In probability theory, a branch of mathematics, a diffusion process is a solution to a stochastic differential equation. It is a continuous-time Markov process with continuous sample paths. For more details see the page about Itō_diffusion.
A sample path of a diffusion process mimics the trajectory of a molecule, which is embedded in a flowing fluid and at the same time subjected to random displacements due to collisions with other molecules, i.e. Brownian motion. The position of this molecule is then random; its probability density function is governed by an advection-diffusion equation.
Read more about Diffusion Process: Mathematical Definition
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