  The dynamics of spin at finite temperature in the spin-1/2 Heisenberg chain
was found to be superdiffusive in numerous recent numerical and experimental
studies. Theoretical approaches to this problem have emphasized the role of
nonabelian SU(2) symmetry as well as integrability but the associated methods
cannot be readily applied when integrability is broken. We examine spin
transport in a spin-1/2 chain in which the exchange couplings fluctuate in
space and time around a nonzero mean $J$, a model introduced by De Nardis et
al. [Phys. Rev. Lett. 127, 057201 (2021)]. We show that operator dynamics in
the strong noise limit at infinite temperature can be analyzed using
conventional perturbation theory as an expansion in $J$. We find that regular
diffusion persists at long times, albeit with an enhanced diffusion constant.
The finite time spin dynamics is analyzed and compared with matrix product
operator simulations.
