Diffusion is defined as the movement of a solute across a membrane that is permeable to that solute along its concentration gradient until it reaches equilibrium. The rate of diffusion can be affected by a number of different factors. Size of the gradient (the difference in concentrations on either side of the membrane) is one factor; the larger the gradient, the greater the rate of diffusion. Some solutes require the use of transport proteins to cross a membrane. But transport proteins can only go so fast, no matter how large the concentration gradient is (this is called saturation). So to increase the rate of diffusion one would need more transport proteins. Pressure is a measurement of the number of times molecules contact the membrane. The more times they contact the membrane, the greater the pressure. And as more molecules contact the membrane in a given time, more will go through during that time, meaning an increase in the rate of diffusion.
