Scanning tunneling microscopy shows that large two-dimensional Ag clusters on Ag(100) can diffuse. The value of the diffusion coefficient at room temperature is of order 10-17 cm2s-1 and varies little, if at all, with cluster size in the range studied, 100 to 720 atoms per cluster. This weak variation rules out periphery diffusion as the main mechanism of cluster diffusion, suggesting instead two-dimensional evaporation-condensation. This conclusion is compatible with the energetics of atomic-scale events within the cluster and with the dissolution of small clusters observed at low coverages.