Diffusion of CO2 in polylactide was modelled by assuming the diffusion coefficient to depend on CO2 concentration, c, according to D[c]=D[0]exp[Ac], where D[0] and A are empirical constants, with the aim of optimizing impregnation of nominally amorphous and semicrystalline polylactide/CO2-based precursors for physical foaming. Numerical simulations provided a consistent description of desorption at different temperatures, T, from polylactide impregnated with liquid CO2 at 10? and 5MPa, and D[0,T] could be represented analytically using Arrhenius or Williams-Landel-Ferry-type expressions, allowing interpolation and extrapolation. Sorption was argued on this basis to involve a step-like diffusion front, such that the CO2 content of a plate of thickness l increased as (D[0]t)(1/2)l(-1)F[Ac-o], where c(o) is the value of c at saturation and F is a function of Ac-o only. A major practical concern with polylactide/CO2 precursors is that the glass transition temperature, T-g, decreases strongly with c, so that amorphous polylactide saturated with CO2 at 10? and 5MPa degasses spontaneously at room temperature and pressure. However, it was inferred from the models and confirmed experimentally that partial impregnation in liquid CO2 for relatively short times could provide a relatively rapid means of preparing precursors with a roughly uniform CO2 content of around 0.1g/g that were stable with respect to rapid CO2 loss on heating to room temperature. The resulting precursors gave satisfactory foam morphologies and densities on foaming at 100?. Moreover, it was also possible to adapt the impregnation conditions so as to obtain partially foamed structures from semicrystalline polylactide under these conditions, in spite of its tendency to undergo cold crystallization during impregnation in liquid CO2, which suppressed expansion of saturated specimens at 100?.