We obtain sharp gradient bounds for perturbed diffusion semigroups. In contrast with existing results, the perturbation is random and the bounds obtained are pathwise. Our approach builds on classical work of Kusuoka and Stroock and extends their program developed for the heat semi-group to solutions of stochastic partial differential equations. The work is motivated by and applied to non-linear filtering, where we derive pathwise gradient bounds for the un-normalised conditional distribution of a partially observed signal.