Blind restoration of blurred images is a classical ill-posed problem. There has been considerable interest in the use of partial differential equations to solve this problem. The blurring of an image has traditionally been modeled by Witkin  and Koenderink  by the heat equation. This has been the basis of the Gaussian scale space. However, a similar theoretical formulation has not been possible for deblurring of images due to the ill-posed nature of the reverse heat equation. Here we consider the stabilization of the reverse heat equation. We do this by damping the distortion along the edges by adding a normal component of the heat equation in the forward direction. We use a stopping criterion based on the divergence of the curvature in the resulting reverse heat flow. The resulting stabilized reverse heat flow makes it possible to solve the challenging problem of blind space varying deconvolution. The method is justified by a varied set of experimental results.