Title: Can Students Outperform Teachers in Knowledge Distillation based Model Compression?. Abstract: Knowledge distillation (KD) is an effective technique to compress a large model (teacher) to a compact one (student) by knowledge transfer. The ideal case is that the teacher is compressed to the small student without any performance dropping. However, even for the state-of-the-art (SOTA) distillation approaches, there is still an obvious performance gap between the student and the teacher. The existing literature usually attributes this to model capacity differences between them. However, model capacity differences are unavoidable in model compression. In this work, we systematically study this question. By designing exploratory experiments, we find that model capacity differences are not necessarily the root reason, and the distillation data matters when the student capacity is greater than a threshold. In light of this, we propose to go beyond in-distribution distillation and accordingly develop KD+. KD+ is superior to the original KD as it outperforms KD and the other SOTA approaches substantially and is more compatible with the existing approaches to further improve their performances significantly.