  The effect of finite coupling corrections to the Langevin diffusion
coefficients on a moving heavy quark in the Super Yang-Mills plasma is
investigated. These corrections are related to curvature squared corrections in
the corresponding gravity sector. We compare the results of both longitudinal
and perpendicular Langevin diffusion coefficients with those in $\mathcal{N}$=4
Super Yang-Mills plasma. It is observed that the curvature-squared corrections
influence the Langevin diffusion coefficients, and the corrections for both
Langevin diffusion coefficients demonstrate the dependence on the velocity of
the moving heavy quark and the specifics of the higher derivative correction.
In addition, we conduct calculations for the Langevin diffusion coefficients of
a moving heavy quark within the Gauss-Bonnet background.
