We propose Emputation, a deep generative framework for learning imputation models. Emputation targets the extrapolation distribution of missing variables given observed variables, and training is guided by specific missingness assumptions that guarantee identification of the target distribution. The training objective, called the emputation risk, is an energy-score-based risk in which the identification assumption determines how observed entries are masked and which observations contribute to training. The resulting framework enables direct conditional sampling for multiple imputation. We show that the population minimizer of the emputation risk recovers the target extrapolation distribution under a broad class of identification assumptions, including several missing-not-at-random assumptions. Simulations show strong performance under both pointwise and distributional evaluation metrics, and an application to an Alzheimer's disease dataset demonstrates its practical value.

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