Clearly the answer will involve some sort of measurement, but what kind of measurement will depend upon the system being observed.
Diffusion is an aspect of the laws of thermodynamics. These laws are often difficult to concisely interpret and easily misconstrued, but they say, in part, that disorder will increase over time. What this really means is that it takes a constant influx of new energy in order to maintain different regions of high and low "order", and that over time these concentrated areas will become averaged with their surroundings. If you build a house, but you don't put any energy into maintaining it, then eventually it will become averaged with its surroundings, i.e. fall apart, and lose its distinctive order.
In all cases, when diffusion has reached an end point, you will not see further dramatic changes, and the system will have reached a state that is different, and more constant, than its initial one.
For example, if we have a glass of clear water and a dropper of food coloring, the initial state of this system is highly ordered; the water and the coloring are isolated and do not interact. If the coloring is added to the water, and we wait for it to mix thoroughly, we will see that the mixture is neither transparent like water, nor as vibrantly colored as the pure food coloring was. Likewise, the color is evenly distributed throughout the water, with no regions of high or low concentration.
We could evaluate temperature the same way. The same water, and an ice cube, are isolated systems; when added to each other, the temperate will essentially be averaged between them. The ice cube will melt, but the water will be chilled.
So, things to look for that indicate an end point of diffusion are;
- visible mixing or lack of distinct physical regions
- an averaging of qualities of the system's components
This could be evaluated,
- with a thermometer
- with your eyes, or with complicated machinery like a spectroscope
- by testing the rate of chemical reactions
- by weight or volume
The method of measurement depends mostly upon the system and the component that is being diffused.
You can tell diffusion has reached the end point when the particles have become evenly distribute. Now it may require different tools for different types of items used to see when it has finished, but if it was a container filled with water for example and a dye is put in. We will know diffusing is occurring when the color spreads and we will know it is the end when there are no more colors spreading and the whole container looks like a uniform shade of a color.
Diffusion has reached end point when the particles are evenly distributed in all the parts of the system .
Diffusion is the process of molecules moving from an area of high concentration to an area of low concentration. When diffusion is over you will have reached what is known as equilibrium. This means that all the molecules are evenly distributed throughout the area. So, depending on your substance, you'll need to look for evenness based on looks (through a microscope), weight, etc.