The talk is devoted to a system of interacting diffusion particles on the real line that start from an infinite set of points, move independently until they meet and then coalesce or sticky-reflect from each other. We additionally assume that particles transfer a mass obeying the conservation law, and their diffusion is inversely proportional to the mass.

We will show that the process describing the evolution of particle mass solves a corrected Dean-Kawasaki equation for particle density in Langevin dynamics. This process also satisfies the Varadhan formula for short times that is governed by the quadratic Wasserstein distance.