Where does the energy needed for the movement of molecules in diffusion and osmosis come from?

Kinetic energy is the form of energy used for any kind of movement, including diffusion and osmosis.

Since all energy is essentially the same, kinetic energy can originate from a wide range of sources, including heat, pressure, friction, sound waves, and even the kinetic energy of molecules bouncing off one another.

Osmosis and diffusion are better understood as laws dictating the direction of motion, whereas environmental energy is what drives the motion in the first place.

Osmosis and diffusion cannot occur in a system without energy; in the presence of energy, molecules will generally gravitate toward directions determined by osmosis and diffusion. Energy can be obtained from a wide variety of sources.

The energy needed for the movement of molecules in diffusion and osmosis comes from the kinetic energy of the molecules themselves.