  Quantum coherences are paramount resources for applications, such as
quantum-enhanced light-harvesting or quantum computing, which are fragile
against environmental noise. We here derive generalized quantum master
equations using perturbation theory in order to describe the effective
ensemble-averaged time-evolution of finite-size quantum systems subject to
static noise on all time scales. We then analyse the time-evolution of the
coherences under energy broadening noise in a variety of systems characterized
by both short and long-range interactions, by strongly correlated and fully
uncorrelated noise -- a single qubit, a lattice model with on-site disorder and
a potential ladder, and bosons in a double-well potential with random
interaction strength -- and show that couplings can partially protect the
system from the ensemble-averaging induced loss of coherence. Our work suggests
that suitably tuned couplings could be employed to counteract part of the
dephasing detrimental to quantum applications. Conversely, tailored noise
distributions can be utilized to reach target non-equilibrium quantum states.
