We show that the actual diffusive dynamics, governing the momentum relaxation of a polymer molecule, and described by a Fokker-Planck equation, may be replaced by a BGK-type relaxation dynamics without affecting the slow (Smoluchowski) dynamics in configuration space. Based on the BGK-type description, we present a lattice-Boltzmann (LB) based direct discretization approach for the phase-space description of inertial polymer dynamics. We benchmark this formulation by determining the bulk rheological properties for both steady and time-dependent shear and extensional flows at moderate to large Weissenberg numbers. Finally, we compare the usefulness of the different discrete velocity models, typically used in the LB framework, for solving diffusive dynamics based on the Fokker-Planck equation.