GeoOPD: Internalizing Visual Search from Privileged Evidence for Remote Sensing Visual Reasoning

Applying multimodal large language models (MLLMs) to remote sensing visual reasoning remains challenging because task-relevant evidence is often fine-grained and sparse. Such evidence can be overwhelmed by extensive background content, leading to incomplete perception and visually unsupported answers. Recent “thinking with images” methods expose local details through iterative cropping, but incur additional inference cost and remain vulnerable to redundant or inaccurate region selection; local views are also insufficient for questions that depend on global context. Motivated by this observation, we introduce GeoOPD, a remote sensing post-training framework that uses Evidence-Privileged On-Policy Distillation (E-OPD) to transfer the benefits of training-time evidence localization into tool-free visual reasoning at deployment. We develop an evidence-driven data synthesis pipeline that constructs marked views and textual evidence privileges according to the spatial organization required by each question. During post-training, the teacher additionally observes the organized evidence and provides token-level distributional supervision over student-generated trajectories. Divergence gating further concentrates the learning signal on response positions where privileged evidence induces substantial predictive changes. Experiments across multiple benchmarks show that GeoOPD consistently improves its backbone and performs favorably against both general-purpose and remote-sensing-specific models. These results suggest that task-relevant evidence available only during training can be partially internalized by a model used for standard inference, complementing iterative visual tool use.