We consider vector space interference alignment strategies over the -user interference channel and derive an upper bound on the achievable degrees of freedom as a function of the channel diversity , where the channel diversity is modeled by real-valued parallel channels with coefficients drawn from a nondegenerate joint distribution. The seminal work of Cadambe and Jafar shows that when is unbounded, vector space interference alignment can achieve 1/2 degrees of freedom per user independent of the number of users . However, wireless channels have limited diversity, in practice, dictated by their coherence time and bandwidth, and an important question is the number of degrees of freedom achievable at finite . When and if is finite, Bresler et al. show that the number of degrees of freedom achievable with vector space interference alignment is bounded away from 1/2, and the gap decreases inversely proportional to . In this paper, we show that when , the gap is significantly larger. In particular, the gap to the optimal 1/2 degrees of freedom per user can decrease at most like , and when is smaller than the order of , it decays at most like $1/\sqrt [{4}]{L}$ .