  We study the Langevin diffusion of a relativistic heavy quark in anisotropic
strongly coupled theories in the local limit. Firstly, we use the axion
space-dependent deformed anisotropic N=4 sYM, where the geometry anisotropy is
always prolate, while the pressure anisotropy may be prolate or oblate. For
motion along the anisotropic direction we find that the effective temperature
for the quark can be larger than the heat bath temperature, in contrast to what
happens in the isotropic theory. The longitudinal and transverse Langevin
diffusion coefficients depend strongly on the anisotropy, the direction of
motion and the transverse direction considered. We analyze the anisotropy
effects to the coefficients and compare them to each other and to them of the
isotropic theory. To examine the dependence of the coefficients on the type of
the geometry, we consider another bottom-up anisotropic model. Changing the
geometry from prolate to oblate, certain diffusion coefficients interchange
their behaviors. In both anisotropic backgrounds we find cases that the
transverse diffusion coefficient is larger than the longitudinal, but we find
no negative excess noise.
