We have studied the “collective” diffusion of a concentrated solution of “living polymers” in brine, which in certain concentration conditions exhibit superdiffusive (Lévy flight) behaviour when tracer diffusion is considered. The concentration profile of the diffusion front is monitored over time using a Michelson interferometer. We show how a concentration dependent diffusion constant can be extracted from the fringe pattern. We find that the diffusion constant decreases linearly with increasing concentration, at variance with a power-law dependence, expected when the interaction between chains is neglected.