Many aquatic environments exhibit soft, muddy substrates, but this important property has largely been ignored in process-based models of Earth-surface flow. Novel laboratory experiments were carried out to shed light on the feedback processes that occur when particulate density currents (turbidity currents) move over a soft mud substrate. These experiments revealed multiple types of flow-bed interaction and large variations in bed deformation and bed erosion, which are interpreted to be related to the interplay between the shear forces of the current and the stabilising forces in the bed. Changes in this force balance were simulated by varying the clay concentrations in the flow and in the bed. Five different interaction types are described, and dimensional and non-dimensional phase diagrams for flow-bed interaction are presented.