The forward-backward ͑FB͒ version of the semiclassical ͑SC͒ initial value representation ͑IVR͒ 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.

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