Diffusion equations have been successfully applied in the field of digital image processing for the past twenty years, describing the random motion of the particles in physics. Image inpainting is a significant research problem in the image processing. Its main intent 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 inpainting, this paper attempts to make an outline of state-of-the-art diffusion based image inpainting models with corresponding mathematical representation. We also compared the state-of-the-art diffusion based inpainting techniques in terms of its main idea, type of distortion, strengths, and weaknesses.