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Despite its theoretical importance, little is known about how semantic memory structure facilitates and constrains creative idea generation. We examine whether the semantic richness of a concept has both benefits and costs to creative idea generation. Specifically, we tested whether cue set size—an index of semantic richness reflecting the average number of elements associated with a given concept—impacts the quantity (fluency) and quality (originality) of responses generated during the Alternate Uses Task (AUT). Across four studies, we show that low-association, sparse, AUT cues benefit originality at the cost of fluency compared to high-association, rich, AUT cues. Furthermore, we found an interaction with individual differences in fluid intelligence in the low-association AUT cues, suggesting that constraints of sparse semantic knowledge can be overcome with top-down intervention. Our findings indicate that semantic richness differentially impacts the quality and quantity of generated ideas, and that cognitive control processes can facilitate idea production when conceptual knowledge is limited.