# Distilling Routed 3D Privilege for Spatial Reasoning in Vision-Language Models

arXiv: https://arxiv.org/abs/2610.12355 · HTML: https://mlsanity.com/paper/2610.12355/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 28 of its 37 references that are in the map.
- First posted on arXiv 8 Oct 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)
- Multimodal LLMs / vision-language models / [Embodied and 3D vision-language models](https://mlsanity.com/mllm/embodied-and-3d-vision-language-models/)

## Builds on (most cited first, 28 of 28)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Gemini 1.5: Unlocking multimodal understanding across millions of tokens of context](https://mlsanity.com/paper/2403.05530/) (2024)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [LLaVA-OneVision: Easy Visual Task Transfer](https://mlsanity.com/paper/2408.03326/) (2024)
- [Grounded SAM: Assembling Open-World Models for Diverse Visual Tasks](https://mlsanity.com/paper/2401.14159/) (2024)
- [Depth Anything 3: Recovering the Visual Space from Any Views](https://mlsanity.com/paper/2511.10647/) (2025)
- [Self-Distilled Reasoner: On-Policy Self-Distillation for Large Language Models](https://mlsanity.com/paper/2601.18734/) (2026)
- [MMSI-Bench: A Benchmark for Multi-Image Spatial Intelligence](https://mlsanity.com/paper/2505.23764/) (2025)
- [SpaceR: Reinforcing MLLMs in Video Spatial Reasoning](https://mlsanity.com/paper/2504.01805/) (2025)
- [From Flatland to Space: Teaching Vision-Language Models to Perceive and Reason in 3D](https://mlsanity.com/paper/2503.22976/) (2025)
- [Self-Distilled RLVR](https://mlsanity.com/paper/2604.03128/) (2026)
- [ViewSpatial-Bench: Evaluating Multi-perspective Spatial Localization in Vision-Language Models](https://mlsanity.com/paper/2505.21500/) (2025)
- [GPT4Scene: Understand 3D Scenes from Videos with Vision-Language Models](https://mlsanity.com/paper/2501.01428/) (2025)
- [MindCube: Spatial Mental Modeling from Limited Views](https://mlsanity.com/paper/2506.21458/) (2025)
- [SpatialLadder: Progressive Training for Spatial Reasoning in Vision-Language Models](https://mlsanity.com/paper/2510.08531/) (2025)
- [Vision-OPD: Learning to See Fine Details for Multimodal LLMs via On-Policy Self-Distillation](https://mlsanity.com/paper/2605.18740/) (2026)
- [SpatialReasoner: Towards Explicit and Generalizable 3D Spatial Reasoning](https://mlsanity.com/paper/2504.20024/) (2025)
- [Rethinking On-Policy Self-Distillation for Thinking Models](https://mlsanity.com/paper/2607.05184/) (2026)
- [Purified OPSD: On-Policy Self-Distillation Without Losing How to Think](https://mlsanity.com/paper/2607.02234/) (2026)
- [TIGeR: Tool-Integrated Geometric Reasoning in Vision-Language Models for Robotics](https://mlsanity.com/paper/2510.07181/) (2025)
- [Think3D: Thinking with Space for Spatial Reasoning](https://mlsanity.com/paper/2601.13029/) (2026)
- [SpatialClaw: Rethinking Action Interface for Agentic Spatial Reasoning](https://mlsanity.com/paper/2606.13673/) (2026)
- [Visual-OPSD: Cross-Modal On-Policy Self-Distillation for Efficient Unified Multimodal Reasoning](https://mlsanity.com/paper/2606.18974/) (2026)
- [Thinking Without Images: Internalizing Visual Manipulation with On-Policy Self-Distillation](https://mlsanity.com/paper/2606.08719/) (2026)
- [OPSD Compresses What RLVR Teaches: A Post-RL Compaction Stage for Reasoning Models](https://mlsanity.com/paper/2605.06188/) (2026)

## Abstract (arXiv)

Spatial reasoning remains a persistent weakness of vision-language models (VLMs), because RGB inputs do not directly provide geometric evidence. Existing remedies either inject 3D into the model at inference, paying architecture and latency costs, or train with outcome rewards that supervise only the final answer. Spatial errors originate in perception: a misjudged depth or direction can be corrected only by the scene's true geometry, which the 3D-scanned sources of spatial training corpora already provide. We propose GPD (Geometry-Privileged Distillation), which makes geometric evidence the privilege in on-policy self-distillation (OPSD). For each question, depth, semantic, and bird's-eye-view (BEV) cues are rendered as compact text and routed to the teacher alongside the reference answer; a privileged KL, applied only to incorrect trajectories, augments GRPO, and the deployed model remains RGB-only. On the 4B backbone, GPD achieves 57.1 on VSI-Bench and 37.6 average across MindCube, SPARBench, MMSI-Bench, and ViewSpatial, outperforming both GRPO and answer-privileged OPSD across spatial reasoning benchmarks. Ablations confirm the complementarity of 3D and answer privilege, the advantage of question-conditioned routing over full-context injection, and the benefit of restricting distillation to incorrect trajectories.