There are many nonlinear partial differential equations (NPDEs) for noise problems. In particular, the heat equation (low-pass filter) is an important partial differential equation that deals with noise problems. This chapter deals with the NPDEs from the heat equation and describes the relationship between the NPDEs from the heat equation and the NPDEs from total variation. Therefore, various NPDEs were studied. However, they are not sufficient to solve various noise problems in the industry. This chapter focuses on several methods based on NPDEs that attempt to solve the various noise problems.