ViCuR: Visual Cues as Recoverable Privilege for Multimodal On-Policy Distillation

Privileged on-policy distillation improves multimodal reasoning by allowing a teacher to evaluate student trajectories using rich, training-only visual evidence. Both models score these trajectories while conditioning on the same student-generated prefix. When a student misinterprets an image early in a response, this accumulating erroneous rationale eventually pulls the teacher away from its visual evidence. The teacher and student converge on the same hallucination, causing standard cross-model supervision to collapse precisely where correction is most needed. We find that the teacher's visual corrective preference is not lost under this misleading agreement. Comparing the predictions of the identical teacher given the real image and a visual null reveals that the privileged evidence still pushes the model toward the correct interpretation. We introduce OPD-Aha, which reconstructs the distillation target directly from this isolated visual preference rather than relying on the fragile teacher-student discrepancy. This reconstructed target aggressively suppresses continuations that contradict the image. Trained with this objective, students learn to naturally interrupt their own flawed reasoning with reflection tokens such as wait and actually. After reflection, subsequent generation relies less on the accumulated erroneous text and more on the visual evidence. Correcting these trajectories mid-generation fundamentally alters the reasoning process, yielding broad and consistent improvements across diverse fine-grained perception and complex multimodal reasoning benchmarks. Our code and models are available at https://github.com/Echochef/OPD-Aha.

Recent post-training methods, particularly Reinforcement Learning with Verifiable Rewards (RLVR), have significantly enhanced the reasoning ability of Large Vision-Language Models (LVLMs). However, the sparse nature of verifiable rewards provides little token-level supervision for failed rollouts, often leading to inefficient exploration in complex multimodal reasoning tasks. Although policy distillation can offer dense guidance, external teacher based methods introduce substantial computational overhead, while answer conditioned tuning methods may expose answer-level information and induce shortcut-like generation behavior. To address these limitations, we propose PTD-PO, a Privileged Tutoring Distillation Policy Optimization framework for RLVR that provides dense guidance without exposing the answer to the student policy. Specifically, PTD-PO constructs structured privileged hints from spatial attention guidance and intermediate textual reasoning steps, and uses them through in-context learning to produce step-wise token-distribution supervision. The student is still optimized under the original answer-free context, and its failed rollouts are aligned with the hint-augmented reference model at the token-distribution level. To further stabilize distillation under the distribution shift between guided and unguided contexts, we introduce a Top-K Jensen-Shannon divergence objective that focuses alignment on informative token probabilities while reducing memory overhead. Experiments on LVLMs ranging from 2B to 8B parameters show that PTD-PO consistently outperforms RLVR and distillation baselines, mitigates entropy collapse, and improves complex multimodal reasoning performance.

Unified multimodal models (UMMs) interleave generated ''visual thoughts'' (VTs) with text reasoning to improve spatial tasks. This incurs roughly an order-of-magnitude inference cost from multi-step diffusion. We find this cost yields limited direct benefit. On ThinkMorph, removing or noising VTs barely changes accuracy across nine benchmarks. Once rendered, attention concentrates on the VT regardless of content. Yet a KL diagnostic shows that conditioning on a privileged VT trace shifts the model's completion distribution. This suggests the generation pathway encodes useful reasoning beyond the rendered pixels. Motivated by this gap, we propose Visual On-Policy Self-Distillation(Visual-OPSD). Teacher and student share identical weights but differ in context: the teacher sees privileged VTs while the student sees only the question. Token-level JSD distillation on on-policy student trajectories transfers the teacher's reasoning to a text-only student. Across nine benchmarks, Visual-OPSD improves over its generative teacher by $+3.40$pp with $14.3\times$ speedup (10.0s vs. 142.8s per sample) and outperforms same-scale VLMs by $+63.83$pp on VSP. A Gaussian-noise control ($+0.40$pp vs. $+10.28$pp for real VTs) and $58.4\%$ closure of the KL gap confirm that gains come from the semantic content of the generation pathway.