CoDA is introduced, a fully unsupervised framework that creates reliable privileged information entirely from the latent uncertainty structure of a model's own unlabeled rollouts and provides robust regularization without requiring the strong assumption that the consensus is the absolute ground truth.
Abstract
On-policy self-distillation improves language-model reasoning by querying a teacher on states actually visited by the student. Recent methods create a powerful information asymmetry by exposing the teacher to privileged context, yet they fundamentally rely on external supervision---such as gold solutions or verifiers---to construct this advantage. We introduce CoDA (Consensus and Disagreement Alignment), a fully unsupervised framework that creates reliable privileged information entirely from the latent uncertainty structure of a model's own unlabeled rollouts. CoDA extracts two complementary signals. In the positive branch, answer-level consensus identifies a stable reasoning mode, which conditions a frozen self-teacher to provide dense distributional guidance on fresh student trajectories. However, because agreement does not guarantee correctness, positive-only distillation risks amplifying correlated errors into a false consensus. To break this harmful feedback loop, CoDA incorporates a negative branch that exploits disagreement: minority trajectories are treated as unstable alternatives and gently penalized via a reference-anchored, KTO-style calibration objective. This unpaired binary feedback provides robust regularization without requiring the strong assumption that the consensus is the absolute ground truth. Empirical evaluations on competition-level mathematical benchmarks demonstrate that CoDA significantly improves reasoning, outperforming self-generated baselines and effectively stabilizing training against erroneous consensus.
Sampling multiple solutions and returning the majority answer is among the most reliable ways to improve the reasoning accuracy of large language models without labels, and a growing family of methods converts this consensus signal into training supervision. However, existing approaches use consensus only in restricted forms: as a filter that selects solutions for fine-tuning, as a preference between answers, or as a scalar reward for reinforcement learning, discarding most of the information that the agreeing solutions contain. We present CANON (Consensus-ANchored self-distillatiON), a label-free training method that turns consensus into dense, token-level supervision. For each unlabeled prompt, CANON samples multiple solutions, extracts the majority answer, and conditions a frozen snapshot of the model on a solution that reaches it; this consensus-anchored teacher then supervises the model on its own rollouts at every token. Experiments on mathematical and scientific reasoning benchmarks show that CANON improves pass@1 by up to 12 points, outperforming label-free reinforcement learning by 6 points at a seventh of its compute and approaching a teacher conditioned on gold solutions; trained on pooled unlabeled data, it transfers to held-out benchmarks, matching training methods that use gold labels. Analysis suggests that the improvements are not pure distribution sharpening: after training, the model solves problems it previously never solved in 32 attempts, and its majority vote itself becomes more accurate.
John Gkountouras, Josip Jukic, Ivan Titov· arXiv.org· 2 citations
On-policy distillation (OPD) trains a student on its own trajectories while a teacher supplies dense token-level likelihoods at student-visited prefixes. These likelihoods are often read locally: agreement appears safe to imitate, whereas disagreement appears to identify an error. We show that both readings are confounded by the outcome of the completed trajectory. We introduce an outcome-resolved diagnostic that crosses pointwise teacher-student divergence with final-answer correctness, separating safe imitation, productive divergence, harmful divergence, and agreement-on-failure. In an eight-seed mathematical-reasoning study with a Qwen3-8B student and Qwen3-32B teacher, agreement-on-failure constitutes 67.84% of pooled response-token mass; with a Qwen2.5-7B/32B pair it remains 67.68%. The result persists across threshold, sequence-level, format, and truncation audits. Even on prompts that the Qwen3 teacher solves in all four independent attempts, student accuracy rises to 86.91% but agreement-on-failure remains 14.76%. We then run three matched training probes that use the available signals to imitate, mask, or contrast whole trajectories; none consistently reduces agreement-on-failure. The result points to a localization limitation: local divergence paired with a trajectory-level outcome does not identify where a failed trajectory became unrecoverable. Addressing this limitation requires additional positional information, such as process labels, teacher continuations from student prefixes, or token-level alignment across rollouts. Our contribution is therefore diagnostic rather than a new training method.
This work introduces Latent On-Policy Self-Distillation (LOPD), which, rather than proposing another hand-crafted OPSD variant with a newly prescribed form of privileged context, makes the teacher's privileged context itself learnable end-to-end from experience.
Gui-Min Zhang, Jiayang Lyu, Ran Sun et al.· 1 citation
U-OPSD first samples multiple rollouts and constructs a pseudo solution by majority vote under a self-consistency threshold, and conditions the model's distribution on the pseudo-solution and distills itself on the disagreeing completions, allowing the model to correct itself precisely where it is confidently wrong.
Yijiang Li, Bingyang Wang, Yijun Liang et al.· 2 citations
Self-Supervised Visual On-Policy Distillation (S$^2$VOPD), a simple yet effective method that constructs on-policy learning signals from asymmetric augmented views, systematically explores a broad design space of visual augmentations and uncover that asymmetry matters.
Yijiang Li, Yijun Liang, Yunjie Tian et al.· 0 citations
Context quality is identified as a central bottleneck in on-policy self-distillation and the value of separating rollout-conditioned guidance from canonical supervision is demonstrated, demonstrating the value of separating rollout-conditioned guidance from canonical supervision.
Meilin Yang, Zixuan Ding, Jianhao Nie et al.· 0 citations
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