Individual molecules move around randomly in three-dimensional space, bumping into other molecules along the way. Their speed depends on many factors, such as their temperature, and the density of the medium through which they move — for example, whether through the air or a coffee slurry. But in spite of the random movement of each individual particle, there is an overall tendency for the molecules in a mixture to migrate from areas of higher concentration towards areas of lower concentration. This process is known as diffusion. This video from the Khan Academy explains the process:
This video from the Khan Academy explains how diffusion of particles occurs down a concentration gradient.
Because coffee grinds include so much soluble material, a coffee slurry always contains an uneven distribution of molecules. Water adjacent to a coffee grind is likely to contain a higher concentration of flavour molecules than does water at a farther distance from the coffee grind. The unevenness of concentration in a slurry is what drives diffusion. When a region of high concentration borders a more dilute region, the term ‘concentration gradient’ describes the difference between them. Molecules travel down the concentration gradient, from an area of higher concentration towards one of lower concentration. The process of diffusion doesn’t require any additional energy; all it requires is a concentration gradient.
For example, if you add a few drops of ink to a bowl of water, the molecules that make up the ink will eventually be distributed in equal concentrations across the entire body of water. When the ink molecules become evenly dispersed, a state of equilibrium has been reached. It could take the solution several hours, even days, to reach equilibrium, especially if the water is cold. In a cold environment, each molecule has less kinetic energy and therefore can’t diffuse as quickly.