On-policy distillation (OPD) supervises student-generated trajectories with token-level teacher signals. Its sampled-token variant avoids the cost of full-vocabulary probabilities.
Yet we find that training on fewer tokens can outperform full-token OPD, challenging the intuition that more supervision improves learning.
This motivates selecting tokens by learning value.
Existing disagreement-based criteria ignore probability scale: tokens assigned negligible probability by both models, termed low-low tokens, can receive large log-ratio rewards and hinder learning.
We propose DIAL-OPD, a token-selection method that bridges log-probability and probability spaces by weighting reward magnitude with the logarithmic mean of teacher and student probabilities.
A parameter beta controls this weighting, and the highest-scoring tokens are retained.
Across 4 teacher-student pairs and 7 mathematical reasoning benchmarks, we compare DIAL-OPD with 9 baselines.
Retaining only 40% of tokens, it outperforms Vanilla OPD and its full-token variants, with mean accuracy gains reaching 5.25 percentage points over Vanilla OPD, and doubles AIME25 Pass@16 from 13.33% to 26.67%.
It also achieves up to an 18% relative improvement in mean accuracy over the strongest token-selection baseline at matched retention ratios.
With a 4B teacher, DIAL-OPD surpasses the strongest full-token baseline using an 8B teacher at both student scales, showing that effective supervision allocation can outweigh teacher scaling.
Further analysis shows that moderate beta balances suppressing low-low tokens against preserving useful disagreements.
Token-level evidence reveals that DIAL-OPD filters high-reward tokens with limited reasoning value while preserving supervision critical to reasoning correctness.