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Machine learning systems typically apply the same model to both easy and tough cases. This is in stark contrast with humans, who tend to evoke either fast (instinctive) or slow (analytical) thinking depending on the problem difficulty, a property called the dual-process theory of mind. We present FLOWGEN, a graph-generation model inspired by the dual-process theory of mind that generates large graphs incrementally. Depending on the difficulty of completing the graph at the current step, graph generation is routed to either a fast (weaker) or a slow (stronger) model. These modules have identical architectures, but vary in the number of parameters and consequently differ in generative power. Experiments on real-world graphs show that ours can successfully generate graphs similar to those generated by a single large model, while being up to 2x faster.