Replacing methane with carbon dioxide in gas hydrates has been suggested as a way of harvesting methane, while at the same time storing carbon dioxide. Experimental evidence suggests that this process is facilitated if gas mixtures are used instead of pure carbon dioxide. We studied the free energy barriers for diffusion of methane, carbon dioxide, nitrogen, and hydrogen in the sI hydrate structure using molecular simulation techniques. Cage hops between neighboring cages were considered with and without a water vacancy and with a potential inclusion of an additional gas molecule in either the initial or final cage. Our results give little evidence for enhanced methane and carbon dioxide diffusion if nitrogen is present as well. However, the inclusion of hydrogen seems to have a substantial effect as it diffuses rapidly and can easily enter occupied cages, which reduces the barriers of diffusion for the gas molecules that co-occupy a cage with hydrogen. Published by AIP Publishing.