One of the most common assumptions for recovering object features in computer vision and rendering objects in computer graphics is that the radiance distribution of diffuse reflection from materials is Lambertian. We propose a reflectance model for diffuse reflection from smooth inhomogeneous dielectric surfaces that is empirically shown to be significantly more accurate than the Lambertian model. The resulting reflected diffuse radiance distribution has a simple mathematical form. The proposed model for diffuse reflection utilizes results of radiative transfer theory for subsurface multiple scattering. For an optically smooth surface boundary this subsurface intensity distribution becomes altered by Fresnel attenuation and Snell refraction making it become significantly non-Lambertian. The reflectance model derived in this paper accurately predicts the dependence of diffuse reflection from smooth dielectric surfaces on viewing angle, always falling off to zero as viewing approaches grazing. This model also accurately shows that diffuse reflection falls off faster than predicted by Lambert's law as a function of angle of incidence, particularly as angle of incidence approaches close to 90 degree(s). We present diffuse reflection effects near occluding contours of dielectric objects that are strikingly deviant from Lambertian behavior, and yet are precisely explained by our diffuse reflection model. An additional feature of our diffuse reflection model is that is predicts the diffuse albedo purely in terms of the physical parameters of a smooth dielectric surface, allowing rigorous derivation of the relative brightness of specular and diffuse reflection.