The shift from individual effort to collaborative output has benefited science, with scientific work pursued collaboratively having increasingly led to more highly impactful research than that pursued individually. However, understanding of how the diversity of a collaborative team influences the production of knowledge and innovation is sorely lacking. Here, we study this question by breaking down the process of scientific collaboration of 32.9 million papers over the last five decades. We find that the probability of producing a top-cited publication increases as a function of the diversity of a team of collaborators---namely, the distinct number of institutions represented by the team. We discover striking phenomena where a smaller, yet more diverse team is more likely to generate highly innovative work than a relatively larger team within one institution. We demonstrate that the synergy of collaboration diversity is universal across different generations, research fields, and tiers of institutions and individual authors. Our findings suggest that collaboration diversity strongly and positively correlates with the production of scientific innovation, giving rise to the potential revolution of the policies used by funding agencies and authorities to fund research projects, and broadly the principles used to organize teams, organizations, and societies.