Diffusion is a time-dependent process, constituted by random motion of given entities and causing the statistical distribution of these entities to spread in space. The concept of diffusion is tied to notion of mass transfer, driven by a concentration gradient.
The concept of diffusion emerged in the physical sciences. The paradigmatic examples were heat diffusion, molecular diffusion and Brownian motion. Their mathematical description was elaborated by Joseph Fourier in 1822, Adolf Fick in 1855 and by Albert Einstein in 1905.
Applications outside physics were pioneered by Louis Bachelier who in 1900 used a random walk model to describe price fluctuations on financial markets. In a less quantitative way, the concept of diffusion is invoked in the social sciences to describe the spread of ideas.