A major challenge in sparsity pattern estimation is that small modes are difficult to detect in the presence of noise. This problem is alleviated if one can observe samples from multiple realizations of the nonzero values for the same sparsity pattern. We will refer to this as ``diversity''. Diversity comes at a price, however, since each new realization adds new unknown nonzero values, thus increasing uncertainty. In this paper, it is shown that diversity introduces a tradeoff between the uncertainty in the noise and the uncertainty in the nonzero values. The optimal amount of diversity is characterized as a function of the number of observations and the accuracy. One question that is addressed is how the optimal amount of diversity behaves as the signal-to-noise ratio increases. Interestingly, the optimal behavior is opposite depending on whether one wishes to minimize the number of observations or maximize the accuracy. This is due to a sharp ``corner'' in the tradeoff between observations and accuracy. 