  Fireballs created in relativistic heavy-ion collisions at different beam
energies have been argued to follow different trajectories in the QCD phase
diagram in which the QCD critical point serves as a landmark. Using a
(1+1)-dimensional model setting with transverse homogeneity, we study the
complexities introduced by the fact that the evolution history of each fireball
cannot be characterized by a single trajectory but rather covers an entire
swath of the phase diagram, with the finally emitted hadron spectra integrating
over contributions from many different trajectories. Studying the phase diagram
trajectories of fluid cells at different space-time rapidities, we explore how
baryon diffusion shuffles them around, and how they are affected by critical
dynamics near the QCD critical point. We find a striking insensitivity of
baryon diffusion to critical effects. Its origins are analyzed and possible
implications discussed.
