  Consider the stochastic heat equation $\partial_t u = \sL u + \dot{W}$, where
$\sL$ is the generator of a [Borel right] Markov process in duality. We show
that the solution is locally mutually absolutely continuous with respect to a
smooth perturbation of the Gaussian process that is associated, via Dynkin's
isomorphism theorem, to the local times of the replica-symmetric process that
corresponds to $\sL$.In the case that $\sL$ is the generator of a L\'evy
process on $\R^d$, our result gives a probabilistic explanation of the recent
findings of Foondun et al.
