A generalized, but simplified, kinetic equation for the distribution F of a dust component in a plasma is derived in the seven-dimensional phase space (r, v, Q), where Q is the dust particle charge. The equation for F (r, v, Q, t) takes into account charging, charge spread, collisions and an electric field. The charge Q is considered to vary continuously. From the equation we find an analytic solution for the evolution of dust in the seven-dimensional phase space that shows collisionless diffusion owing to the combined effects of charging, charge spread and a constant electric field. We also derive a 'vector kinetic equation' of dust and subsequently a set of macroscopic equations, and show that the equations lead to a generalized classical diffusion of dust particles owing to fields and nonuniformities, collisions and charging, including charge spread, and to plasma wave effects including damping caused by charging and charge spread in the collisionless case.