Visual on-policy distillation relies heavily on an informative teacher-student asymmetry, through either a larger, stronger teacher or privileged supervision, such as reference answers or ground-truth regions of interest. This raises a fundamental question: where can informative asymmetry come from when nothing privileged is available? We answer this by inverting where the asymmetry comes from. Rather than adding privileged information to the teacher, we subtract information from the student. This asymmetry creates the same effective learning signal for free as a teacher with access to information unavailable to the student, without ground-truth annotations, rewards, or a separate stronger teacher model. Building on this principle, we introduce Self-Supervised Visual On-Policy Distillation (S$^2$VOPD), a simple yet effective method that constructs on-policy learning signals from asymmetric augmented views. S$^2$VOPD distills the teacher's distribution conditioned on the original image on-policy into the student distribution conditioned on a strongly augmented view of the same image. We systematically explore a broad design space of visual augmentations and uncover that (1) asymmetry matters: all four augmentation families improve performance, while symmetric self-distillation degrades it; (2) strength matters: performance peaks at a moderate strength; and (3) the gap must remain task-consistent: augmentations that completely remove the question-relevant evidence can induce large but uninformative discrepancies. Across six fine-grained perception benchmarks, S$^2$VOPD improves Qwen3.5-4B from 70.7% to 77.4%, above all open-source models compared, up to Qwen3-VL at 235B, and surpasses GPT-5.4. While holding training data the same, it recovers 96% of the improvement achieved by methods with privileged information. Website is at https://williamium3000.github.io/s2vopd
While Multimodal Large Language Models (MLLMs) demonstrate impressive general capabilities, they struggle with fine-grained perception in ultra-high-resolution (UHR) images, particularly for tiny objects in cluttered scenes. Existing methods face a dilemma: they either rely on inefficient prior-free scanning, or depend on static prior-driven heuristics that lack posterior correction to rectify initial model biases. To address this, we propose BVS (Bayesian Visual Search), a framework that formulates perception as a global optimization problem over a continuous spatial-scale manifold. Specifically, BVS bridges prior guidance with posterior correction: it utilizes an early-stop attention rollout of MLLM to construct reasoning-aware priors, while employing a scale-aware non-stationary kernel and GP-UCB to dynamically rectify noise and recover missing information in the prior through iterative local observations. We provide theoretical guarantees via sub-linear regret bounds, and extensive experiments demonstrate that BVS significantly outperforms state-of-the-art baselines with a superior trade-off between accuracy and efficiency.