Training-free embedding methods directly leverage pretrained large language models (LLMs) to embed text, bypassing the costly and complex procedure of contrastive learning. Previous training-free embedding methods have mainly focused on optimizing embedding prompts and have overlooked the benefits of utilizing the generative abilities of LLMs. We propose a novel method, GenEOL, which uses LLMs to generate diverse transformations of a sentence that preserve its meaning, and aggregates the resulting embeddings of these transformations to enhance the overall sentence embedding. GenEOL significantly outperforms the existing training-free embedding methods by an average of 2.85 points across several LLMs on the sentence semantic text similarity (STS) benchmark. GenEOL also achieves notable gains in clustering, reranking, and pair-classification tasks from the MTEB benchmark. Additionally, GenEOL stabilizes representation quality across LLM layers and remains robust to perturbations of embedding prompts.