Recent advances in 3D shape recognition have shown that kernels based on diffusion geometry can be effectively used to describe local features of deforming surfaces. In this paper, we introduce a new framework that allows using these kernels on 2D local patches, yielding a novel feature point descriptor that is both invariant to non-rigid image deformations and illumination changes. In order to build the descriptor, 2D image patches are embedded as 3D surfaces, by multiplying the intensity level by an arbitrarily large and constant weight that favors anisotropic diffusion and retains the gradient magnitude information. Patches are then described in terms of a heat kernel signature, which is made invariant to intensity changes, rotation and scaling. The resulting feature point descriptor is proven to be significantly more discriminative than state of the art ones, even those which are specifically designed for describing non-rigid image deformations.