Recently the phase-field crystal method has attracted considerable attention because it can simulate the atomic behavior of a system on a diffusive timescale. In this study an atomistic simulation model is proposed, which is an extension of the cluster-activation method (CAM) from discrete to continuous space. This approach, called the continuous CAM, can simulate various physical phenomena of atomistic systems on diffusive timescales and employs well-defined atomistic properties, such as interatomic interaction energies, as the main input parameters. The versatility of the continuous CAM was investigated by performing simulations of crystal growth in an undercooled melt, homogeneous nucleation during solidification, and formation of grain boundaries in pure metal.