Domain generalization aims at training machine learning models to perform robustly across different and unseen domains. Several recent methods use multiple datasets to train models to extract domain-invariant features, hoping to generalize to unseen domains. Instead, first we explicitly train domain-dependant representations by using ad-hoc batch normalization layers to collect independent domain’s statistics. Then, we propose to use these statistics to map domains in a shared latent space, where membership to a domain can be measured by means of a distance function. At test time, we project samples from an unknown domain into the same space and infer properties of their domain as a linear combination of the known ones. We apply the same mapping strategy at training and test time, learning both a latent representation and a powerful but lightweight ensemble model. We show a significant increase in classification accuracy over current state-of-the-art techniques on popular domain generalization benchmarks: PACS, Office-31 and Office-Caltech.