  A compressible Oldroyd--B type model with stress diffusion is derived from a
compressible Navier--Stokes--Fokker--Planck system arising in the kinetic
theory of dilute polymeric fluids, where polymer chains immersed in a
barotropic, compressible, isothermal, viscous Newtonian solvent, are idealized
as pairs of massless beads connected with Hookean springs. We develop a-priori
bounds for the model, including a logarithmic bound, which guarantee the
nonnegativity of the elastic extra stress tensor, and we prove the existence of
large data global-in-time finite-energy weak solutions in two space dimensions.
