Self-distillation bootstraps large language models (LLMs) by training on their own generations. However, existing methods either rely on external signals to curate self-generated outputs (e.g., correctness filtering, execution feedback, and reward search), which are costly and unavailable for the best-performing frontier models, or skip curation entirely and train on all raw outputs, an approach that is often domain-specific and hard to generalize. Both also share a deeper weakness that self-generated outputs entangle task-relevant capability with others, such as stylistic patterns, formatting artifacts, and model-specific errors, diluting the signal for the specific capability one aims to improve. In this paper, we propose Self-Policy Distillation (SPD), which achieves generalizable, capability selective with only minimal external signal (<5% labeled data in each domain). Specifically, SPD extracts a low-rank capability subspace from the model's own gradients on correctness-defining tokens, projects key-value (KV) activations into this subspace during self-generation, and fine-tunes on the resulting raw outputs with standard next-token prediction loss.Through extensive experiments across code generation, mathematical reasoning, and multiple-choice QA, we show that SPD achieves up to 13% improvement over state-of-the-art self-distillation methods and up to 16.3% improvement over pre-trained baselines. Notably,SPD demonstrates superior generalizability, achieving 15.7% better performance under out-of-domain generalization settings.

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