# DMuon: Efficient Distributed Muon Training with Near-Adam Overhead

arXiv: https://arxiv.org/abs/2606.27153 · HTML: https://mlsanity.com/paper/2606.27153/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 36 references that are in the map.
- First posted on arXiv 25 Jun 2026.

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

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [OpenVLA: An Open-Source Vision-Language-Action Model](https://mlsanity.com/paper/2406.09246/) (2024)
- [π0: A Vision-Language-Action Flow Model for General Robot Control](https://mlsanity.com/paper/2410.24164/) (2024)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [π0.5: a Vision-Language-Action Model with Open-World Generalization](https://mlsanity.com/paper/2504.16054/) (2025)
- [ZeRO: Memory Optimizations Toward Training Trillion Parameter Models](https://mlsanity.com/paper/1910.02054/) (2019)
- [DeepSeek-V4: Towards Highly Efficient Million-Token Context Intelligence](https://mlsanity.com/paper/2606.19348/) (2026)
- [PaliGemma: A versatile 3B VLM for transfer](https://mlsanity.com/paper/2407.07726/) (2024)
- [PyTorch FSDP: Experiences on Scaling Fully Sharded Data Parallel](https://mlsanity.com/paper/2304.11277/) (2023)
- [Kimi K2: Open Agentic Intelligence](https://mlsanity.com/paper/2507.20534/) (2025)
- [Muon is Scalable for LLM Training](https://mlsanity.com/paper/2502.16982/) (2025)
- [Shampoo: Preconditioned Stochastic Tensor Optimization](https://mlsanity.com/paper/1802.09568/) (2018)
- [Ansor: Generating High-Performance Tensor Programs for Deep Learning](https://mlsanity.com/paper/2006.06762/) (2020)
- [SOAP: Improving and Stabilizing Shampoo using Adam](https://mlsanity.com/paper/2409.11321/) (2024)
- [Learning to Optimize Tensor Programs](https://mlsanity.com/paper/1805.08166/) (2018)
- [The Polar Express: Optimal Matrix Sign Methods and Their Application to the Muon Algorithm](https://mlsanity.com/paper/2505.16932/) (2025)
- [A Pragmatic VLA Foundation Model](https://mlsanity.com/paper/2601.18692/) (2026)
- [Tensor Comprehensions: Framework-Agnostic High-Performance Machine Learning Abstractions](https://mlsanity.com/paper/1802.04730/) (2018)
- [TorchTitan: One-stop PyTorch native solution for production ready LLM pre-training](https://mlsanity.com/paper/2410.06511/) (2024)
- [NorMuon: Making Muon more efficient and scalable](https://mlsanity.com/paper/2510.05491/) (2025)
- [A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale](https://mlsanity.com/paper/2309.06497/) (2023)
- [Dion: Distributed Orthonormalized Updates](https://mlsanity.com/paper/2504.05295/) (2025)
- [TileLang: A Composable Tiled Programming Model for AI Systems](https://mlsanity.com/paper/2504.17577/) (2025)
- [The Newton-Muon Optimizer](https://mlsanity.com/paper/2604.01472/) (2026)
- [Canzona: A Unified, Asynchronous, and Load-Balanced Framework for Distributed Matrix-based Optimizers](https://mlsanity.com/paper/2602.06079/) (2026)

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

- [Scaling Muon for Diffusion Transformers](https://mlsanity.com/paper/2608.20818/) (2026)
- [From Parallel to Sequential: Small-Batch Noise Restores Simplicity Bias of Muon](https://mlsanity.com/paper/2610.16868/) (2026)
- [Monarch-Muon: Structure-Aware Muon for Fast and Memory-Efficient Pretraining](https://mlsanity.com/paper/2610.17429/) (2026)

## Abstract (arXiv)

Matrix-orthogonalization-based optimizers, exemplified by Muon, have demonstrated strong convergence behavior across a wide range of modern deep learning workloads. The matrix-aware updates offer a compelling alternative to conventional element-wise optimization, particularly as model architectures continue to grow in scale and heterogeneity. Yet contemporary distributed training infrastructure built around the assumption of element-wise optimizers is poorly matched to matrix-level optimizers such as Muon, whose updates couple entire weight matrices and require costly Newton-Schulz iterations. Vanilla Muon implementations incur more than 2x the cost of forward and backward passes. To close this gap, we present DMuon, an open-source distributed Muon implementation that integrates into existing training pipelines as a drop-in module, with no framework-level modifications. Across both embodied foundation model and large language model (LLM) training workloads, DMuon achieves a 1.48x-3.01x speedup in end-to-end step time and a 6.85x-163.00x speedup in optimizer-step time, bringing per-step latency to near-AdamW levels and enabling efficient scaling in our model training.