  The generalized hydrodynamics (GHD) formalism has become an invaluable tool
for the study of spatially inhomogeneous quantum quenches in (1+1)-dimensional
integrable models. The main paradigm of the GHD is that at late times local
observables can be computed as generalized Gibbs ensemble averages with
space-time dependent chemical potentials. It is, however, still unclear how
this semiclassical GHD picture emerges out of the full quantum dynamics. We
evaluate the quantum time evolution of local observables in spatially
inhomogeneous quenches, based on the quench action method, where observables
can be expressed in terms of a form factor expansion around a finite-entropy
state. We show how the GHD formalism arises as the leading term in the form
factor expansion, involving one particle-hole pair on top of the finite-entropy
state. From this picture it is completely transparent how to compute quantum
corrections to GHD, which arise from the higher terms in the form factor
expansion. Our calculations are based on relativistic field theory results,
though our arguments are likely generalizable to generic integrable models.
