We construct dynamical partitions of the torus for a diffeomorphism that is isotopic to the identity. The existence and the combinatorics of the partitions is solely determined by the rotation set of the diffeomorphism. When the rotation set consists of a single non-resonant vector, there is a whole hierarchy of partitions analogous to the partitions of the circle into the closest return intervals under an irrational circle rotation. In particular, all such torus maps are infinitely renormalizable in a natural sense.