Is it from high concentration to low that particles move across a membrane move?

Yes. It is called Osmosis. Particles move across the membrane in order to balance the concentration of particles on both sides of the membrane.

Since the membrane tends to block the larger particles,

its the smaller molecules that move,

so what happens across membranes is that the motion (of say water) is from low concentration toward higher - but the result is to even the concentration on both sides of the membrane,

Pure diffusion is always from higher concentration to lower.