The optimal DMT (diversity and multiplexing tradeoff) of interference channel is still unknown. In this paper, we investigate the maximum diversity gain of interference channel and try to answer two questions. Firstly, it is known that no two links can achieve their maximum DoF (degree of freedom) simultaneously in an interference channel. The question is whether two links can achieve their maximum diversity gains simultaneously over MIMO or diagonal interference channel? Secondly, it has been shown in the literature that, with IA (interference alignment) and single-beam transmission, only one-side diversity gain (transmit or receive) is achievable in MIMO interference channel. The question is whether IA is optimal in achieving diversity gain and whether both of the transmit and receive diversity gains of MIMO interference channel can be obtained simultaneously? The major contribution of this paper is to show that, although two links in MIMO interference channel can not obtain their maximum diversity gains at the same time, both the transmit and receive diversity gains are achievable. On the other hand, two links in diagonal interference channel can obtain their maximum channel freedoms at the same time, which correspond to the maximum diversity gains.