  We study a fully discrete finite element approximation of a model for
unsteady flows of rate-type viscoelastic fluids with stress diffusion in two
and three dimensions. The model consists of the incompressible Navier--Stokes
equation for the velocity, coupled with a diffusive variant of a combination of
the Oldroyd-B and the Giesekus model for the left Cauchy--Green tensor. The
discretization of the model is chosen such that an energy inequality is
preserved at the fully discrete level. Thus, unconditional solvability and
stability for the discrete system are guaranteed and the discrete Cauchy--Green
tensor is positive definite. Moreover, subsequences of discrete solutions
converge to a global-in-time weak solution, as the discretization parameters
tend to zero. In the end, we present numerical convergence tests.
