  We develop a model for the magnonic contribution to the unidirectional spin
Hall magnetoresistance (USMR) of heavy metal/ferromagnetic insulator bilayer
films. We show that diffusive transport of Holstein-Primakoff magnons leads to
an accumulation of spin near the bilayer interface, giving rise to a
magnoresistance which is not invariant under inversion of the current
direction. Unlike the electronic contribution described by Zhang and Vignale
[Phys. Rev. B 94, 140411 (2016)], which requires an electrically conductive
ferromagnet, the magnonic contribution can occur in ferromagnetic insulators
such as yttrium iron garnet. We show that the magnonic USMR is, to leading
order, cubic in the spin Hall angle of the heavy metal, as opposed to the
linear relation found for the electronic contribution. We estimate that the
maximal magnonic USMR in Pt|YIG bilayers is on the order of $10^{-8}$, but may
reach values of up to $10^{-5}$ if the magnon gap is suppressed, and can thus
become comparable to the electronic contribution in, e.g., Pt|Co. We show that
the magnonic USMR at a finite magnon gap may be enhanced by an order of
magnitude if the magnon diffusion length is decreased to a specific optimal
value that depends on various system parameters.
