We describe our custom processing of the entire Wide-field Infrared Survey Explorer (WISE) 12 micron imaging data set, and present a high-resolution, full-sky map of diffuse Galactic dust emission that is free of compact sources and other contaminating artifacts. The principal distinctions between our resulting co-added images and the WISE Atlas stacks are our removal of compact sources, including their associated electronic and optical artifacts, and our preservation of spatial modes larger than 1.5 degrees. We provide access to the resulting full-sky map via a set of 430 12.5 degree by 12.5 degree mosaics. These stacks have been smoothed to 15 resolution and are accompanied by corresponding coverage maps, artifact images, and bit-masks for point sources, resolved compact sources, and other defects. When combined appropriately with other mid-infrared and far-infrared data sets, we expect our WISE 12 micron co-adds to form the basis for a full-sky dust extinction map with angular resolution several times better than Schlegel et al. (1998).