Processes involving liquid-to-gas phase change in porous media are routinely encountered. Growth of a gas phase by solute diffusion in the liquid is typical of the `solution gas-drive` process for the recovery of oil. The growth of a single gas cluster in a porous medium driven by a constant supersaturation is examined. Patterns and rates of growth are derived. It is shown that the growth pattern is not compact and changes from pure percolation to pure Diffusion-Limited-Aggregation (DLA) as the size of the cluster increases. The scaling of the cluster sizes that delineate these patterns, with supersaturation and diffusivity is presented for the case of quasi-static diffusion. In 3-D, the diffusive growth law is found to be R{sub g} {approximately} t{sup 2/3}, which is different than the classical R{sub g} {approximately} t{sup 1/2}.