When we need to deal with diffuse roughness to increase backscattering while approaching ie. potteries, ceramic etc. the classic Oren-Nayar is not a great choice because it's based on single scattering microfacets and so it gets darker and darker the more we increase roughness. With a principled implementation instead we get nice roughness and back scattering ...
Here we approach analytically sparse sphere packing that happens in porous materials like dust sand powder soot etc. Having a certain appearance itself, it can be used anywhere we wanna approach a kind of look where diffuse appears flat and without too much shading itself. We use it for example for woods and as base for toon shading ...
This is the classic Oren-Nayar model that introduced a generalization of the Lambert model based on microfaceting to model a general roughness parameter. The problem with this is that the microfaceting is single scattering and so pushing too much roughness into the model it will unrealistically darken its whole appearance but with minor values it will play its part fairly ...
Here we use a multi-scatter microfacet implementation for lambertian diffusion instead to go for the usual cosine hemispherical sampling. This comes at a expense of having a little longer render times but backscattering quality is unmatched compared to any other diffuse model. Great for potteries, walls etc ...
This model accounts also for the transmission at the interface and not only for the Fresnel reflection. It's intuitive to see that if we have a physical layer above our diffuse layer when light passes through .. well the transmission factor should also be accounted for because if we see the diffuse component, it means the specular layer on top is of course transparent ...