This paper aims to introduce a diffusion filtering based on the Laplacian map. Classical non-linear diffusion filtering using the gradient-map-controlled local diffusivity. The Laplacian maps has similar geometric properties with the gradient map for the extraction of the region boundaries. Laplacian-based diffusion function has the same property with the Perona-Malik type and the Weickert type diffusion functions for the small scale. However, for the large scale, the diffusion operation has similar geometrical properties with the linear diffusion filtering. Therefore, the filtering operation in this paper provides a method for the combination of hierarchical expression based on linear and non-linear diffusion filtering operations.