The ground-state energies of the two isomers of the methanol-water dimer, with water-donor (WM) and methanol-donor (MW) structures, have been calculated using the diffusion Monte Carlo (DMC) method with constraint dynamics. Unlike the rigid-body DMC, this method permits the, internal rotations of the hydroxyl and methyl groups of methanol about the C-O bond. The DMC calculations-were performed for the isotopomers CH3OH . . .H2O, CH3OD . . .H2O, and CD3OH . . .H2O. The calculations with the internal rotation of the methyl and hydroxyl groups of methanol included resulted in a much larger ground-state energy gap between the WM and MW isomers than those in which these internal rotations were frozen. This result demonstrated the critical importance of including the internal hydroxyl and methyl rotations in the DMC calculations aimed at predicting accurately the relative stabilities of the two isomers of the methanol-water dimer.