Figure: Brownian motion illustrated

Caption: Click on the displayed image to see the image in the original source. Brownian motion is illustrated in the film version (duration 1 minute 53 seconds) of the displayed image which is obtained by clicking on the image in the original source. The film illustrates that Brownian motion causes a random walk diffusion process. In the case of the film, the random walk is in three dimensions and follows a particle of red dye released into a container of water. (Slightly edited.)

The film is is NOT a photon case, of course, but it gives you the right idea of how an indestructible photon packet does a random walk scattering its way through a gas of atoms and/or molecules.