  For the discovery of the QCD critical point it is crucial to develop
dynamical models of the fluctuations of the net-baryon number that can be
embedded in simulations of heavy-ion collisions. In this proceeding, we study
the dynamical formation of the critical fluctuations of the net-baryon number
near the QCD critical point and their survival in the late stages in an
expanding system. The stochastic diffusion equation with a non-linear free
energy functional is employed for describing the evolution of conserved-charge
fluctuations along trajectories in the crossover and first-order transition
regions near the QCD critical point.
