  We show that self-similar solutions for the mean curvature flow, surface
diffusion and Willmore flow of entire graphs are stable upon perturbations of
initial data with small Lipschitz norm. Roughly speaking, the perturbed
solutions are asymptotically self-similar as time tends to infinity. Our
results are built upon the global analytic solutions constructed by Koch and
Lamm \cite{KochLamm}, the compactness arguments adapted by Asai and Giga
\cite{Giga2014}, and the spatial equi-decay properties on certain weighted
function spaces. The proof for all of the above flows are achieved in a unified
framework by utilizing the estimates of the linearized operator.
