At high temperature and low stresses, deformation of fine-grained materials proceeds by mutually accommodating grain-boundary sliding and transport of matter. According to which mechanism provides the greater amount of strain, one speaks of diffusion creep or grain-boundary sliding but they are never really dissociated.

Diffusion creep was predicted theoretically before being observed. If the transport of matter occurs by lattice diffusion, it is Nabarro–Herring creep and the viscosity varies as the grain size squared; if the transport of matter occurs by grain-boundary diffusion, it is Coble creep and the viscosity varies as the grain size raised to the third power.

Grain-boundary sliding accommodated by diffusion creep is described by the same kind of equations as diffusion creep. In most materials, if the grain size is small and stable there is a domain of strain-rate where the strain-rate sensitivity is higher than for dislocation creep and where tensile deformation can take place in a stable manner up to very large strains: it is the superplastic domain. Models for superplastic flow account for the high strain-rate sensitivity and the possibility of large strains, by grain-boundary sliding during grain-shifting events, locally accommodated by diffusion creep or climb and glide of grain-boundary dislocations in the mantle of the grains.