Humans excel in grasping objects through diverse and robust policies, many of which are so probabilistically rare that exploration-based learning methods hardly observe and learn. Inspired by the human learning process, we propose a method to extract and exploit latent intents from demonstrations, and then learn diverse and robust grasping policies through self-exploration. The resulting policy can grasp challenging objects in various environments with an off-the-shelf parallel gripper. The key component is a learned intention estimator, which maps gripper pose and visual sensory to a set of sub-intents covering important phases of the grasping movement. Sub-intents can be used to build an intrinsic reward to guide policy learning. The learned policy demonstrates remarkable zero-shot generalization from simulation to the real world while retaining its robustness against states that have never been encountered during training, novel objects such as protractors and user manuals, and environments such as the cluttered conveyor.