This phenomina I really don't undertsand. I know that a difference in 2 pressures will cause a force through P= F/A, but what I want to know is, what is type of force of it, whats going on, on the quantum level?
Diffusion isn't so much a pressure driven phenomenon as it is a random walk phenomenon. At the atomic level, a gas has atoms or molecules each at a specific location and with a specific velocity. It doesn't take much time for any of them to bump into another. When that happens, the atom or molecule changes direction. This process repeats over and over.
So, for example, I open my bottle of cologne and set it on the counter. Some of the molecules head straight out into the air. They don't travel very far before changing direction because they collide with the air molecules. After billions of deflections left and right, forward and back, up and down a few of them finally make their way to my olfactory nerves and I detect the fragrance.
For the first question, the rate at which the cologne molecules travel toward the "destination" depends on how many molecules of air there are in between.
And for the second question, you're really asking about the density of cologne molecules. If there is no gradient in the density of cologne molecules then the average rate at which one small region of space sends cologne molecules to, say, a neighboring region of space is exactly the same as the rate at which molecules from the second region are transported to the first.
In the presence of a density gradient of cologne molecules, molecules from a denser region will, on average, enter a region of lower density more frequently than those going from the lower density region to the higher density region.