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Leveraging the power of Large Language Models (LLMs) through preference optimization is crucial for aligning model outputs with human values. Direct Preference Optimization (DPO) has recently emerged as a simple yet effective method by directly optimizing on preference data without the need for explicit reward models. However, DPO typically relies on human-labeled preference data, which can limit its scalability. Self-Play Fine-Tuning (SPIN) addresses this by allowing models to generate their own rejected samples, reducing the dependence on human annotations. Nevertheless, SPIN uniformly applies learning signals across all tokens, ignoring the fine-grained quality variations within responses. As the model improves, rejected samples increasingly contain high-quality tokens, making the uniform treatment of tokens suboptimal. In this paper, we propose SWIFT (Self-Play Weighted Fine-Tuning), a fine-grained self-refinement method that assigns token-level importance weights estimated from a stronger teacher model. Beyond alignment, we also demonstrate that SWIFT serves as an effective knowledge distillation strategy by using the teacher not for logits matching, but for reward-guided token weighting. Extensive experiments on diverse benchmarks and settings demonstrate that SWIFT consistently surpasses both existing alignment approaches and conventional knowledge distillation methods.