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The development of machine-learning models for atomic-scale simulations has greatly benefited from the large databases of materials and molecular properties, computed using electronic-structure calculations. Recently, these databases enabled the training of “universal” models that aim to make accurate predictions for arbitrary atomic geometries and compositions. However, many of these databases were originally designed for materials discovery, focusing primarily on equilibrium structures. Here, we introduce a dataset designed to train machine-learning models to make reasonable predictions for arbitrary structures. Starting with relatively small sets of stable structures, we built the dataset aiming to achieve “massive atomic diversity” (MAD) by aggressively modifying these structures and utilizing highly consistent electronic-structure settings for property calculations. Despite containing fewer than 100,000 entries, the MAD dataset has already enabled the training of universal interatomic potentials that rival those trained on datasets containing two to three orders of magnitude more data. We detail the design philosophy of the dataset and introduce low-dimensional structural latent space descriptors that can be used as a general-purpose materials cartography tool.