Growth and imports are correlated across countries, but the mechanisms underlying this relationship are not well understood. I develop a multi-country model in which imports and growth are connected by technological innovations and their international diffusion through trade. Fitting the model to data on innovation, productivity, and trade in varieties, I find that most of the growth-imports correlation is explained by these two mechanisms. I also find that the trade channel has been particularly important in developing countries, accounting for about three-fourths of their growth. Finally, I run counterfactuals analysis.