  We consider a class of infinite-dimensional diffusions where the interaction
between the components is both spatial and temporal. We start the system from a
Gibbs measure with finite-range uniformly bounded interaction. Under suitable
conditions on the drift, we prove that there exists $t_0>0$ such that the
distribution at time $t\leq t_0$ is a Gibbs measure with absolutely summable
interaction. The main tool is a cluster expansion of both the initial
interaction and certain time-reversed Girsanov factors coming from the
dynamics.
