Abstract: We discuss a variant of IDLA, where a compact domain grows according to reflecting Brownian motion. The average “shape” of the growing set is given by a flow-type PDE. For fluctuations, if we consider “radially outward” growth and let the interface be “self-smoothing” (i.e. introduce an additional parabolic operator in the PDE), then we can derive a KPZ-type equation in any dimension.