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We propose a new method to construct discrete Voronoi diagrams, which we call the direct diffusion method. Once we implement it as software, we can easily modify it for various types of digital Voronoi diagrams by changing only the the distance function from a point to a generator represented by a general shape. Our method can construct discrete Voronoi diagrams even if the generator points are not at the centers of pixels. Furthermore, our method can construct the Voronoi diagrams without approximating general shapes by sets of pixels.