Does anyone know what is the assumption of BRDF that is violated by subsurface scattering? Also, is BSSRDF a 3-dimensional distribution that describes how light is reflected within the object?

Does BSSRDF really trace how the light scatter within the surface? Or is it another math equation to simulate the process?

A good paper for more on BSSRDF:

https://graphics.stanford.edu/papers/bssrdf/bssrdf.pdf

BRDF assumes reflection where w_i and w_r start at the same point, but subsurface scattering has w_r at a different point.