Learning What Not to Impute: An Uncertainty-Aware Diffusion Framework for Meaningful Missingness

Missing data frequently arises across diverse domains, including time-series and image domains. In the real world, missing occurrences often depend on the unobservable values themselves, which are referred to as Missing Not at Random (MNAR). In this work, we introduce the Missing Pattern Recognized Diffusion Imputation Model (PRDIM), a novel framework that explicitly captures the missing pattern and precisely imputes unobserved values. PRDIM iteratively maximizes the likelihood of the joint distribution for observed values and missing mask under an Expectation-Maximization (EM) algorithm. In this sense, we first employ a pattern recognizer, which approximates the underlying missing pattern and provides guidance during every inference toward more plausible imputations with respect to the missing information. Through extensive experiments, we demonstrate that PRDIM consistently achieves strong imputation performance under MNAR settings across multiple data modalities.

Missing data imputation remains a fundamental challenge in modern data science, especially when uncertainty quantification is essential. In this work, we propose MissBGM, an AI-powered missing data imputation method via Bayesian generative modeling that bridges the expressive flexibility of neural networks with the statistical rigor of Bayesian inference. Unlike existing methods that often focus on point estimates or treat the missingness mechanism implicitly, MissBGM explicitly and jointly models the data-generating and missingness mechanisms, providing principled posterior uncertainty over imputations rather than a single point estimate. We develop a stochastic optimization framework with alternating updates among missing values, model parameters, and latent variables until convergence. Our theoretical analysis shows that estimates of missing values from MissBGM converge consistently under mild assumptions. Empirically, we demonstrate that MissBGM achieves superior performance over traditional imputers and recent neural network-based methods across extensive experimental settings. These results establish MissBGM as a principled and scalable solution for modern missing data imputation. The code for MissBGM is open sourced at https://github.com/liuq-lab/MissBGM.

Missing values are ubiquitous in heterogeneous data mining, where numerical, categorical, and binary variables often coexist. Many imputation methods, especially diffusion-based ones, treat discrete variables through continuous surrogates such as one-hot relaxations rather than modeling them natively. This creates a mismatch between the model state space and the mixed discrete and continuous structure of the data. We propose Impute-EM, an Expectation Maximization style framework that alternates between imputing missing entries with the current model and refitting a diffusion backbone on completed data. We instantiate Impute-EM with native mixed-state diffusion backbones for heterogeneous data, combining Gaussian and masked categorical components without one-hot relaxations. In exact settings, we characterize the update and show that the observed mask-indexed marginals match the targets at the limit, while making explicit that the full data distribution is generally non-identifiable from incomplete observations alone. Empirically, Impute-EM delivers the best distributional fidelity on mixed-type tabular imputation, on which downstream modeling relies, with text imputation serving as a controlled validation of the native discrete backbone.