Fine-grained semantic understanding of 3D objects is crucial in many applications such as object manipulation. However, it is hard to give a universal definition of point-level semantics that everyone would agree on. We observe that people are pretty sure about semantic correspondences between two areas from different objects, but less certain about what each area means in semantics. Therefore, we argue that by providing human labeled correspondences between different objects from the same category, one can recover rich semantic information of an object. In this paper, we propose a method that outputs dense semantic embeddings based on a novel geodesic consistency loss. Accordingly, a new dataset named CorresPondenceNet and its corresponding benchmark are designed. Several state-of-the-art networks are evaluated based on our proposed method. We show that our method could boost the fine-grained understanding of heterogeneous objects and the inference of dense semantic information is possible.