The paper investigates investments in gas infrastructure considering uncertainties in European gas markets. Furthermore, the study addresses the question of whether (more) diversification provides a (better) security of supply improvement. Thus, a stochastic optimization approach is introduced. The uncertainties focus on 2030 and 2045 in three dimensions, namely the Ukraine gas transit, future LNG prices, and the expected gas demand. Considering three diversification strategies, the model GAMAMOD-EU.sto optimizes investments in pipelines, LNG import terminals and gas storages as well as the gas dispatch. Results illustrate trade-offs between optimal gas supply and diversification strategies. Investments in pipelines to North African suppliers are made across all strategies, while the building of the Nord Stream 2 pipeline depend on the respective diversification strategy. Diversification through LNG quota changes the dispatch results significantly. Investments in storages are almost not necessary over all strategies, however, storages provide flexibility to prevent supply shortages, when diversification strategies are applied. Conclusion for policy makers regarding what is needed for preventing malinvestments and high costs in the European gas market are: an enhanced relationship between Russia and the EU and a clear vision on the role of gas in the future European energy system that reduces demand uncertainty.