In image processing, in order to well preserve corners, peaks, and thin edges of the image, a new biharmonic diffusion model is established, which takes into account the stress balance of the biharmonic equation and local maximum values of higher-order partial derivatives. If the noise is very strong in the image, some isolated spots will leave on the processed image, and texture of the image has statistical properties in a large range, and the new model retains only local details, the information of image in a wide range is not kept well. Further improvement on the above model is made by using the wavelet transform to extract the high frequency part of the image, and by processing this part with stress balance to establish wave field biharmonic diffusion model, which stably controls the image details locally. Analysis and simulation results show that this model retains more image information than the Perona-Mailik model, effectively well preserves the edges, corners, peaks of the image, and also maintains thin edges of the image. So it is an ideal model.