- Abstract: Missing data imputation methods based on deep generative models often perform poorly in real-world applications, due to the heterogeneity of natural data sets. Heterogeneity arises from data containing different types of features (categorical, ordinal, continuous, etc.) and features of the same type having different marginal distributions. We propose an extension of variational autoencoders (VAEs) called VAEM to handle such heterogeneous data. We develop a corresponding efficient inference method, provide extensions, and demonstrate the performance of VAEM in missing data imputation tasks. Our results show that VAEM broadens the range of real-world applications where deep generative models can be successfully deployed.