This paper presents a physical perspective to understand visual saliency on the scene and develops an anisotropic heat diffusion based formulation, named visual attention diffusion (VAD), to detect salient regions in natural images. Our idea is based on the assumption that the visual attention can be diffused from a part of the most representative salient elements to other salient regions for a given image. In particular, we first design a corner-points-driven technique to simultaneously identify candidate foreground and background regions on the image. Then both the local object location and the nonlocal background structure can be estimated accordingly. Finally, we design a geometry-driven anisotropic Poisson system with Dirichlet boundary for saliency detection which uses the representative salient elements in the candidate foreground as heat sources and both local and nonlocal priors as guidance. After heat diffusion reaches a stable state, salient regions can be easily detected based on the temperatures (i.e., score value) of the image elements. Experiments show that the proposed system can produce more precise and reliable results compared to state-of-the-art saliency detectors.