Abstract: An efficient numerical method for accurately rendering translucent materials using photon beam diffusion is provided that can account for multilayer materials and directional incident and exitant effects at the surface. In an embodiment, refracted incident light is represented continuously as a photon beam instead of as discrete photons. An integration scheme for calculating a radiant exitance value at a point on the surface of the translucent material is disclosed that uses importance sampling and evaluates a radiant function at a limited number of points along the beam.