Physical mechanisms of Osmosis
Based on Chemical potentials, Solution (Chemistry)
The solution-diffusion model: a review
MECHANISM OF OSMOTIC FLOW IN POROUS MEMBRANES
The standard chemical potential explanation still holds as part of the mechanism. See here. The energy comes from the expansion of the solute (which works like an ideal gas), just like in quasistatic adiabatic expansion.
However, the boundary layer given by a Diffusio-osmotic effect, enhances the checmical potential difference at the pore increasing the osmotic pressure. The extra work done in the process, I think, ultimately comes from the fact that the potential energy near the wall is lowered as the solute concentration decreases during the process.
When membrane is semi-permeable (as in Osmosis proper), then I think that the main effect would be an excluded volume effect (this appears to be indeed the case, at least for purely semi-impermeable membranes see Negative osmosis), giving rise to an effective repulsive potential, like that in Nelson's Biological physics book, or those that appear in Diffusio-osmosis, or Diffusiophoresis.
Molecular mechanisms of osmosis Mechanism of osmosis
OSMOSIS: A MACROSCOPIC PHENOMENON, A MICROSCOPIC VIEW
Osmosis is not driven by water dilution, here too. See Nelson's Biological physics book for more details
The mechanism is based on the wall repelling the solute molecules. See analysis here.
Alternative mechanisms: Osmosis, colligative properties, entropy, free energy and the chemical potential Osmosis and thermodynamics explained by solute blocking http://www.circle4.com/biophysics/chapters/BioPhysCh05.pdf
Brownian motion, hydrodynamics, and the osmotic pressure
Molecular Understanding of Osmosis in Semipermeable Membranes
See also Negative osmosis for more resources.