Interfacing two liquid mixtures in a diffusion cell induces noise in the initial state of the diffusing system, which produces a gap between the diffusion boundary and the ideally boundary assumed in the theory. Measured diffusivity values systematically drift with time and they are often corrected by using a linear shift of the zero-time of the process after sufficiently long time when the system reaches the free one-dimensional diffusion regime. In data analysis methods which involve optical correlation between pairs of successive digital images of the cell, it is not easy to establish how long the transient lasts. We show that when the initial perturbation between solution and solvent relaxes slowly toward the diffusive regime no simple zero-time correction can be applied.