  We consider the topic of data imputation, a foundational task in machine
learning that addresses issues with missing data. To that end, we propose
MCFlow, a deep framework for imputation that leverages normalizing flow
generative models and Monte Carlo sampling. We address the causality dilemma
that arises when training models with incomplete data by introducing an
iterative learning scheme which alternately updates the density estimate and
the values of the missing entries in the training data. We provide extensive
empirical validation of the effectiveness of the proposed method on standard
multivariate and image datasets, and benchmark its performance against
state-of-the-art alternatives. We demonstrate that MCFlow is superior to
competing methods in terms of the quality of the imputed data, as well as with
regards to its ability to preserve the semantic structure of the data.
