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A simulation formalism for the nonlinear response of vibrational excitons is presented and applied to the OH stretching vibrations of neat liquid H2O. The method employs numerical integration of the Schrödinger equation and allows explicit treatment of fluctuating transition frequencies, vibrational couplings, dipole moments, and the anharmonicities of all these quantities, as well as nonadiabatic effects. The split operator technique greatly increases computational feasibility and performance. The electrostatic map for the OH stretching vibrations in liquid water employed in our previous study [A. Paarmann et al., J. Chem. Phys. 128, 191103 (2008)] is presented. The two-dimensional spectra are in close agreement with experiment. The fast 100 fs dynamics are primarily attributed to intramolecular mixing between states in the two-dimensional OH stretching potential. Small intermolecular couplings are sufficient to reproduce the experimental energy transfer time scales. Interference effects between Liouville pathways in excitonic systems and their impact on the analysis of the nonlinear response are discussed. [ABSTRACT FROM AUTHOR]