Osmosis is a special kind of diffusion
First, we told you that diffusion through a membrane was just a special case of diffusion — we got you to assume that there were only two compartments of interest (left and right), which simplified the maths a lot.
Now, we’re going to tell you that osmosis is a special case of diffusion through the membrane. And it’s the membrane that makes it special. Recall that membranes vary in terms of their permeability. Some might be like the proverbial brick wall, while others might be ‘as leaky as a sieve’. Imagine a membrane with gaps* just big enough to let water through, but too small to let anything else across.
How is this a special case of diffusion through a membrane? Basically, water can diffuse through the membrane, but nothing else in the water — salt, sugar, or other solute – can.
Instead of general permeability of the membrane, what we care about now is permeability to water, or Pwater.
*More properly, permeability of the membrane has to do with selective gateways and polarity and so on, but imagining gaps in the membrane will work too.