Diverse input data modalities can provide complementary cues for several tasks, usually leading to more robust algorithms and better performance. However, while a (training) dataset could be accurately designed to include a variety of sensory inputs, it is often the case that not all modalities could be available in real life (testing) scenarios, where a model has to be deployed. This raises the challenge of how to learn robust representations leveraging multimodal data in the training stage, while considering limitations at test time, such as noisy or missing modalities. This paper presents a new approach for multimodal video action recognition, developed within the unified frameworks of distillation and privileged information, named generalized distillation. Particularly, we consider the case of learning representations from depth and RGB videos, while relying on RGB data only at test time. We propose a new approach to train an hallucination network that learns to distill depth features through multiplicative connections of spatiotemporal representations, leveraging soft labels and hard labels, as well as distance between feature maps. We report state-of-the-art results on video action classification on the largest multimodal dataset available for this task, the NTU RGB+D. Code available at https://github.com/ncgarcia/ modality-distillation