Diffusion equations have been successfully applied in the field of image processing for the past two decades, describing the random motion of the particles in physics. Image in painting is a significant research problem in the image processing. Its main purpose is to complete the unknown parts of the image from the knowledge of known parts of the image. This research problem can be used to restore damaged photograph, random loss of wavelet coefficients during transmission, superimposed text, noise, and/or blur. According to available models on digital image in painting, this paper attempts to make an outline of state-of-the-art diffusion-based image in painting models with corresponding mathematical representation. We also compared the state-of-the-art diffusion based in painting models in terms of its main idea, type of distortion, strengths, and weaknesses.