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In this paper, we are interested in exploring fine-tuning strategies that enhance the detectability of hallucinations in the resulting model. Focusing on semantic-entropy-based detection, we observe that many erroneous outputs remain undetected because the model produces nearly identical incorrect answers across multiple runs. To address this, we propose diversity-oriented fine-tuning to encourage more varied generations. We introduce two specific strategies: one based on Supervised Fine-Tuning (SFT) and the other on Direct Preference Optimization (DPO). Extensive experiments are conducted to evaluate our approach and analyze the behavior of the models before and after fine-tuning. 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