Background: Machine learning methods for clinical named entity recognition and entity normalization systems can utilize both labeled corpora and Knowledge Graphs (KGs) for learning. However, infrequently occurring concepts may have few mentions in training corpora and lack detailed descriptions or synonyms, even in large KGs. For Disease Entity Recognition (DER) and Disease Entity Normalization (DEN), this can result in fewer high quality training examples relative to the number of known diseases. Large Language Model (LLM) generation of synthetic training examples could improve performance in these information extraction tasks. Methods: We fine-tuned a LLaMa-2 13B Chat LLM to generate a synthetic corpus containing normalized mentions of concepts from the Unified Medical Language System (UMLS) Disease Semantic Group. We measured overall and Out of Distribution (OOD) performance for DER and DEN, with and without synthetic data augmentation. We evaluated performance on 3 different disease corpora using 4 different data augmentation strategies, assessed using BioBERT for DER and SapBERT and KrissBERT for DEN. Results: Our synthetic data yielded a substantial improvement for DEN, in all 3 training corpora the top 1 accuracy of both SapBERT and KrissBERT improved by 3-9 points in overall performance and by 20-55 points in OOD data. A small improvement (1-2 points) was also seen for DER in overall performance, but only one dataset showed OOD improvement. Conclusion: LLM generation of normalized disease mentions can improve DEN relative to normalization approaches that do not utilize LLMs to augment data with synthetic mentions. Ablation studies indicate that performance gains for DEN were only partially attributable to improvements in OOD performance. The same approach has only a limited ability to improve DER. We make our software and dataset publicly available.