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We report on a systematic study of guest cation (i.e., Li, Na, or Mg) diffusion within spinel intercalation compounds, a promising class of materials for Li-, Na-, and Mg-ion batteries. Using kinetic Monte Carlo simulations, we identify factors that are responsible for a strong concentration dependence of the cation diffusion coefficient. We focus on spinels in which the guest cations prefer the octahedral sites and where diffusion is mediated by vacancy clusters. Starting with MgyTiS2, we predict an abrupt drop in the Mg diffusion coefficient that spans several orders of magnitude around y ≈ 0.5 due to the onset of highly correlated Mg diffusion. The prediction is consistent with previous experimental studies that are only able to achieve half the theoretical capacity of MgyTiS2. We next perform a parametric study of diffusion in spinels using kinetic Monte Carlo simulations applied to lattice model Hamiltonians and identify a critical topological weakness of the spinel crystal structure that makes it prone to highly correlated cation diffusion at intermediate-to-high guest cation concentrations. We find that the onset of this highly correlated diffusion becomes more pronounced as the nearest-neighbor repulsion between pairs of guest cations becomes stronger, since this increases the dependence of long-range cation diffusion on triple-vacancy clusters. The results of this study provide guidance with which the concentration dependence of cation diffusion coefficients in spinel can be tailored to reduce the onset of sluggish diffusion at high cation concentrations. The conclusions drawn from this study also apply to other close-packed anion hosts such as disordered rocksalt electrodes and partially ordered spinels.