Water vapor transport has been highlighted as a critical process in Arctic snowpacks, shaping the snow cover structure in terms of density, thermal conductivity, and temperature profile among others. Here, we present an attempt to describe the thermally-induced vertical diffusion of water vapor in the snow cover and its effects of the snowpack structure using the SNOWPACK model. Convection, that may also constitute a significant part of vapor transport, is not addressed. Assuming saturated conditions at the upper boundary of the snowpack and as initial condition, the vapor flux between snow layers is expressed by a 1-dimensional transient diffusion equation, which is solved with a finite difference routine. The implications on the snowpack of this vertical diffusive flux, are analyzed using metrics such as the cumulative density change due to diffusive vapor transport, the degree of over- or undersaturation, the instantaneous snow density change rate, and the percentage of snow density change. We present results for four different regions sampling the space of natural snow cover variability: Alpine, Subarctic, Arctic, and Antarctic sea ice. The largest impact of diffusive water vapor transport is observed in snow on sea ice in the Weddell Sea and the shallow Arctic snowpack. The simulations show significant density reductions upon inclusion of diffusive water vapor transport: cumulative density changes from diffusive vapor transport can reach -62 and -66 kg m^-3 for the bottom layer in the shallow Arctic snowpack and snow on sea ice, respectively. For comparison, in deeper snow covers, they rarely exceed -40 kg m^-3. This leads to changes in density for shallow snowpacks at the soil-snow interface in the range of -5 to -21%. Mirroring the density decease at depth is a thicker deposition layer above it with increase in density around 7.5%. Similarly, for the sea ice, the density decreased at the sea ice-snow interface by -20%. We acknowledge that vapor transport by diffusion may in some snow covers - such as in thin tundra snow - be small compared to convective transport, which will have to be addressed in future work.