On the one hand, the basics of diffusion seem easy to understand: random motion, a Gaussian distribution of steps, and linear (in time) mean-squared distance behavior. On the other hand, the diffusion equation is a partial differential equation ... and it only describes simple diffusion, whereas observed diffusion in cells is rarely simple and requires still more complicated math. Here you can deepen your understanding of the math and physics underlying diffusive behavior.
Zuckerman, Daniel M., "Physical Lens on the Cell: Advanced Diffusion and the Fokker-Planck Picture" (2018). Scholar Archive. 4079.
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