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The term that describes the diffusion of water across a semi-permeable membrane is osmosis. This process occurs when water moves through the membrane from an area of lower solute concentration to an area of higher solute concentration, ultimately seeking to achieve equilibrium on both sides of the membrane. Osmosis is vital for maintaining cellular homeostasis and is a key mechanism in various physiological processes, such as nutrient absorption and waste elimination in biological systems.

Diffusion refers to the movement of molecules from an area of higher concentration to an area of lower concentration, which can pertain to any type of molecules, not just water, and doesn't specifically involve a semi-permeable membrane. Filtration involves the movement of substances through a membrane under pressure and typically applies to larger particles, while concentration refers to the amount of solute in a given volume of solvent and does not describe a movement process. Therefore, osmosis is the precise term that accurately represents the movement of water across a semi-permeable membrane.