# Interpolated Policy Distillation: A Controllable Continuum Between Off-Policy and On-Policy Distillation

arXiv: https://arxiv.org/abs/2609.37170 · HTML: https://mlsanity.com/paper/2609.37170/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 25 of its 28 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Placed in

- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

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

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Are We on the Right Way for Evaluating Large Vision-Language Models?](https://mlsanity.com/paper/2403.20330/) (2024)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [Measuring Multimodal Mathematical Reasoning with MATH-Vision Dataset](https://mlsanity.com/paper/2402.14804/) (2024)
- [MMMU-Pro: A More Robust Multi-discipline Multimodal Understanding Benchmark](https://mlsanity.com/paper/2409.02813/) (2024)
- [Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe](https://mlsanity.com/paper/2604.13016/) (2026)
- [We-Math: Does Your Large Multimodal Model Achieve Human-like Mathematical Reasoning?](https://mlsanity.com/paper/2407.01284/) (2024)
- [Skywork Open Reasoner 1 Technical Report](https://mlsanity.com/paper/2505.22312/) (2025)
- [Distilling Reasoning Capabilities into Smaller Language Models](https://mlsanity.com/paper/2212.00193/) (2022)
- [NVIDIA Nemotron Nano 2: An Accurate and Efficient Hybrid Mamba-Transformer Reasoning Model](https://mlsanity.com/paper/2508.14444/) (2025)
- [Speculative Knowledge Distillation: Bridging the Teacher-Student Gap Through Interleaved Sampling](https://mlsanity.com/paper/2410.11325/) (2024)
- [Autoregressive Knowledge Distillation through Imitation Learning](https://mlsanity.com/paper/2009.07253/) (2020)
- [Pass the Baton: Trajectory-Relayed On-Policy Distillation](https://mlsanity.com/paper/2607.26057/) (2026)
- [Escaping the KL Agreement Trap in On-Policy Distillation](https://mlsanity.com/paper/2606.09471/) (2026)
- [Innovator-VL: A Multimodal Large Language Model for Scientific Discovery](https://mlsanity.com/paper/2601.19325/) (2026)
- [CA-OPD: Confidence-Aware On-Policy Distillation for Structured Visual Prediction](https://mlsanity.com/paper/2609.02401/) (2026)

## Abstract (arXiv)

Off-policy and on-policy distillation have traditionally been formulated as separate paradigms, each favoring a different property of distillation trajectories. Teacher-generated (off-policy) traces are typically high-quality but lie far from the student's distribution, whereas student-generated (on-policy) rollouts are more learnable but often contain erroneous reasoning. We view these paradigms as the endpoints of a policy continuum and posit that a more effective rollout policy may lie in between. We introduce Interpolated Policy Distillation (IPD), which defines the next-token distribution at every decoding step as an explicit linear interpolation between the student and teacher distributions. The interpolation operates at the distribution level, token by token, and its coefficient provides direct control over the balance between trajectory quality and student learnability. Naively sampling from this policy would require sequentially querying the teacher at every token and is thus expensive. To make IPD practical, we accelerate it with a new speculative-decoding rule while exactly preserving the interpolated next-token distribution.At the trajectory level, the resulting rollouts naturally interleave student- and teacher-generated segments. Unlike recent heuristic segment-interleaving methods, however, this interleaving is induced by an exactly realized token-level interpolated policy rather than by hand-designed switching rules. Across text-only and multimodal reasoning benchmarks, IPD consistently outperforms both endpoint policies (SFT and OPD), their conventional two-stage combination (SFT-then-OPD), and recent heuristic segment-interleaving methods, demonstrating that token-level policy interpolation better balances trajectory quality and student learnability.