  We present room-temperature measurements of magnon spin diffusion in
epitaxial ferrimagnetic insulator MgAl$_{0.5}$Fe$_{1.5}$O$_{4}$ (MAFO) thin
films near zero applied magnetic field where the sample forms a multi-domain
state. Due to a weak uniaxial magnetic anisotropy, the domains are separated
primarily by 180$^\circ$ domain walls. We find, surprisingly, that the presence
of the domain walls has very little effect on the spin diffusion -- nonlocal
spin transport signals in the multi-domain state retain at least 95% of the
maximum signal strength measured for the spatially-uniform magnetic state, over
distances at least five times the typical domain size. This result is in
conflict with simple models of interactions between magnons and static domain
walls, which predict that the spin polarization carried by the magnons reverses
upon passage through a 180$^\circ$ domain wall.
