We statistically analyze the dynamics of vibrational energy flow in a model system of anharmonic oscillators which are nonlinearly coupled, with a local topology. The spectra of many basis states of similar energy are computed, for different values of the magnitude of the coupling in the Hamiltonian between these states. From individual spectra of zero order basis states at each coupling strength the individual survival probabilities are determined, which are then used in computing statistical averages. When the average fluctuation of the survival probability is small, in the strongly coupled limit, the average survival probability closely follows a semiclassical diffusion prediction and reflects a predicted linear dependence of the rate of energy flow on coupling strength. When the average fluctuation is large, in the weakly coupled limit, the average survival probability closely follows a power law decay of t(-1), in agreement with a quantum extension of the diffusion picture. In this regime, individual survival probabilities show strong quantum beats. We conclude that these large variations reflect a strong influence of quantum interference in the weakly coupled limit.