Generalized ideas of unified dark matter and dark energy in the context of dynamical space time theories with a diffusive transfer of energy are studied. The dynamical space-time theories introduce a vector field whose equation of motion guarantees a conservation of a certain energy momentum tensor, which may be related, but in general is not the same as the gravitational energy momentum tensor. This particular energy momentum tensor is built from a general combination of scalar fields derivatives as the kinetic terms, and possibly potentials for the scalar field. By demanding that the dynamical space vector field be the gradient of a scalar the dynamical space time theory becomes a theory for diffusive interacting dark energy and dark matter. These generalizations produce nonconserved energy momentum tensors instead of conserved energy momentum tensors which lead at the end to a formulation for interacting dark energy and dark matter (DE-DM). We solved analytically the theories and we show that the ACDM is a fixed point of these theories at large times. A particular case has asymptotic correspondence to previously studied non-Lagrangian formulations of diffusive exchange between dark energy and dark matter.