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Sensor fusion can significantly improve the performance of many computer vision tasks. However, traditional fusion approaches are either not data-driven and cannot exploit prior knowledge nor find regularities in a given dataset or they are restricted to a single application. We overcome this shortcoming by presenting a novel deep hierarchical variational autoencoder called FusionVAE that can serve as a basis for many fusion tasks. Our approach is able to generate diverse image samples that are conditioned on multiple noisy, occluded, or only partially visible input images. We derive and optimize a variational lower bound for the conditional log-likelihood of FusionVAE. In order to assess the fusion capabilities of our model thoroughly, we created three novel datasets for image fusion based on popular computer vision datasets. In our experiments, we show that FusionVAE learns a representation of aggregated information that is relevant to fusion tasks. The results demonstrate that our approach outperforms traditional methods significantly. Furthermore, we present the advantages and disadvantages of different design choices.