Weakly Supervised Object Localization (WSOL) aims to localize objects with only image-level labels, which has better scalability and practicability than fully supervised methods in the actual deployment. However, a common limitation for available techniques based on classification networks is that they only highlight the most discriminative part of the object, not the entire object. To alleviate this problem, we propose a novel end-to-end part discovery model (PDM) to learn multiple discriminative object parts in a unified network for accurate object localization and classification. The proposed PDM enjoys several merits. First, to the best of our knowledge, it is the first work to directly model diverse and robust object parts by exploiting part diversity, compactness, and importance jointly for WSOL. Second, three effective mechanisms including diversity, compactness, and importance learning mechanisms are designed to learn robust object parts. Therefore, our model can exploit complementary spatial information and local details from the learned object parts, which help to produce precise bounding boxes and discriminate different object categories. Extensive experiments on two standard benchmarks demonstrate that our PDM performs favorably against state-of-the-art WSOL approaches.