  We show precompactness results for solutions to parabolic fourth order
geometric evolution equations. As part of the proof we obtain smoothing
estimates for these flows in the presence of a curvature bound, an improvement
on prior results which also require a Sobolev constant bound. As consequences
of these results we show that for any solution with a finite time singularity,
the $L^{\infty}$ norm of the curvature must go to infinity. Furthermore, we
characterize the behavior at infinity of solutions with bounded curvature.
