More than 3 billion people lack access to care for skin disease. AI diagnostic tools may aid in early skin cancer detection; however most models have not been assessed on images of diverse skin tones or uncommon diseases. To address this, we curated the Diverse Dermatology Images (DDI) dataset - the first publicly available, pathologically confirmed images featuring diverse skin tones. We show that state-of-the-art dermatology AI models perform substantially worse on DDI, with ROC-AUC dropping 29-40 percent compared to the models' original results. We find that dark skin tones and uncommon diseases, which are well represented in the DDI dataset, lead to performance drop-offs. Additionally, we show that state-of-the-art robust training methods cannot correct for these biases without diverse training data. Our findings identify important weaknesses and biases in dermatology AI that need to be addressed to ensure reliable application to diverse patients and across all disease.