The diffusion coefficient is the dimensionful constant that appears in the diffusion equation. Any book on stochastic processes describes this material; one example would be ``Stochastic processes in physics and chemistry'' by van Kampen.

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Diffusion coefficient is the rate of diffusion equal to the amount of substance (in mass units) passing per unit time through a section of unit area (for example, 1 m2) as a result of the thermal movement of molecules with a concentration gradient equal to unity.

Self-diffusion, a special case of diffusion in a pure substance or solution of constant composition, in which the substance’s own particles diffuse. The atoms (molecules) involved in self-diffusion have the same chemical properties, but may differ in molecular weight.

Uphill diffusion see https://www.researchgate.net/post/Difference_between_self_diffusivity_and_diffusion_coefficient?isAnswerFieldFocused=true

See diffusion through membranes

https://www.researchgate.net/publication/359368949_Supplementary_information_for_Nuclear_quantum_effect_in_aqueous_micellar_surfactant_solutions