We present an interpretation of the self diffusion propagator for a molecular fluid confined in a porous medium. Breaking with conventional routes of interpretation, we focus in reciprocal space on the time dependence of the propagator at a fixed wave vector q. New theoretical results are reported, as well as NMR measurements on a water-saturated packing of glass beads and on a stack of plastic platelets with rough surfaces. It is shown that at least three time regimes may be distinguished, characteristic of new ways in which the propagator is affected by the geometry of the system: a short-time exponential regime of almost unrestricted diffusion, a pseudo-exponential regime probing the transport process across the material at the length scale λ=2π/q, and an algebraic regime at long times with exponent -d/2, where d is the dimensionality of connected parts of the pore space.