# WaveFront Decoding: Parallelized Self-Speculative Decoding for Looped Language Models

arXiv: https://arxiv.org/abs/2609.23033 · HTML: https://mlsanity.com/paper/2609.23033/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Speculative decoding, one of 12 directions in Efficient LLM inference and serving.
- Builds on 25 of its 29 references that are in the map.
- First posted on arXiv 19 Sep 2026.

## Placed in

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

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

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [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)
- [Fast Transformer Decoding: One Write-Head is All You Need](https://mlsanity.com/paper/1911.02150/) (2019)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Efficiently Scaling Transformer Inference](https://mlsanity.com/paper/2211.05102/) (2022)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [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)
- [Unlocking Efficiency in Large Language Model Inference: A Comprehensive Survey of Speculative Decoding](https://mlsanity.com/paper/2401.07851/) (2024)
- [Scaling Latent Reasoning via Looped Language Models](https://mlsanity.com/paper/2510.25741/) (2025)
- [Mixture-of-Recursions: Learning Dynamic Recursive Depths for Adaptive Token-Level Computation](https://mlsanity.com/paper/2507.10524/) (2025)
- [LoopFormer: Elastic-Depth Looped Transformers for Latent Reasoning via Shortcut Modulation](https://mlsanity.com/paper/2602.11451/) (2026)
- [Parcae: Scaling Laws For Stable Looped Language Models](https://mlsanity.com/paper/2604.12946/) (2026)
- [Understanding and Mitigating Numerical Sources of Nondeterminism in LLM Inference](https://mlsanity.com/paper/2506.09501/) (2025)
- [Teaching Pretrained Language Models to Think Deeper with Retrofitted Recurrence](https://mlsanity.com/paper/2511.07384/) (2025)
- [Parallel Loop Transformer for Efficient Test-Time Computation Scaling](https://mlsanity.com/paper/2510.24824/) (2025)
- [LoopUS: Recasting Pretrained LLMs into Looped Latent Refinement Models](https://mlsanity.com/paper/2605.11011/) (2026)
- [Memory-Efficient Looped Transformer: Decoupling Compute from Memory in Looped Language Models](https://mlsanity.com/paper/2605.07721/) (2026)
- [Nanbeige4.2-3B: Unlocking Agentic Capabilities in a Compact Model](https://mlsanity.com/paper/2607.22083/) (2026)
- [Efficient Parallel Samplers for Recurrent-Depth Models and Their Connection to Diffusion Language Models](https://mlsanity.com/paper/2510.14961/) (2025)
- [Looped Latent Attention: Cross-Loop KV Compression for Looped Transformers](https://mlsanity.com/paper/2607.15456/) (2026)
- [LoopCoder-v2: Only Loop Once for Efficient Test-Time Computation Scaling](https://mlsanity.com/paper/2606.18023/) (2026)

## Abstract (arXiv)

Looped language models repeatedly apply a weight-shared block to increase effective depth without increasing parameter count, but the resulting T sequential recurrent-block calls per generated token substantially increase decoding latency. To address the issue, we introduce Wavefront Decoding (WFD), a training-free self-speculative decoding framework designed for looped language models. WFD exploits two properties of these architectures: intermediate recurrence outputs provide effective draft predictions, and weight sharing allows token states at different positions and recurrence depths to be processed in one batched recurrent-block call. WFD organizes these mixed-depth states into a diagonal wavefront, continuously drafting new positions at shallow depth while advancing earlier positions toward full-depth verification. Unlike the phase-separated draft-then-verify schedule, WFD therefore concurrently batches drafting and verification within the same recurrent calls, while rejected drafts are corrected using full-depth predictions. Across six Spec-Bench task categories, WFD achieves 2.42x speedup on Ouro-2.6B and 3.54x on Huginn-3.5B over autoregressive decoding, consistently outperforming draft-then-verify. Cross-recurrence KV sharing further reduces wavefront KV traffic and increases WFD's speedup to 4.81x on Huginn-3.5B. The code is available at https://github.com/summerbro-hhj/wavefront-decoding.