improving Generative Imputation Models](https://mlsanity.com/paper/2108.02566/) (2021)
- [CoreFlow: Low-Rank Matrix Generative Models](https://mlsanity.com/paper/2604.24959/) (2026)
- [Deep Distribution-preserving Incomplete Clustering with Optimal Transport](https://mlsanity.com/paper/2103.11424/) (2021)
- [Towards a methodology for addressing missingness in datasets, with an application to demographic health datasets](https://mlsanity.com/paper/2211.02856/) (2022)
- [Monotone deep Boltzmann machines](https://mlsanity.com/paper/2307.04990/) (2023)
- [FlexSSL : A Generic and Efficient Framework for Semi-Supervised Learning](https://mlsanity.com/paper/2312.16892/) (2023)
- [NeuralPrefix: A Zero-shot Sensory Data Imputation Plugin](https://mlsanity.com/paper/2502.05883/) (2025)
- [Global Ease of Living Index: a machine learning framework for longitudinal analysis of major economies](https://mlsanity.com/paper/2502.06866/) (2025)

## Abstract (arXiv)

We consider the topic of data imputation, a foundational task in machine learning that addresses issues with missing data. To that end, we propose MCFlow, a deep framework for imputation that leverages normalizing flow generative models and Monte Carlo sampling. We address the causality dilemma that arises when training models with incomplete data by introducing an iterative learning scheme which alternately updates the density estimate and the values of the missing entries in the training data. We provide extensive empirical validation of the effectiveness of the proposed method on standard multivariate and image datasets, and benchmark its performance against state-of-the-art alternatives. We demonstrate that MCFlow is superior to competing methods in terms of the quality of the imputed data, as well as with regards to its ability to preserve the semantic structure of the data.