The similarity of the observed baryon and dark matter densities suggests that they are physically related, either via a particle physics mechanism or anthropic selection. A pre-requisite for anthropic selection is the generation of superhorizon-sized domains of different Omega(B)/Omega(DM). Here we consider generation of domains of different baryon density via random variations of the phase or magnitude of a complex field Phi during inflation. Baryon isocurvature perturbations are a natural consequence of any such mechanism. We derive baryon isocurvature bounds on the expansion rate during inflation H-I and on the mass parameter mu which breaks the global U(1) symmetry of the Phi potential. We show that when mu less than or similar to H-I (as expected in SUSY models) the baryon isocurvature constraints can be satisfied only if H-I is unusually small, H-I <10(7) GeV, or if non-renormalizable Planck-suppressed corrections to the alpha potential are excluded to a high order. Alternatively, an unsuppressed Phi potential is possible if mu is sufficiently large, mu greater than or similar to 10(16) GeV. We show that the baryon isocurvature constraints can be naturally satisfied in Affleck-Dine baryogenesis, as a result of the high-order suppression of non-renormalizable terms along MSSM flat directions.