When clusters of deuterium are irradiated with an intense, ultrafast laser pulse, the clusters explode, generating ions with kinetic energies high enough to produce nuclear-fusion events. Here we present experimental measurements of the dependence of the fusion yield of an exploding deuterium-cluster plasma on pulse energy up to the 10-J level for incident pulse durations of 100 fs and 1 ps. These energies correspond to peak vacuum intensities of 2×1020 and 2×1019 W/cm2, respectively. We also present measurements of the resulting plasma ion spectra that possess features indicative of a Coulomb explosion and discuss the yield scaling and its relation to previous findings based on the differences in laser focal geometry and pulse duration.