We demonstrate that a homogeneous porous medium composed of sedimentary particles develops channels due to curvature driven growth of fluid flow coupled with an increase in porosity. While the flux is increased linearly, the evolution of porosity is observed to be intermittent with erosion occurring at the boundaries between low and high porosity regions. Calculating the spatial distribution of the flow within the medium and the fluid stress given by the product of the fluid flux and the volume fraction of the particles, we find that the system organizes itself to be locally near the threshold needed to erode the weakest particles. A statistical model simulating the coupling of the erosion, transport, and deposition of the particles to the local fluid flow and porosity is found to capture the overall development of the observed channels.