The forward-backward (FB) version of the semiclassical (SC) initial value representation (IVR) is used to study quantum coherence effects in the time-dependent probability distribution of an anharmonic vibrational coordinate and its quenching when coupled to a thermal bath. It is shown that the FB-IVR accurately reproduces the detailed quantum coherent structure in the weak coupling regime, and also describes how this coherence is quenched with an increase of the system-bath coupling and/or the bath temperature. Comparisons are made with other approximations and the physical implications are discussed. (C) 2001 American Institute of Physics.