# SODA: Semi On-Policy Black-Box Distillation for Large Language Models

arXiv: https://arxiv.org/abs/2604.03873 · HTML: https://mlsanity.com/paper/2604.03873/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Knowledge distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 21 of its 31 references that are in the map.
- First posted on arXiv 4 Apr 2026.

## Placed in

- Knowledge distillation / [Knowledge distillation for LLMs](https://mlsanity.com/distill/knowledge-distillation-for-llms/)

## Builds on (most cited first, 21 of 21)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [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)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Large Language Models are not Fair Evaluators](https://mlsanity.com/paper/2305.17926/) (2023)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/1606.07947/) (2016)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [LMSYS-Chat-1M: A Large-Scale Real-World LLM Conversation Dataset](https://mlsanity.com/paper/2309.11998/) (2023)
- [SeqGAN: Sequence Generative Adversarial Nets with Policy Gradient](https://mlsanity.com/paper/1609.05473/) (2016)
- [f-Divergence Minimization for Sequence-Level Knowledge Distillation](https://mlsanity.com/paper/2307.15190/) (2023)
- [Provably Mitigating Overoptimization in RLHF: Your SFT Loss is Implicitly an Adversarial Regularizer](https://mlsanity.com/paper/2405.16436/) (2024)
- [Black-Box On-Policy Distillation of Large Language Models](https://mlsanity.com/paper/2511.10643/) (2025)
- [Direct Preference Knowledge Distillation for Large Language Models](https://mlsanity.com/paper/2406.19774/) (2024)
- [PLaD: Preference-based Large Language Model Distillation with Pseudo-Preference Pairs](https://mlsanity.com/paper/2406.02886/) (2024)
- [Reinforcement Learning Fine-Tuning Enhances Activation Intensity and Diversity in the Internal Circuitry of LLMs](https://mlsanity.com/paper/2509.21044/) (2025)

## Built on by (most cited first, 7 of 7)

- [SOD: Step-wise On-policy Distillation for Small Language Model Agents](https://mlsanity.com/paper/2605.07725/) (2026)
- [Adaptive Teacher Exposure for Self-Distillation in LLM Reasoning](https://mlsanity.com/paper/2605.11458/) (2026)
- [Tailoring Teaching to Aptitude: Direction-Adaptive Self-Distillation for LLM Reasoning](https://mlsanity.com/paper/2605.22263/) (2026)
- [PriFT: Prior-Support Guided Supervised Fine-Tuning](https://mlsanity.com/paper/2606.09396/) (2026)
- [Smaller Models, Better Rejects: Preference Distillation Scaling](https://mlsanity.com/paper/2609.38987/) (2026)
- [USA: Update-aware SAM for Cross-domain On-Policy Disitllation of Language Agents](https://mlsanity.com/paper/2609.34225/) (2026)
- [MAS-OPD: On-Policy Distillation for Multi-agent Systems](https://mlsanity.com/paper/2609.34234/) (2026)

## Abstract (arXiv)

Black-box knowledge distillation for large language models presents a strict trade-off. Simple off-policy methods (e.g., sequence-level knowledge distillation) struggle to correct the student's inherent errors. Fully on-policy methods (e.g., Generative Adversarial Distillation) solve this via adversarial training but introduce well-known training instability and crippling computational overhead. To address this dilemma, we propose SODA (Semi On-policy Distillation with Alignment), a highly efficient alternative motivated by the inherent capability gap between frontier teachers and much smaller base models. Because a compact student model's natural, zero-shot responses are almost strictly inferior to the powerful teacher's targets, we can construct a highly effective contrastive signal simply by pairing the teacher's optimal response with a one-time static snapshot of the student's outputs. This demonstrates that exposing the small student to its own static inferior behaviors is sufficient for high-quality distribution alignment, eliminating the need for costly dynamic rollouts and fragile adversarial balancing. Extensive evaluations across four compact Qwen2.5 and Llama-3 models validate this semi on-policy paradigm. SODA matches or outperforms the state-of-the-art methods on 15 out of 16 benchmark results. More importantly, it achieves this superior distillation quality while training 10 times faster, consuming 27% less peak GPU memory, and completely eliminating adversarial instability.