We present an active learning strategy for training parametric models of distance metrics, given triplet-based similarity assessments: object $x_i$ is more similar to object $x_j$ than to $x_k$. In contrast to prior work on class-based learning, where the fundamental goal is classification and any implicit or explicit metric is binary, we focus on perceptual metrics that express the degree of (dis)similarity between objects. We find that standard active learning approaches degrade when annotations are requested for batches of triplets at a time: our studies suggest that correlation among triplets is responsible. In this work, we propose a novel method to decorrelate batches of triplets, that jointly balances informativeness and diversity while decoupling the choice of heuristic for each criterion. Experiments indicate our method is general, adaptable, and outperforms the state-of-the-art.