PHF: Privileged Hidden Flow for On-Policy Self-Distillation

On-policy self-distillation (OPSD) trains a reasoning model on rollouts sampled from its own policy by matching a privileged teacher that also sees verified reference solutions. Existing OPSD objectives supervise only the output distribution, so privileged context affects training through a token-level divergence without directly supervising the internal computation that produced that distribution. We propose Privileged Hidden Flow (PHF), which additionally distills how a privileged teacher's hidden states move along the same rollout. Rather than forcing each student hidden vector to match the