  Differential cross sections are measured for the standard model Higgs boson
produced in association with vector bosons (W, Z) and decaying to a pair of b
quarks. Measurements are performed within the framework of the simplified
template cross sections. The analysis relies on the leptonic decays of the W
and Z bosons, resulting in final states with 0, 1, or 2 electrons or muons. The
Higgs boson candidates are either reconstructed from pairs of resolved b-tagged
jets, or from single large distance parameter jets containing the particles
arising from two b quarks. Proton-proton collision data at $\sqrt{s}$ = 13 TeV,
collected by the CMS experiment in 2016-2018 and corresponding to a total
integrated luminosity of 138 fb$^{-1}$, are analyzed. The inclusive signal
strength, defined as the product of the observed production cross section and
branching fraction relative to the standard model expectation, combining all
analysis categories, is found to be $\mu$ = 1.15 $^{+0.22}_{-0.20}$. This
corresponds to an observed (expected) significance of 6.3 (5.6) standard
deviations.
