# Trees from Marginals: Autoregressive drafting with factorized priors

arXiv: https://arxiv.org/abs/2607.06763 · HTML: https://mlsanity.com/paper/2607.06763/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Speculative decoding, one of 12 directions in Efficient LLM inference and serving.
- Builds on 53 of its 66 references that are in the map.
- First posted on arXiv 7 Jul 2026.

## Placed in

- Efficient LLM inference and serving / [Speculative decoding](https://mlsanity.com/inference/speculative-decoding/)

## Builds on (most cited first, 30 of 53)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Fast Inference from Transformers via Speculative Decoding](https://mlsanity.com/paper/2211.17192/) (2022)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [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)
- [EAGLE: Speculative Sampling Requires Rethinking Feature Uncertainty](https://mlsanity.com/paper/2401.15077/) (2024)
- [Gated Delta Networks: Improving Mamba2 with Delta Rule](https://mlsanity.com/paper/2412.06464/) (2024)
- [The Entropy Mechanism of Reinforcement Learning for Reasoning Language Models](https://mlsanity.com/paper/2505.22617/) (2025)
- [LMSYS-Chat-1M: A Large-Scale Real-World LLM Conversation Dataset](https://mlsanity.com/paper/2309.11998/) (2023)
- [Muon is Scalable for LLM Training](https://mlsanity.com/paper/2502.16982/) (2025)
- [Fast-dLLM: Training-free Acceleration of Diffusion LLM by Enabling KV Cache and Parallel Decoding](https://mlsanity.com/paper/2505.22618/) (2025)
- [Block Diffusion: Interpolating Between Autoregressive and Diffusion Language Models](https://mlsanity.com/paper/2503.09573/) (2025)
- [Understanding the Effects of RLHF on LLM Generalisation and Diversity](https://mlsanity.com/paper/2310.06452/) (2023)
- [Parallelizing Linear Transformers with the Delta Rule over Sequence Length](https://mlsanity.com/paper/2406.06484/) (2024)
- [EAGLE-2: Faster Inference of Language Models with Dynamic Draft Trees](https://mlsanity.com/paper/2406.16858/) (2024)
- [LayerSkip: Enabling Early Exit Inference and Self-Speculative Decoding](https://mlsanity.com/paper/2404.16710/) (2024)
- [MT-Bench-101: A Fine-Grained Benchmark for Evaluating Large Language Models in Multi-Turn Dialogues](https://mlsanity.com/paper/2402.14762/) (2024)
- [AReaL: A Large-Scale Asynchronous Reinforcement Learning System for Language Reasoning](https://mlsanity.com/paper/2505.24298/) (2025)
- [A* Sampling](https://mlsanity.com/paper/1411.0030/) (2014)
- [Accelerating LLM Inference with Staged Speculative Decoding](https://mlsanity.com/paper/2308.04623/) (2023)
- [Fast-dLLM v2: Efficient Block-Diffusion LLM](https://mlsanity.com/paper/2509.26328/) (2025)
- [DFlash: Block Diffusion for Flash Speculative Decoding](https://mlsanity.com/paper/2602.06036/) (2026)
- [SpecTr: Fast Speculative Decoding via Optimal Transport](https://mlsanity.com/paper/2310.15141/) (2023)
- [The Mamba in the Llama: Distilling and Accelerating Hybrid Models](https://mlsanity.com/paper/2408.15237/) (2024)

## Built on by (most cited first, 3 of 3)

- [LiLiCorr: Lightweight Likelihood Correlation of Parallel Drafts for Speculative Decoding](https://mlsanity.com/paper/2608.20530/) (2026)
- [LumoTree: Path-Parallel Speculative Verification for Hybrid Language Models](https://mlsanity.com/paper/2609.23900/) (2026)
- [AdaSpark: Adaptive DSpark with Online Learning for Tree Verification and N-gram Fill](https://mlsanity.com/paper/2610.05774/) (2026)

## Abstract (arXiv)

Speculative decoding greatly increases the interactivity of autoregressive language models by trading off computation for extra tokens generated in a single forward pass. Factorized draft models are especially efficient because they predict future-token marginals in parallel, but their independence assumption causes acceptance rates to degrade sharply as the speculative budget grows. We analyze this limitation and introduce Weaver, a lightweight autoregressive adapter that constructs proposal trees from the top-K marginals of a factorized drafter. Weaver restores conditional dependencies between proposed tokens while avoiding a full-vocabulary projection. To support fast verification for models with Gated Delta Net layers, we derive a rollback-free tree-verification algorithm and implement optimized CUDA kernels in SGLang. By combining these model and systems contributions we achieve a 4.37-fold speedup over autoregressive decoding, and outperform a highly optimized DFlash baseline by 24.7%.