Osmosis is defined as the movement if solvent from the area of high concentration to the area of low concentration.
Diffusion is when molecules spread out, move from high concentration to low concentration.
Therefore I would assume that during diffusion water gets inside the cell by utilizing the aquaporins. Hydrogen ions would utilize ion pumps to diffuse across the membrane. I don't think water gets in with the hydrogen ions. That would be more of a cotransport thing. The cell would burst in that case.
~Nav