Why does diffusion occur, even when the pressure at both regions are equal
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Pressure is just the average force on the boundary of a fluid from the internal motion inside it. Unlike a solid where there is a hard boundary, fluids are lots of small things moving around at random.
If you have 2 volumes of fluid right next to each other at equal pressure then there’s no difference in resistance for the small parts to move from one fluid to the other compared to moving around inside the one they started in. This means that the random motion can cross the boundary and, being random, sooner or later it will
If you have a higher pressure on one side then the tiny parts are moving more from the higher pressure fluid to the lower pressure fluid. If the difference in pressure is high enough and the space is open enough (think a pipe discharging out the side of a building into the atmosphere) then you’ll get effectively no back flow until it starts to equalise
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