# Generative Modeling under Non-Monotone MAR Missingness via Approximate Wasserstein Gradient Flows

arXiv: https://arxiv.org/abs/2604.04567 · HTML: https://mlsanity.com/paper/2604.04567/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 31 references that are in the map.
- First posted on arXiv 6 Apr 2026.

## Builds on (most cited first, 10 of 10)

- [OpenML: networked science in machine learning](https://mlsanity.com/paper/1407.7722/) (2014)
- [GAIN: Missing Data Imputation using Generative Adversarial Nets](https://mlsanity.com/paper/1806.02920/) (2018)
- [HyperImpute: Generalized Iterative Imputation with Automatic Model Selection](https://mlsanity.com/paper/2206.07769/) (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)
- [What Is Meant by "Missing at Random"?](https://mlsanity.com/paper/1306.2812/) (2013)
- [Minimizing f-Divergences by Interpolating Velocity Fields](https://mlsanity.com/paper/2305.15577/) (2023)
- [Missing Data Imputation by Reducing Mutual Information with Rectified Flows](https://mlsanity.com/paper/2505.11749/) (2025)
- [Parametric MMD Estimation with Missing Values: Robustness to Missingness and Data Model Misspecification](https://mlsanity.com/paper/2503.00448/) (2025)
- [A Unified Inference Framework for Multiple Imputation Using Martingales](https://mlsanity.com/paper/1911.04663/) (2019)

## Abstract (arXiv)

The prevalence of missing values in data science poses a substantial risk to any further analyses. Despite a wealth of research, principled nonparametric methods to deal with general non-monotone missingness are still scarce. Instead, ad-hoc imputation methods are often used, for which it remains unclear whether the correct distribution can be recovered. In this paper, we propose FLOWGEM, a principled iterative method for generating a complete dataset from a dataset with values Missing at Random (MAR). Motivated by convergence results of the ignoring maximum likelihood estimator, our approach minimizes the expected Kullback-Leibler (KL) divergence between the observed data distribution and the distribution of the generated sample over different missingness patterns. To minimize the KL divergence, we employ a discretized particle evolution of the corresponding Wasserstein Gradient Flow, where the velocity field is approximated using a local linear estimator of the density ratio. This construction yields a data generation scheme that iteratively transports an initial particle ensemble toward the target distribution. Simulation studies and real-data benchmarks demonstrate that FLOWGEM achieves state-of-the-art performance across a range of settings, including the challenging case of non-monotone MAR mechanisms. Together, these results position FLOWGEM as a principled and practical alternative to existing imputation methods, and a decisive step towards closing the gap between theoretical rigor and empirical performance.