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Generative adversarial networks (GANs) are quickly becoming a ubiquitous approach to procedurally generating video game levels. While GAN generated levels are stylistically similar to human-authored examples, human designers often want to explore the generative design space of GANs to extract interesting levels. However, human designers find latent vectors opaque and would rather explore along dimensions the designer specifies, such as number of enemies or obstacles. We propose using state-of-the-art quality diversity algorithms designed to optimize continuous spaces, i.e. MAP-Elites with a directional variation operator and Covariance Matrix Adaptation MAP-Elites, to efficiently explore the latent space of a GAN to extract levels that vary across a set of specified gameplay measures. In the benchmark domain of Super Mario Bros, we demonstrate how designers may specify gameplay measures to our system and extract high-quality (playable) levels with a diverse range of level mechanics, while still maintaining stylistic similarity to human authored examples. An online user study shows how the different mechanics of the automatically generated levels affect subjective ratings of their perceived difficulty and appearance.