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Diffusion is the tendency of molecules to spread into an available space. Without other outside forces at work, substances will diffuse from a more concentrated environment to a less concentrated environment.
Passive transport is the diffusion of substances across a membrane. This is a spontaneous process and cellular energy is not expended. Molecules will move from where the substance is more concentrated to where it is less concentrated. The rate of diffusion for different substances is affected by membrane permeability. For instance, water diffuses freely across cell membranes but other molecules can not. They must be helped across the cell membrane through a process called facilitated diffusion.
Osmosis is a special case of passive transport. In osmosis, water diffuses from a hypotonic (low solute concentration) solution to a hypertonic (high solute concentration) solution. Generally speaking, the direction of water flow is determined by the solute concentration and not by the "nature" of the solute molecules themselves.