Automated generation of conversational dialogue using modern neural architectures has made notable advances. However, these models are known to have a drawback of often producing uninteresting, predictable responses; this is known as the diversity problem. We introduce a new strategy to address this problem, called Diversity-Informed Data Collection. Unlike prior approaches, which modify model architectures to solve the problem, this method uses dynamically computed corpus-level statistics to determine which conversational participants to collect data from. Diversity-Informed Data Collection produces significantly more diverse data than baseline data collection methods, and better results on two downstream tasks: emotion classification and dialogue generation. This method is generalizable and can be used with other corpus-level metrics.