The processes described by Andre work by having the interaction act at the level of the mobility of the particles.
There are other ways, too. One is in the work of Philipowski (see also Figalli & Philipowski). Here the idea is to take interacting diffusionsinteractions of potential type, i.e. for instance
$ dX^i = -\sum_{j\not=i} \nabla W_\epsilon(X^i-X^j)\, dt + \delta \, dB^i. $
The parameter $\epsilon$ is the spatial range of $W$, and pass to a in the limit where $\epsilon\to0$ the interaction distance tends to zero becomes purely local, and the strength of the Browian leads to a nonlinear diffusion term. If one also lets $\delta\to0$, then the purely Brownian contribution also vanishes. What remains is the nonlinear-diffusive effect of Only the interactions, which now have become localnonlinear diffusion is then left.
