In this paper, we introduce a technique called filter spreading, which provides a novel mechanism for filtering signals such as images. By using the repeated-integration technique of Heckbert, and the fast summed-area table construction technique of Hensley, we can implement fast filter spreading in real-time using current graphics processors. Our fast implementation of filter spreading is achieved by running the operations of the standard summed-area technique in reverse --- e.g. instead of computing a summed-area table and then sampling from a table to generate the output, data is first placed in the table, and then an image is computed by taking the summed-area table of the generated table. While filter spreading with a spatially invariant kernel results in the same image as one produced using a traditional filter, by using a spatially varying filter kernel, our technique enables numerous interesting possibilities. (For example, filter spreading more naturally mimics the effects of real lenses, such as a limited depth of field.)