Countries that trade more with each other tend to have more correlated business cycles. Yet, traditional international business cycle models predict a much weaker link between trade and business cycle comovement. We propose that the international diffusion of technology through trade in varieties may be driving this comovement by increasing TFP correlation. Our hypothesis is that business cycles should be more correlated between countries that trade a wider variety of goods. We find empirical support for this hypothesis. Decomposing trade into its extensive and intensive margins, we find that the extensive margin explains most of the trade-TFP and trade-output comovement. This finding is striking since the extensive margin accounts for only one third of total trade. We then develop a three-country model of technology innovation and international diffusion through trade, in which TFP correlation increases with trade in varieties. A numerical exercise shows that the proposed mechanism increases business cycle synchronization relative to traditional models. Computing impulse responses to a TFP shock in one country, we find a strong positive effect on the output of its trading partner. Finally, our model implies a trade-output coefficient that is 40% of that in the data and five times higher than that in standard models.