Recently, a finite temperature semiclassical quantum dynamics method based on the use of classical trajectories generated on the centroid potential of mean force, the free energy surface associated with the path integral centroid [Cao and Voth, J. Chem. Phys. 99, 10070 (1993)], was presented. It is natural to consider whether or not a similar theory can be constructed using classical trajectories generated on the true quantum mechanical potential mean force, the free energy surface associated with a single path integral bead (canonical Wigner-type approximations). Here, Wigner schemes are derived that give the exact quantum dynamics of quadratic actions, contain the classical limit and when used as a statistical theories give the correct rate constant for a parabolic barrier. The fundamental difference between the two types theories, Wigner and centroid, is that the Wigner formalism at very least requires a set of instantaneous normal modes while the centroid method is normal mode free.