  We study the transport dynamics of matter-waves in the presence of disorder
and nonlinearity. An atomic Bose-Einstein condensate that is localized in a
quasiperiodic lattice in the absence of atom-atom interaction shows instead a
slow expansion with a subdiffusive behavior when a controlled repulsive
interaction is added. The measured features of the subdiffusion are compared to
numerical simulations and a heuristic model. The observations confirm the
nature of subdiffusion as interaction-assisted hopping between localized states
and highlight a role of the spatial correlation of the disorder.
