Man, you and the other what-are-fields post just started me thinking about whether diffusion and fields are just things bumping into things. I know that at the QFT level things like the classical E-field can be expressed as interchange of mediator particles. But then QFT says it's all fields. Hmm...
To clarify: a "point particle" is an object with no internal structure, that is, it can be fully described by its coordinates wrt time (ignoring relativity for now). This is a concept, a model which explains many phenomena, a model on top of which you can build many theories. It does not, however, explain the conjunction of QM with special relativity.