I've never heard the expression "pressure on diffusion," unless you mean "What is the effect of pressure on diffusion?" In general, the diffusion coefficient associated with some diffusion process will vary with pressure. read more
For example, the diffusion pressure of air inside a balloon is higher than the diffusion pressure of the air outside. Consequently, if the balloon bursts, the air inside the balloon spreads throughout the surrounding air due to its higher diffusion pressure. read more
That swelling is the result of pressure from more water being on the inside. The water will diffuse across a semipermeable (selectively permeable) membrane from higher concentration to lower. it is impossible to have more concentrated water than pure water. read more