  Extending previous work [arXiv:1408.0628] by the first author we present a
variant of the Arratia flow, which consists of a collection of coalescing
Brownian motions starting from every point of the unit interval. The important
new feature of the model is that individual particles carry mass which
aggregates upon coalescence and which scales the diffusivity of each particle
in an inverse proportional way. In this work we relate the induced measure
valued process to the Wasserstein diffusion of [arXiv:0704.0704]. First, we
present the process as a martingale solution to a SPDE similar to
[arXiv:0704.0704]. Second, as our main result we show a Varadhan formula for
short times which is governed by the quadratic Wasserstein distance.
