Query Expansion (QE) improves retrieval performance by enriching queries with related terms. Recently, Large Language Models (LLMs) have been used for QE, but existing methods face a trade-off: generating diverse terms boosts performance but increases computational cost. To address this challenge, we propose Candidate Token Query Expansion (CTQE), which extracts diverse and relevant terms from a single LLM decoding pass by leveraging unselected candidate tokens. These tokens, though not part of the final output, are conditioned on the full query and capture useful information. By aggregating them, CTQE achieves both relevance and diversity without extra inference, reducing overhead and latency. Experiments show that CTQE delivers strong retrieval performance with significantly lower cost, outperforming or comparable to more expensive methods. Code is available at: https://github.com/bluejeans8/CTQE