We investigate the relationship between the presence of migrant inventors and the dynamics of innovation in the migrants' receiving countries. We find that countries are 25 to 50 percent more likely to gain advantage in patenting in certain technologies given a twofold increase in the number of foreign inventors from other nations that specialize in those same technologies. For the average country in our sample this number corresponds to only 25 inventors and a standard deviation of 135. We deal with endogeneity concerns by using historical migration networks to instrument for stocks of migrant inventors. Our results generalize the evidence of previous studies that show how migrant inventors "import" knowledge from their home countries which translate into higher patenting. We complement our results with micro-evidence showing that migrant inventors are more prevalent in the first bulk of patents of a country in a given technology, as compared to patents filed at later stages. We interpret these results as tangible evidence of migrants facilitating the technology-specific diffusion of knowledge across nations.