A coupling by reflection of a time-inhomogeneous diffusion process on amanifold are studied. The condition we assume is a natural time-inhomogeneousextension of lower Ricci curvature bounds. In particular, it includes the caseof backward Ricci flow. As in time-homogeneous cases, our coupling provides agradient estimate of the diffusion semigroup which yields the strong Fellerproperty. To construct the coupling via discrete approximation, we establishthe convergence in law of geodesic random walks as well as a uniformnon-explosion type estimate.

Coupling by reflection of diffusion processes via discrete approximation under a backward Ricci flow