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

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.

Powerful AI models that can both see images and reason about them are usually very large and expensive to run. A common way to build smaller, cheaper versions is to have a big teacher model train a small student model, much like an experienced tutor guiding a beginner. But we discovered a hidden problem in how this teaching works for vision-and-language models: the student is being pulled in two different directions at once, learning how to talk and learning how to look, and these two skills turn out to be almost unrelated. Standard training treats them as equally important and ends up settling for an unhelpful compromise. Our method, Visual Gradient Steering, fixes this by deliberately steering the training to prioritize seeing, since that is where small models struggle most, without harming their language skills. As a result, our smaller models reason about images far more accurately, narrowing the gap to much larger models.