# Divergence Decoding: Training-Free Capability Fusion

arXiv: https://arxiv.org/abs/2607.27248 · HTML: https://mlsanity.com/paper/2607.27248/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 34 of its 45 references that are in the map.
- First posted on arXiv 28 Jul 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 34)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [Accelerating Large Language Model Decoding with Speculative Sampling](https://mlsanity.com/paper/2302.01318/) (2023)
- [Medusa: Simple LLM Inference Acceleration Framework with Multiple Decoding Heads](https://mlsanity.com/paper/2401.10774/) (2024)
- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [Mixture-of-Experts with Expert Choice Routing](https://mlsanity.com/paper/2202.09368/) (2022)
- [EAGLE: Speculative Sampling Requires Rethinking Feature Uncertainty](https://mlsanity.com/paper/2401.15077/) (2024)
- [EAGLE-2: Faster Inference of Language Models with Dynamic Draft Trees](https://mlsanity.com/paper/2406.16858/) (2024)
- [BioMistral: A Collection of Open-Source Pretrained Large Language Models for Medical Domains](https://mlsanity.com/paper/2402.10373/) (2024)
- [A Comprehensive Survey of Scientific Large Language Models and Their Applications in Scientific Discovery](https://mlsanity.com/paper/2406.10833/) (2024)
- [ProLLaMA: A Protein Large Language Model for Multi-Task Protein Language Processing](https://mlsanity.com/paper/2402.16445/) (2024)
- [Developing ChemDFM as a large language foundation model for chemistry](https://mlsanity.com/paper/2401.14818/) (2024)
- [Beyond Chemical QA: Evaluating LLM's Chemical Reasoning with Modular Chemical Operations](https://mlsanity.com/paper/2505.21318/) (2025)
- [TxGemma: Efficient and Agentic LLMs for Therapeutics](https://mlsanity.com/paper/2504.06196/) (2025)
- [A Survey of Scientific Large Language Models: From Data Foundations to Agent Frontiers](https://mlsanity.com/paper/2508.21148/) (2025)
- [CITER: Collaborative Inference for Efficient Large Language Model Decoding with Token-Level Routing](https://mlsanity.com/paper/2502.01976/) (2025)
- [Toward 3D Spatial Reasoning for Human-like Text-based Visual Question Answering](https://mlsanity.com/paper/2209.10326/) (2022)
- [MoleculeQA: A Dataset to Evaluate Factual Accuracy in Molecular Comprehension](https://mlsanity.com/paper/2403.08192/) (2024)
- [FreestyleRet: Retrieving Images from Style-Diversified Queries](https://mlsanity.com/paper/2312.02428/) (2023)
- [ChemDFM-R: A Chemical Reasoning LLM Enhanced with Atomized Chemical Knowledge](https://mlsanity.com/paper/2507.21990/) (2025)

## Abstract (arXiv)

While large language models excel in reasoning, these generalists often lack knowledge for specialized scientific domains. Conversely, domain models~(specialists), while knowledgeable, suffer from specialization side-effects including diminished logic and reduced robustness.To address this dilemma, we introduce Divergence Decoding, a training-free framework for capability fusion. It reconstructs the "draft-and-verify" skeleton of speculative decoding into an adaptive routing mechanism. The core is using Jensen-Shannon divergence to monitor the distributional disagreement between the two models at each token. When the specialist exhibits significant divergence, our method identifies it as a potential reasoning risk and instantaneously routes control to the generalist. This allows the dynamic injection of general reasoning while preserving domain expertise, achieving inference-time policy composition of the generalist and the specialist.We evaluate Divergence Decoding across diverse model families (Qwen and Llama series) on challenging scientific benchmarks (GPQA, ChemBench, and ChemCoTBench). Experimental results demonstrate that Divergence Decoding outperforms both the domain-specialized and general-purpose models, effectively surpassing the performance of most single-model baseline. This suggests that Divergence Decoding provides a general, training-free paradigm for fusing diverse LLM capabilities through adaptive inference-time collaboration.