This paper introduces DiffPuter, an iterative method for missing data
imputation that leverages the Expectation-Maximization (EM) algorithm and
Diffusion Models. By treating missing data as hidden variables that can be
updated during model training, we frame the missing data imputation task as an
EM problem. During the M-step, DiffPuter employs a diffusion model to learn the
joint distribution of both the observed and currently estimated missing data.
In the E-step, DiffPuter re-estimates the missing data based on the conditional
probability given the observed data, utilizing the diffusion model learned in
the M-step. Starting with an initial imputation, DiffPuter alternates between
the M-step and E-step until convergence. Through this iterative process,
DiffPuter progressively refines the complete data distribution, yielding
increasingly accurate estimations of the missing data. Our theoretical analysis
demonstrates that the unconditional training and conditional sampling processes
of the diffusion model align precisely with the objectives of the M-step and
E-step, respectively. Empirical evaluations across 10 diverse datasets and
comparisons with 16 different imputation methods highlight DiffPuter's superior
performance. Notably, DiffPuter achieves an average improvement of 8.10% in MAE
and 5.64% in RMSE compared to the most competitive existing method.

DiffPuter 是一种迭代方法，利用期望最大化算法和扩散模型进行缺失数据填补，其通过将缺失数据视为可在模型训练过程中更新的隐藏变量，并将缺失数据填补任务作为 EM 问题来处理。DiffPuter 通过扩散模型来学习观测到的数据和当前估计的缺失数据的联合分布，然后根据给定观测数据的条件概率利用在 M-step 学习的扩散模型重新估计缺失数据，通过这个迭代过程，DiffPuter 逐步改进了完整数据分布，产生了对缺失数据越来越准确的估计，理论分析和实证评估表明 DiffPuter 的优越性，与 16 种不同的填补方法相比，在 10 个不同的数据集上，DiffPuter 的 MAE 平均改善了 8.10％，RMSE 平均改善了 5.64％。