The Schr\"odinger equation corresponding to the potential profile resulting from manganese diffusion in CdTe-${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Te quantum wells has been solved using a numerical method. Calculation of the exciton binding energies has allowed predictions of the effect of diffusion on the resulting optical properties of such quantum-well structures. In addition to the magnetic-field-dependent potential profiles that accompany the diffusion process, it is shown that the ratio of the Zeeman splitting of the light- and heavy-hole excitonic transitions is strongly dependent on the extent of the manganese diffusion. Consequently, this ratio can be used as a measure of the diffusion coefficient.