The critical determinants of the speed of an invading cell front are not well known. We performed a "wound-healing" experiment that quantifies the migration of human peritoneal mesothelial cells over components of the extracellular matrix. Results were interpreted in terms of Fisher's equation, which includes terms for the modeling of random cell motility (diffusion) and proliferation. The model predicts that, after a short transient, the invading cell front will move as a traveling wave at constant speed. This is consistent with the experimental findings. Using the model, a relationship between the rate of cell proliferation and the diffusion coefficient was obtained. We used the model to deduce the cell diffusion coefficients under control conditions and in the presence of collagen IV and compared these with other published data. The model may be useful in analyzing the invasive capacity of cancer cells as well in predicting the efficacy of growth factors in tissue reconstruction, including the development of monolayer sheets of cells in skin engineering or the repair of injured corneas using grafts of cultured cells.