We present a theoretical analysis of bubble growth in porous media by solute diffusion. Based on visualization experiments, a theoretical model is developed for bubble growth driven by a constant or a time-varying supersaturation in the far-field. It is shown that in porous media, gas evolution (patterns and rates) is much different than in the bulk. Patterns and rates of growth are identified for single and multiple gas clusters, using statistical models, such as percolation and diffusion-limited-aggregation (DLA). The effect of (heterogeneous) nucleation on the growth of multiple clusters is analyzed. Particular emphasis is placed on the critical gas saturation, S-gc which denotes the critical value of the pore volume fraction occupied by the gas for the formation of a sample-spanning cluster. This quantity is studied in terms of the system parameters, notably the nucleation fraction and the pressure decline rate (pressure/time). S-gc is found to increase with the nucleation fraction and the pressure decline rate at relatively high rates, but to be independent of the latter at sufficiently small rates. The scaling of these results is also discussed.