We investigate the manner in which quantum interference is suppressed when a particle interacts with a spatially localized, dynamical environment. To do so we examine a model with two classical paths along which an electron can travel and allow it to interact with a bath of harmonic oscillators on one path and travel freely on the other. In particular, we show that the quantum fluctuations of the path of the particle can couple to the environment and thus lead to dephasing and calculate the dephasing time in the high-temperature limit. We compare this result to other views of how propagating electrons lose phase coherence.