# Decomposed On-Policy Distillation for Vision-Language Reasoning: Steering Gradients for Visual Grounding

arXiv: https://arxiv.org/abs/2606.00564 · HTML: https://mlsanity.com/paper/2606.00564/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 25 of its 42 references that are in the map.
- First posted on arXiv 30 May 2026.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)
- Knowledge distillation / [Multimodal distillation](https://mlsanity.com/distill/multimodal-distillation/)

## Builds on (most cited first, 25 of 25)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [MMMU-Pro: A More Robust Multi-discipline Multimodal Understanding Benchmark](https://mlsanity.com/paper/2409.02813/) (2024)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [LogicVista: Multimodal LLM Logical Reasoning Benchmark in Visual Contexts](https://mlsanity.com/paper/2407.04973/) (2024)
- [Vision language models are blind: Failing to translate detailed visual features into words](https://mlsanity.com/paper/2407.06581/) (2024)
- [Perception-Aware Policy Optimization for Multimodal Reasoning](https://mlsanity.com/paper/2507.06448/) (2025)
- [Self-Rewarding Vision-Language Model via Reasoning Decomposition](https://mlsanity.com/paper/2508.19652/) (2025)
- [Training Large Language Models for Reasoning through Reverse Curriculum Reinforcement Learning](https://mlsanity.com/paper/2402.05808/) (2024)
- [VisualPuzzles: Decoupling Multimodal Reasoning Evaluation from Domain Knowledge](https://mlsanity.com/paper/2504.10342/) (2025)
- [ProgRM: Build Better GUI Agents with Progress Rewards](https://mlsanity.com/paper/2505.18121/) (2025)
- [CompoDistill: Attention Distillation for Compositional Reasoning in Multimodal LLMs](https://mlsanity.com/paper/2510.12184/) (2025)
- [Supervised Reinforcement Learning: From Expert Trajectories to Step-wise Reasoning](https://mlsanity.com/paper/2510.25992/) (2025)
- [Rethinking Reward Models for Multi-Domain Test-Time Scaling](https://mlsanity.com/paper/2510.00492/) (2025)
- [PACR: Progressively Ascending Confidence Reward for LLM Reasoning](https://mlsanity.com/paper/2510.22255/) (2025)
- [PDCR: Perception-Decomposed Confidence Reward for Vision-Language Reasoning](https://mlsanity.com/paper/2605.13467/) (2026)

## Built on by (most cited first, 10 of 10)

- [Visual Contrastive Self-Distillation](https://mlsanity.com/paper/2607.21556/) (2026)
- [Weak-to-Strong On-Policy Distillation](https://mlsanity.com/paper/2607.26246/) (2026)
- [VAD: Attributing Visual Evidence for Target Reconstruction in Multimodal On-Policy Distillation](https://mlsanity.com/paper/2607.28590/) (2026)
- [Self-Supervised Visual On-Policy Distillation](https://mlsanity.com/paper/2608.14144/) (2026)
- [Deep Thought Alignment: Trajectory-Level Latent Distillation for Video Reasoning](https://mlsanity.com/paper/2608.16316/) (2026)
- [Token-level Response-visual Attention Guidance for Multimodal LLMs Knowledge Distillation](https://mlsanity.com/paper/2607.02593/) (2026)
- [OPD-Aha: From Linguistic Momentum to Visual Reflection in Multimodal On-Policy Distillation](https://mlsanity.com/paper/2609.16459/) (2026)
- [Distill the Visual Evidence, Not Just the Answer: Cross-World On-Policy Distillation for Vision-Language Models](https://mlsanity.com/paper/2609.38777/) (2026)
- [LEGO-OPD: Factorized Teacher Composition for Multimodal On-Policy Distillation](https://mlsanity.com/paper/2610.00333/) (2026)
- [CV-OPD: Contrastive Vision On-policy Distillation](https://mlsanity.com/paper/2610.13264/) (2026)

## Abstract (arXiv)

While on-policy distillation offers dense supervision for training small reasoning models, its optimization dynamics in the multimodal domain remain under-explored. In this work, we challenge the standard monolithic view of Vision-Language Model (VLM) distillation by mathematically decomposing the loss into two distinct components: the language prior and visual grounding. Our analysis uncovers that gradient vectors for these components are nearly orthogonal, indicating that the objective of aligning with the teacher's language distribution is geometrically independent from the objective of matching its visual perception. Consequently, standard optimization passively follows a suboptimal compromise trajectory that implicitly balances the two objectives. Hypothesizing that visual grounding constitutes the primary bottleneck for vision-language reasoning, we introduce Visual Gradient Steering (VGS), a method that dynamically reorients the update vector to prioritize the visual subspace. Experimental results on multiple distillation settings and complex multimodal benchmarks demonstrate that VGS significantly outperforms the standard monolithic formulation of on-policy distillation, achieving superior grounding with minimal training overhead.