Electron-vibrational spectra of impurity-related optical centers of diamond are analyzed in terms of interaction with quasilocal and local vibrations connected with impurity atoms as well as with the short-wavelength lattice phonons. It is shown that the theoretical expressions for the energy and resonance width of quasilocal vibrations in crystals caused by heavy isotopic impurity atoms [Brout and Visscher, Phys. Rev. Lett. 9, 54 (1962)] can be satisfactorily applied for description of the acousticlike quasilocal vibrations in the diamond lattice caused by chemically different impurities. The model of quasilocal vibrations can also be successively applied for impurities (e.g., nitrogen) with masses comparable with the mass of the host carbon atom, provided these impurities form rigid clusters with host atoms vibrating as heavy units. The model is used for analysis of the optical centers in diamond containing Ti, Cr, Zn, Ag, Tl, W, Ni, Co, Ta, Si, and N impurities. Based on the results of this analysis, atomic models of the 3.188 eV N-related, 1.249 eV Ti-related, and 2.56 eV Ni-related centers are proposed.