Learning high-quality, self-supervised, visual representations is essential to advance the role of computer vision in biomedical microscopy and clinical medicine. Previous work has focused on self-supervised representation learning (SSL) methods developed for instance discrimination and applied them directly to image patches, or fields-of-view, sampled from gigapixel whole-slide images (WSIs) used for cancer diagnosis. However, this strategy is limited because it (1) assumes patches from the same patient are independent, (2) neglects the patient-slide-patch hierarchy of clinical biomedical microscopy, and (3) requires strong data augmentations that can degrade downstream performance. Importantly, sampled patches from WSIs of a patient's tumor are a diverse set of image examples that capture the same underlying cancer diagnosis. This motivated HiDisc, a data-driven method that leverages the inherent patient-slide-patch hierarchy of clinical biomedical microscopy to define a hierarchical discriminative learning task that implicitly learns features of the underlying diagnosis. HiDisc uses a self-supervised contrastive learning framework in which positive patch pairs are defined based on a common ancestry in the data hierarchy, and a unified patch, slide, and patient discriminative learning objective is used for visual SSL. We benchmark HiDisc visual representations on two vision tasks using two biomedical microscopy datasets, and demonstrate that (1) HiDisc pretraining outperforms current state-of-the-art self-supervised pretraining methods for cancer diagnosis and genetic mutation prediction, and (2) HiDisc learns high-quality visual representations using natural patch diversity without strong data augmentations.