If reflection was diffusive it would be more or less trivial. If the room is connected, the is a path from the source A to any chosen point B (by definition).

If reflection was diffusive it would be more or less trivial. If the room is connected, the is a path from the source A to any chosen point B (by definition). Now take this path and modify it such that it is composed of straight lines, and may touch walls. This new path is a diffuse light path from A to B. Specular reflection seems much more difficult.