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Abstract. Focus fusion methods combine a set of images focused at different depths into a single image where all parts are in focus. The quality of the fusion result strongly depends on a decision map that determines the in-focus areas. Most approaches in the literature achieve this by local decisions without explicitly enforcing smoothness of the depth map. The goal of our paper is to introduce a modern regularisation strategy where we assume that neighbouring pixels in the resulting image have a similar depth. To this end, we consider a partial differential equation (PDE) for the depth map. It combines a robustified data fidelity term with an anisotropic diffusion strategy that involves a matrix-valued diffusion tensor. Experiments with synthetic and real-world data show that this depth map regularisation can improve existing fusion methods substantially. Our methodology is general and can be applied to improve many existing fusion methods.