Three types of aliphatic alcohols (methanol, ethanol, and 1-propanol) are used to actuate a programmed ESTANE ETE 75DT3 (abb. SMP-E), a polyether-based polyurethane shape memory polymer (SMP). In this paper, we analyze the diffusion behavior of these small molecules in SMP E and the relationship between the solvent diffusion and shape recovery using a weight gain study and small-angle x-ray scattering (SAXS). From the results, all three alcohols show behavior similar to Fickian diffusion in SMP-E. During the diffusion process, the molecular switch of thermoplastic SMP-E transforms from the glassy state to the rubber like state depending on the time-dependent local alcohol concentration. The diffusion of small molecules enhances shape recovery and the related evolution of the polymer structure. As a feedback effect, the rate of diffusion changes as small molecules penetrate into the sample. To study this issue, we used three methods to determine the diffusion coefficients at short, intermediate and long times. The data on short time diffusion reflects the glassy state of the sample. The intermediate times correspond to 50% solvent saturation, where the shape recovery is nearly completed. The long-time analysis, on the other hand, provides an average diffusion coefficient for the entire process. The SAXS results show the diffusion path and provide evidence that the alcohol molecules equally diffuse into both molecular switch (MS) and entropy elastic component (EE) phase of SMP E.