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.