Experimental design techniques such as active search and Bayesian optimization are widely used in the natural sciences for data collection and discovery. However, existing techniques tend to favor exploitation over exploration of the search space, which causes them to get stuck in local optima. This “collapse” problem prevents experimental design algorithms from yielding diverse high-quality data. In this paper, we extend the Vendi scores—a recently introduced family of diversity metrics—to account for quality. We then leverage these quality-weighted Vendi scores to tackle many experimental design problems across various applications such as product recommendation, drug and materials discovery, and reinforcement learning. We found that quality-weighted Vendi scores allow us to construct policies for experimental design that flexibly balance quality and diversity, and ultimately assemble rich and diverse sets of high-performing data points.