This talk will focus on two novel well-posed regularizations of the classical anisotropic diffusion of Perona and Malik. One delivers a classically (locally) well-posed evolution with non-trivial dynamics due to the existence of non-trivial equilibria, the other preserves the forward-backward nature of PME but yields a global semi-flow of weak Young measure valued solutions and offers some insight into the staircasing phenomenon known from numerical implementations of PME. A connection between PME and the TV flow will also be established.