We present direct experimental evidence for position-dependent diffusion in open random media. The interference of light in time-reversed paths results in renormalization of the diffusion coefficient, which varies spatially. To probe the wave transport inside the system, we fabricate two-dimensional disordered waveguides and monitor the light intensity from the third dimension. Change the geometry of the system or dissipation limits the size of the loop trajectories, allowing us to control the renormalization of the diffusion coefficient. This work shows the possibility of manipulating wave diffusion via the interplay of localization and dissipation.