On the basis of a previous theoretical approach to the plastic flow of highly refined materials, a physical explanation for diffusion bonding is essayed, which yields closed--form equations relating the bonding progress with time, temperature, applied pressure and the constants characterizing the material. Excellent agreement with experiment is attained, with no adjustable parameter. In the novel scheme, diffusion bonding is caused by the interpenetration of the two sufaces at the grain level. The process is driven by the strong tensile stress field induced in the plane of the interface by the plastic deformation in the normal direction. The grain boundaries of each joining surface yield to host grains of the other surface, releasing this way the internally generated tensile stresses. Voids gradually close with the increment of the interpenetrated areas. In this scheme bonding is not a matter of contacting and atomic interdiffusion, but of grain exchange.