Multimodal learning assumes all modality combinations of interest are available during training to learn cross-modal correspondences. In this paper, we challenge this modality-complete assumption for multimodal learning and instead strive for generalization to unseen modality combinations during inference. We pose the problem of unseen modality interaction and introduce a first solution. It exploits a module that projects the multidimensional features of different modalities into a common space with rich information preserved. This allows the information to be accumulated with a simple summation operation across available modalities. To reduce overfitting to less discriminative modality combinations during training, we further improve the model learning with pseudo-supervision indicating the reliability of a modality’s prediction. We demonstrate that our approach is effective for diverse tasks and modalities by evaluating it for multimodal video classification, robot state regression, and multimedia retrieval.