  We study the effects of diffusion on the non-linear corotation torque, or
horseshoe drag, in the two-dimensional limit, focusing on low-mass planets for
which the width of the horseshoe region is much smaller than the scale height
of the disc. In the absence of diffusion, the non-linear corotation torque
saturates, leaving only the Lindblad torque. Diffusion of heat and momentum can
act to sustain the corotation torque. In the limit of very strong diffusion,
the linear corotation torque is recovered. For the case of thermal diffusion,
this limit corresponds to having a locally isothermal equation of state. We
present some simple models that are able to capture the dependence of the
torque on diffusive processes to within 20% of the numerical simulations.
