Measurements of differential production cross sections of the Higgs boson in pp collisions at $\sqrt{s}=13$ TeV are performed using events where the Higgs boson decays into a pair of W bosons which subsequently decay into an electron, a muon, and a pair of neutrinos. The analysis is based on data collected by the CMS detector at the LHC in 2016, 2017, and 2018, and corresponds to an integrated luminosity of 137 ${fb}^{-1}$. Production cross sections with respect to the transverse momentum of the Higgs boson and the number of hadronic jets are considered. Higgs boson signal spectra are extracted and simultaneously unfolded to correct for selection efficiency and resolution effects by means of maximum likelihood fits to the observed event distributions. No significant deviation from the Standard Model expectations is observed in the differential measurements.