We theoretically investigate the relationship between impurity diffusion profiles and the underlying atomic-scale diffusion mechanisms that occur via intermediate species in elemental semiconductors. We focus particularly on diffusion regimes characterized by short versus long diffusion times and low versus high transport capacities. Based on analytic derivations and numerical simulations, we show that, in the absence of any external point defect perturbation, there is usually no unique correspondence between a microscopic diffusion mechanism and a macroscopic impurity diffusion profile. Complementary experiments have to be performed to gain more conclusive information about the microscopic diffusion mechanisms. Examples of these experiments are perturbing the point defect concentrations from equilibrium by thermal oxidation and nitridation, particularly in the short-time diffusion regime, and studying the growth or shrinkage of stacking faults and dislocation loops. Finally, a wide range of impurity diffusion phenomena result from the presence of intermediate species, and can be analytically derived or numerically computed starting from the same set of diffusion equations.