The solute does not cross the membrane in osmosis. Only the solvant (water for exemple) crosses the membrane. The solute (sugar for example) is dissolved in different concentrations in both solutions. But usually it is dissolved in only one of the two solutions. The other liquid phase is pure solvant.
The membrane has plenty of tiny holes, small enough to allow tiny molecules like water molecules to pass. But the holes are not large enough to allow big molecules of solute (like sugar) to do the same. So these big molecules are partly blocking some holes. Only water can push such big sugar molecules blocking the holes and from the other side cross the membrane. As a consequence, on the long range, water is slowly flowing from the pure solvant (or diluted solution) to the second, more concentrated solution, on the other side of the membrane. And this concentrated solution gets more and more diluted.
The difference of concentration between both sides of the membrane is called the concentration gradient. It goes slightly decreasing with the time.