The interplay between diffusional and displacive atomic movements is a key to understanding deformation mechanisms and microstructure evolution in solids. The ability to handle the diffusional time scale and the structural complexity in these problems poses a general challenge to atomistic modeling. We present here an approach called diffusive molecular dynamics (DMD), which can capture the diffusional time scale while maintaining atomic resolution, by coarse-graining over atomic vibrations and evolving a smooth site-probability representation. The model is applied to nanoindentation and sintering, where intimate coupling between diffusional creep, displacive dislocation nucleation, and grain rotation are observed.