Do migrants shape the dynamic comparative advantage of their sending and receiving countries? To answer this question we study the drivers of knowledge diffusion by looking at the dynamics of the export basket of countries, with particular focus on migration. The fact that knowledge diffusion requires direct human interaction implies that the international diffusion of knowledge should follow the pattern of international migration. This is what this paper documents. Our main finding is that migration, and particularly skilled immigration, is a strong and robust driver of productive knowledge diffusion as measured by the appearance and growth of tradable goods in the migrants' receiving and sending countries. We find that a 10% increase in the stock of immigrants from countries exporters of a given product is associated with a 2% increase in the likelihood that the host country will start exporting that good "from scratch" in the following 10-year period. In terms of ability to expand the export basket of countries, a migrant with college education or above is about ten times more "effective" than an unskilled migrant. The results are robust to accounting for shifts in product-specific global demand, to excluding bilateral trade possibly generated by network effects, as well as to instrumenting for migration using a gravity model.