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This issue is exacerbated in long-form generation due to hallucination snowballing, a phenomenon where early errors propagate and compound into subsequent outputs. To address this challenge, we propose a novel inference-time hallucination mitigation framework, named Segment-wise HAllucination Rejection Sampling (SHARS), which uses an arbitrary hallucination detector to identify and reject hallucinated segments during generation and resample until faithful content is produced. By retaining only confident information and building subsequent generations upon it, the framework mitigates hallucination accumulation and enhances factual consistency. 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