The nonlinear diffusion filtering in image processing bases on the heat diffusion equations. Its key is the control of diffusion amount. In the previous models, the diffusivity depends on the gradients of images. So it is easily affected by noises. This paper first gives a new multiscale computational technique for diffusivity. Then we proposed a class of nonlinear wavelet diffusion (NWD) models that are used to restore images. The NWD model has strong ability to resist noise.But it, like the previous models, requires higher computational effort. Thus, by simplifying the NWD, we establish linear wavelet diffusion (LWD) models that consist of advection and diffusion. Since there exists the advection, the LWD filter is anisotropic, and hence can well preserve edges although the diffusion at edges is isotropic. The advantage is that the LWD model is easy to be analyzed and has lesser computational load. Finally, a variety of numerical experiments compared with the previous model are shown.