Infiltration of diffusing particles from one material to another where the diffusion mechanism is either normal or  anomalous is a widely observed phenomena. When the diffusion is anomalous we find interesting behavior: diffusion may lead to an averaged net drift from one material to another even if all particles eventually flow in the opposite direction. Furthermore, averaged net drift does not depend on the properties of the medium in which it is situated, indicating nonlocality of the process. Starting with an underlying continuous time random walk model we solve diffusion equations describing this problem. Similar drift against flow is found in the quenched trap model. We argue that such behavior is a general feature of diffusion in disordered systems.