The classic variational image diffusion models for planar image processing are extended to image diffusion on implicit surfaces using intrinsic image gradients defined based on implicit surfaces and expressed by zero level set functions

which can preserve edges effectively during image diffusion. But the models using only intrinsic gradients of image intensity show staircase effects beyond edges. In order to reduce the staircase effects

a general hybrid variational diffusion model is presented including regularizers based on intrinsic gradients and intrinsic divergence. The TV model and PM model are implemented as examples to validate the formulation in reducing staircase effects.