On-policy self-distillation has recently emerged as an effective approach for improving language-model reasoning by supervising students with a frozen or EMA version of themselves that receives privileged information. Its application to multimodal large language models (MLLMs), however, remains largely unexplored. Recent approaches use privileged visual information, such as image crops corresponding to a question, to improve fine-grained perception, but their gains are confined to tasks that benefit from such visual zooming and require either human-annotated grounding data or external teacher models. This paper introduces a different form of on-policy self-distillation for MLLMs that provides the teacher with textual, spatially grounded guidance identifying the visual elements relevant to a query.

The authors use procedurally generated scenes with automatically available object identities and spatial coordinates, enabling scalable and annotation-free post-training. The teacher uses this spatial guidance to locate and integrate evidence from multiple relevant image regions, while the student learns to reproduce the resulting behavior from the image and question alone. The approach consistently improves performance on counting, document and chart understanding benchmarks across multiple models. Importantly, although post-training uses only synthetic scenes, the resulting improvements transfer to real-world perception benchmarks, yielding a 3.23-point gain in average performance across CVBench, V*, ZoomBench, BLINK, HR-Bench, and MME-RealWorld. These results show that spatially grounded privileged information can induce broader perceptual capabilities through on-policy self-distillation, enabling substantial synthetic-to-real transfer beyond the task and data distribution used for post-training.

Spatial guidance as privileged information for MLLM post-training

On-policy self-distillation (OPSD) supervises student-generated trajectories with teacher predictions at states the student actually visits, better aligning training with inference-time behavior. Prior work on OPSD for MLLMs has primarily created the teacher–student difference by giving the teacher better visual access to the image, such as cropped or zoomed-in views of question-relevant regions. These approaches can yield strong improvements when fine-grained or localized visual evidence is critical, but their gains do not necessarily transfer uniformly across visual tasks. For instance, Vision-OPD improves Qwen3.5-4B by 8.90 points on V* and 14.56 points on ZoomBench, yet decreases performance on CountQA by 10.73 points. This motivates exploring forms of privileged information that may support broader improvements in visual perception.

The core observation driving this work is whether privileged information can specify not what the teacher should see, but where in the image the relevant evidence can be found. Many visual tasks require identifying question-relevant elements distributed across an image and using them to produce an answer. Counting requires finding all instances matching a query; reading may require collecting text from different regions; and chart understanding often requires associating labels, values, and graphical elements. For such tasks, knowing which visual elements are relevant and where they are located could provide useful guidance without giving the teacher a different view of the image.

Procedural scene generation with auto-available coordinates

A practical challenge is obtaining spatial guidance at scale without human annotations or an external grounding model. The authors address this by procedurally generating post-training data, such that the identities, attributes, and locations of all visual elements are known from the scene-generation process. Each training example is built from a scene: a synthetic canvas on which simple visual elements, colored geometric shapes, are placed at non-overlapping positions over a uniform background. A scene is described by its state, which records the identity, attributes, and location of every element, and rendering the state produces the corresponding image.

For each scene, the authors sample a counting question targeting a category present in the scene. Since the complete scene specification is known, they can directly identify all question-relevant elements and their locations. They then construct the privileged textual hint using a fixed template, which names the target category, lists the location of each matching instance, and concludes with their count. For example, for the question "How many green crosses are there?", if two matching objects occur at specified coordinates, the privileged hint is: "Scanning for green crosses: found one near (377, 400), found one near (213, 805). Counting: 2 total."

The complete training tuple (image, question, answer, hint) is generated automatically from the scene state, without human annotations, region proposals, or an external higher-capacity MLLM. The authors generate 1024×1024 scenes containing colored geometric objects from seven shape classes and twelve colors on a flat background. Each scene contains between 12 and 40 objects, each drawn with a radius between 14 and 64 pixels. Questions ask for the number of objects belonging to a sampled color–shape category. The main post-training set contains 3,000 image–question pairs with their corresponding privileged hints.

Teacher reasoning with spatially grounded hints

In the Where-OPD framework, both student and teacher are initialized from the same pretrained checkpoint. For each training example, the student receives (image, question) while the teacher additionally receives the spatial hint. The hint identifies the visual elements relevant to the question and points to their locations in the image. The teacher therefore has explicit access to the locations of the evidence needed to answer the question, while the student must infer the relevant visual evidence from the image and question alone. The privileged guidance is used only during post-training and is absent at inference time.

The authors minimize the generalized Jensen–Shannon divergence between the student and privileged teacher distributions, with a temperature parameter of 0.5. For computational efficiency, the divergence is computed over the student's top 100 tokens and the corresponding teacher logits, alongside a tail-probability term. The privileged teacher distribution is treated as a fixed target, so gradients flow only through the student.

Student distillation from evidence-integrated teacher behavior

The student learns to reproduce the teacher's behavior from the image and question alone. During post-training, teacher and student receive the same image and question, but only the teacher receives the hint; the student learns from the teacher's scored predictions on the prefixes it generates. At inference time, the model receives only (image, question); the privileged hint is not provided. This design ensures that the student internalizes a strategy for identifying and using relevant visual evidence without relying on the hint at deployment.

Across three MLLMs—Qwen3.5-4B, Qwen3.5-9B, and Qwen3-VL-4B—the approach improves performance on counting benchmarks such as CountQA, document understanding benchmarks such as DocVQA and OCRBench, and chart understanding benchmarks such as ChartQA and EvoChart. On Qwen3.5-4B, Where-OPD improves ChartQA by 7.20 points and EvoChart by 10.11 points, while also improving CountQA by 2.53 points and OCRBench by 1.93 points.

Benchmark results across counting document and chart tasks

Table 1 in the paper presents main results across the three MLLMs and 15 benchmarks. Where-OPD achieves the highest average accuracy on each model. Improvements span multiple visual capabilities: CountQA, ChartQA, EvoChart, and HallusionBench improve consistently across all three MLLMs, while document understanding performance is largely preserved or improved. In contrast, methods based on enhanced or localized visual observations achieve substantial gains on high-resolution visual-search benchmarks, particularly V* and ZoomBench, but show less consistent improvements across other tasks and often degrade performance on counting and hallucination-sensitive benchmarks.

The average gain across CVBench, V*, ZoomBench, BLINK, HR-Bench, and MME-RealWorld is 3.23 points for the model family as a whole. Per-model gains are 1.07 points for Qwen3.5-4B, 1.29 points for Qwen3.5-9B, and 1.01 points for Qwen3-VL-4B. These gains appear on benchmarks that involve real-world images and tasks beyond counting, demonstrating that the benefits of the training approach extend beyond both the visual appearance and the counting task of the synthetic training data.

Real-world transfer beyond synthetic training distribution

Despite using only procedurally generated geometric scenes for post-training, Where-OPD improves performance on diverse benchmarks involving real-world images. MME-RealWorld, HallusionBench, V*, HR-Bench 8K, GQA, and AMBER improve across all three MLLMs, alongside gains in chart and document understanding. This indicates that the skills learned on rendered training scenes transfer to substantially different real-world visual tasks.

The synthetic-to-real transfer is notable because the post-training data distribution consists of simple rendered scenes with known object identities and coordinates, while the evaluation benchmarks contain natural images with complex backgrounds, varying lighting, and occlusions. The fact that improvements transfer suggests that spatially grounded privileged guidance induces broader perceptual capabilities that are not tied to the specific appearance of the training scenes.

Ablations confirm spatial grounding matters

  1. Without any privileged information, OPSD remains at the base-model average, highlighting the importance of teacher–student information asymmetry.
  2. Providing the correct answer alone improves performance, but spatial coordinates without the final count yield a higher average than answer-only hints.
  3. Combining coordinates with the count achieves the highest average performance, confirming that both location and quantity information in the hint contribute to the distillation signal.
  4. Providing cropped images of the target objects, as in Vision-OPD, reduces the average and substantially degrades CountQA, further confirming that spatially grounded textual guidance is a more effective form of privileged information for broad improvements.

What the results indicate about synthetic-to-real transfer

The authors' findings suggest that spatially grounded privileged information can induce perceptual capabilities that transfer from simple procedurally generated scenes to real-world visual tasks. The 3.23-point average gain across six real-world perception benchmarks demonstrates that the student models learn a strategy for identifying and integrating question-relevant visual evidence that generalizes beyond the synthetic distribution. This transfer occurs without any real-image data or human annotations during post-training.

The paper's contributions are threefold: spatially grounded privileged guidance for OPSD, annotation-free generation of spatially grounded hints from procedurally generated scenes, and broad improvements with synthetic-to-real transfer across counting, reading, and chart-understanding benchmarks. The work opens a pathway for developing MLLMs with stronger visual perception through on-policy self-distillation with automatically generated guidance, without the cost of collecting and annotating real-image datasets.