Diversity tends to generate more and better ideas in social settings, ranging in scale from small-deliberative groups to tech-clusters and cities. Implicit in this research is that there are knowledge-generating benefits from diversity that comes from mixing different individuals, ideas, and perspectives. Here, we utilize agent-based modeling to examine the emergent outcomes resulting from the manipulation of how diversity is distributed and how knowledge is generated within communicative social structures. In the context of problem solving, we focus on cognitive diversity and its two forms: ability and knowledge. For diversity of ability, we find that local diversity (intermixing of different agents) performs best at all time scales. However, for diversity of knowledge, we find that local homogeneity performs best in the long-run, because it maintains global diversity, and thus the knowledge-generating ability of the group, for a longer period.