High-resolution studies of the transmitted divergent-beam diffraction pattern of a perfect diamond are reported. The specimen has damage-free polished surfaces, and is dislocation-free. A 2 mu m thick copper film evaporated on to one surface acts as source of Cu K alpha X-rays, being irradiated by a focused electron beam while the specimen is inside a scanning electron microscope. The X-ray source diameter is <10 mu m, the camera length is 700 mm, nuclear emulsions are used for pattern recording and specimen temperature is well controlled. Fine structures on an angular scale of a few arcseconds are revealed within the much larger areas of overlap of intersecting wavelength-dispersion-broadened Kossel lines, both within accidental intersections of a pair of lines (in the three-beam case, 0, g1 and g2) and in systematic intersections, for the n-beam case, n>or=4. Observations were made under conditions of moderate absorption, mu t=1.7. The fine structures delineate loci of coherent multiple diffraction within the overlap areas. They impose "markers' on an otherwise relatively diffuse diffraction pattern and are demonstrated to be usable in diamond lattice parameter measurements. Their further exploitability is examined.