  We discuss the recently proposed multiboson domain-decomposed factorization
of the gauge-field dependence of the fermion determinant in lattice QCD. In
particular, we focus on the case of a lattice divided in an arbitrary number of
thick time slices. As a consequence, multiple space-time regions can be updated
independently. This allows to address the exponential degradation of the
signal-to-noise ration of correlation functions with multilevel Monte Carlo
sampling. We show numerical evidence of the effectiveness of a two-level
integration for pseudoscalar propagators with momentum and for vector
propagators, in a two active regions setup. These results are relevant to
lattice computation of the hadronic contributions to the anomalous magnetic
moment of the muon and to heavy meson decay form factors.
