The recent literature on idea flows studies technology diffusion in isolation, in environments without the generation of new ideas. Without new ideas, growth cannot continue forever if there is a finite technology frontier. In an economy in which firms choose to innovate, adopt technology, or keep producing with their existing technology, we study how innovation and diffusion interact to endogenously determine the productivity distribution with a finite but expanding frontier. There is a tension in the determination of the productivity distribution—innovation tends to stretch the distribution, while diffusion compresses it. Finally, we analyze the degree to which innovation and technology diffusion at the firm level contribute to aggregate economic growth and can lead to hysteresis.