  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.
