The diffusion propagator fully characterizes the diffusion process, which is highly sensitive to the confining boundaries and the structure within enclosed pores. While magnetic resonance has extensively been used to observe various features of the diffusion process, its full characterization has been elusive. Here, we address this challenge by employing a special sequence of magnetic field gradient pulses for measuring the diffusion propagator, which allows for "listening to the drum," mapping structural dispersity, and determining not only the pores shape but also diffusive dynamics within it.