The local monomer model is applied, with ab initio potential energy and dipole moment surfaces, to a calculation of the IR spectrum of liquid D2O at 300 K, over the spectral range 0 to 4000 cm(-1). The spectrum is an incoherent superposition of spectra of many monomers over snapshots of a molecular dynamics trajectory, where both intramolecular and intermolecular coupling in each monomer is treated. The comparison to experiment shows an unprecedented level of agreement for the stretch, bend, and libration bands and also the bend+libration and stretch+bend combination bands. This indicates that the incoherent approach captures much of the dynamics underlying the spectrum, provided monomer couplings are considered. The calculated spectrum is compared to the recently calculated IR spectrum of H2O, using the same method and potential energy and dipole moment surfaces, and shifts relative to that spectrum are presented and discussed.