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

• URL: http://arxiv.org/abs/2604.04567v1
• Date: Mon, 06 Apr 2026 09:56:08 GMT
• Title: Generative Modeling under Non-Monotonic MAR Missingness via Approximate Wasserstein Gradient Flows
• Abstract summary: We propose a principled iterative method for generating a complete dataset from a dataset with values Missing at Random (MAR)<n>FLOWGEM minimizes the expected Kullback-Leibler (KL) divergence between the observed data distribution and the distribution of the generated sample over different missingness patterns.<n>It achieves state-of-the-art performance across a range of settings, including the challenging case of non-monotonic MAR mechanisms.
• Score: 6.221876252052772
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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-monotonic 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.

Related papers

• Impute-EM: Native Mixed-State Diffusion Models for Heterogeneous Data Imputation [71.74203645336385]
  Impute-EM alternates between imputing missing entries with the current model and refitting a diffusion backbone on completed data.<n>We characterize the update and show that the observed mask-indexed marginals match the targets at the limit.
  arXiv  Detail & Related papers  (2026-09-14T09:39:13Z)
• Distributionally Faithful Imputation via Positive Semi-Definite Kernel Density Estimation [55.47411235954028]
  We recast imputation under missing completely at random as density estimation from masked observations.<n>We obtain a convex empirical risk problem with closed form marginals, solvable by a Newton interior point method.<n>The resulting PSD Impute model yields both single and multiple imputations from the same fitted density.
  arXiv  Detail & Related papers  (2026-07-08T15:51:05Z)
• A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models [0.3222802562733787]
  We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via deterministic dynamics.<n>We present a unified framework in which diffusion models, score-based generative models, and flow matching are instances of learning a time-dependent vector field.
  arXiv  Detail & Related papers  (2026-05-07T18:32:15Z)
• Flow Matching is Adaptive to Manifold Structures [32.55405572762157]
  Flow matching is a simulation-based alternative to diffusion-based generative modeling.<n>We show how flow matching adapts to data geometry and circumvents the curse of dimensionality.
  arXiv  Detail & Related papers  (2026-02-25T23:52:32Z)
• Dimension-free error estimate for diffusion model and optimal scheduling [22.20348860913421]
  Diffusion generative models have emerged as powerful tools for producing synthetic data from an empirically observed distribution.<n>Previous analyses have quantified the error between the generated and the true data distributions in terms of Wasserstein distance or Kullback-Leibler divergence.<n>In this work, we derive an explicit, dimension-free bound on the discrepancy between the generated and the true data distributions.
  arXiv  Detail & Related papers  (2025-12-01T15:58:20Z)
• Generative Modeling with Continuous Flows: Sample Complexity of Flow Matching [60.37045080890305]
  We provide the first analysis of the sample complexity for flow-matching based generative models.<n>We decompose the velocity field estimation error into neural-network approximation error, statistical error due to the finite sample size, and optimization error due to the finite number of optimization steps for estimating the velocity field.
  arXiv  Detail & Related papers  (2025-12-01T05:14:25Z)
• On the Wasserstein Convergence and Straightness of Rectified Flow [54.580605276017096]
  Rectified Flow (RF) is a generative model that aims to learn straight flow trajectories from noise to data.<n>We provide a theoretical analysis of the Wasserstein distance between the sampling distribution of RF and the target distribution.<n>We present general conditions guaranteeing uniqueness and straightness of 1-RF, which is in line with previous empirical findings.
  arXiv  Detail & Related papers  (2024-10-19T02:36:11Z)
• Convergence of Score-Based Discrete Diffusion Models: A Discrete-Time Analysis [56.442307356162864]
  We study the theoretical aspects of score-based discrete diffusion models under the Continuous Time Markov Chain (CTMC) framework.<n>We introduce a discrete-time sampling algorithm in the general state space $[S]d$ that utilizes score estimators at predefined time points.<n>Our convergence analysis employs a Girsanov-based method and establishes key properties of the discrete score function.
  arXiv  Detail & Related papers  (2024-10-03T09:07:13Z)
• Spatially-Aware Diffusion Models with Cross-Attention for Global Field Reconstruction with Sparse Observations [1.371691382573869]
  We develop and enhance score-based diffusion models in field reconstruction tasks. We introduce a condition encoding approach to construct a tractable mapping mapping between observed and unobserved regions. We demonstrate the ability of the model to capture possible reconstructions and improve the accuracy of fused results.
  arXiv  Detail & Related papers  (2024-08-30T19:46:23Z)
• Collaborative Heterogeneous Causal Inference Beyond Meta-analysis [68.4474531911361]
  We propose a collaborative inverse propensity score estimator for causal inference with heterogeneous data. Our method shows significant improvements over the methods based on meta-analysis when heterogeneity increases.
  arXiv  Detail & Related papers  (2024-04-24T09:04:36Z)
• Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distribution [2.1146241717926664]
  We show that the Wasserstein GAN, constrained to left-invertible push-forward maps, generates distributions that avoid replication and significantly deviate from the empirical distribution. Our most important contribution provides a finite-sample lower bound on the Wasserstein-1 distance between the generative distribution and the empirical one. We also establish a finite-sample upper bound on the distance between the generative distribution and the true data-generating one.
  arXiv  Detail & Related papers  (2023-07-31T06:11:57Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.