Why is diffusion a spontaneous process?
Here is a nice video about diffusion:
First of all: A spontaneous process is the time-evolution of a system in which it releases free energy and moves to a lower, more thermodynamically stable energy state. Every thing or reaction in nature is spontaneous and it means that it doesn't require work or energy to happen.
What is diffusion? Well, it is clear that it is spontanous process because you don't need energy to, for example, dissolve sugar.
Diffusion is the chemical process when molecules from a material move from an area of high concentration (where there are lots of molecules) to an area of low concentration (where there are fewer molecules). This happens through otherwise random movement.