We investigate ballistic vibrational energy transport through optical phonon band in oligomeric chains in the presence of decoherence. An exact solution is obtained for the excitation density in the space-time representation in the continuous limit and this solution is used to characterize the energy transport time and intensity. Three transport mechanisms are identified such as ballistic, diffusive, and directed diffusive regimes, occurring at different distances and time scales. The crossover between the two diffusive regimes is continuous, while the switch between the ballistic and diffusive mechanisms occurs in a discontinuous manner in accord with the recent experimental results on energy transport in perfluoroalkanes.