  We calculate the Chern-Simons diffusion rate in a strongly coupled N=4 SUSY
Yang-Mills plasma in the presence of a constant external $U(1)_R$ magnetic flux
via the holographic correspondence. Due to the strong interactions between the
charged fields and non-Abelian gauge fields, the external Abelian magnetic
field affects the thermal Yang-Mills dynamics and increases the diffusion rate,
regardless of its strength. We obtain the analytic results for the Chern-Simons
diffusion rate both in the weak and strong magnetic field limits. In the latter
limit, we show that the diffusion rate scales as $B\times T^2$ and this can be
understood as a result of a dynamical dimensional reduction.
