Tunneling dynamics in metastable and bistable potentials driven by correlat
ed noise is studied. For barriers fluctuating randomly in time we show by e
xact numerical and approximate analytical calculations the significant impa
ct on the incoherent and coherent decay. Thereby we make use of both a stoc
hastic Schrodinger equation and the corresponding exact master equation. Th
e crucial role of synchronization of barrier flippings with intrinsic syste
m dynamics is revealed.