Animating digital characters has an important role in computer assisted experiences, from video games to movies to interactive robotics. A critical challenge in the field is to generate animations which accurately reflect the state of the animated characters, without looking repetitive or unnatural. In this work, we investigate the problem of procedurally generating a diverse variety of facial animations that express a given semantic quality (e.g., very happy). To that end, we introduce a new learning heuristic called Precision Variety Learning (PVL) which actively identifies and exploits the fundamental trade-off between precision (how accurate positive labels are) and variety (how diverse the set of positive labels is). We both identify conditions where important theoretical properties can be guaranteed, and show good empirical performance in variety of conditions. Lastly, we apply our PVL heuristic to our motivating problem of generating smile animations, and perform several user studies to validate the ability of our method to produce a perceptually diverse variety of smiles for different target intensities.