  Depinning transitions occur when a threshold force must be applied to drive
an otherwise immobile system. For the depinning of colloidal particles from a
corrugated landscape, we show how active noise due to self-propulsion impacts
the nature of this transition, depending on the speed and the dimensionality
$d$ of rotational Brownian motion: the drift velocity exhibits the critical
exponent 1/2 for quickly reorienting particles, which changes to $d/2$ for slow
ones; in between these limits, the drift varies superexponentially. Different
giant diffusion phenomena emerge in the two regimes. Our predictions extend to
systems with a saddle-node bifurcation in the presence of a bounded noise.
Moreover, our findings suggest that nonlinear responses are a sensitive probe
of nonequilibrium behavior in active matter.
