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Diffusion
In diffusion, molecules spread randomly from the high concentration region into lower concentration regions until the substance reaches an state of equal concentration. The process dilutes the higher concentration substance by mixing it with the lower concentration; for example, like concentrated soup mixes with water. Without any added energy, the process depends on the natural energy of the high concentration molecules pushing away from one another. The less energy the molecules in the concentrate have, the slower the diffusion.
Heat
Heat adds energy to molecules, causing them to push and bump against one another. Thus, they take up more space but become less concentrated. An example of heat's effect on molecules is found in boiling water, where the heat causes the molecules on the surface to become so charged that they escape from the water as steam. Heat speeds diffusion by making the molecules move away from one another and push into the lower concentration areas.
Friction
Friction, the rubbing of molecules together, adds heat and, therefore, energy to a substance, speeding diffusion. The preferred method of adding friction depends on the particular substance being diffused. Typically for diffusion into liquids, the preferred method is through stirring, whether the substance being diffused is a liquid or a solid. Other methods, such as shaking, also add friction but don't do so as steadily as stirring does.
Concentration
Diffusion is based on a substance of high molecule concentration having another of lower concentration to spread into. Thus, the process can be sped up by adding more of the lower concentration substance. While this likely is the slowest method of accelerating diffusion, adding more of the lower concentration substance can be helpful when it is impossible to add heat or friction. However, it is worth noting that adding more lower concentration molecules also adds to the amount of overall substance, which may delay equilibrium and dilute the end mixture.