We demonstrate the occurrence of anomalous diffusion of dissipative solitons in a ``simple'' and deterministic prototype model: the cubic-quintic complex Ginzburg-Landau equation in two spatial dimensions. The main features of their dynamics, induced by symmetric-asymmetric explosions, can be modeled by a subdiffusive continuous-time random walk, while in the case dominated by only asymmetric explosions, it becomes characterized by normal diffusion.
