# CMuon: Accelerating and Stabilizing Diffusion Transformer Training via Chunked Momentum Orthogonalization

arXiv: https://arxiv.org/abs/2608.02502 · HTML: https://mlsanity.com/paper/2608.02502/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 36 of its 44 references that are in the map.
- First posted on arXiv 3 Aug 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 30 of 36)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Qwen-Image Technical Report](https://mlsanity.com/paper/2508.02324/) (2025)
- [FLUX.1 Kontext: Flow Matching for In-Context Image Generation and Editing in Latent Space](https://mlsanity.com/paper/2506.15742/) (2025)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think](https://mlsanity.com/paper/2410.06940/) (2024)
- [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)
- [Reconstruction vs. Generation: Taming Optimization Dilemma in Latent Diffusion Models](https://mlsanity.com/paper/2501.01423/) (2025)
- [SANA: Efficient High-Resolution Image Synthesis with Linear Diffusion Transformers](https://mlsanity.com/paper/2410.10629/) (2024)
- [Z-Image: An Efficient Image Generation Foundation Model with Single-Stream Diffusion Transformer](https://mlsanity.com/paper/2511.22699/) (2025)
- [REPA-E: Unlocking VAE for End-to-End Tuning with Latent Diffusion Transformers](https://mlsanity.com/paper/2504.10483/) (2025)
- [Training Deep Learning Models with Norm-Constrained LMOs](https://mlsanity.com/paper/2502.07529/) (2025)
- [HunyuanVideo 1.5 Technical Report](https://mlsanity.com/paper/2511.18870/) (2025)
- [The Polar Express: Optimal Matrix Sign Methods and Their Application to the Muon Algorithm](https://mlsanity.com/paper/2505.16932/) (2025)
- [DDT: Decoupled Diffusion Transformer](https://mlsanity.com/paper/2504.05741/) (2025)
- [Fantastic Pretraining Optimizers and Where to Find Them](https://mlsanity.com/paper/2509.02046/) (2025)
- [LongCat-Image Technical Report](https://mlsanity.com/paper/2512.07584/) (2025)
- [PixelDiT: Pixel Diffusion Transformers for Image Generation](https://mlsanity.com/paper/2511.20645/) (2025)
- [Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)](https://mlsanity.com/paper/2505.13416/) (2025)

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

- [Scaling Muon for Diffusion Transformers](https://mlsanity.com/paper/2608.20818/) (2026)
- [Optimizers for Diffusion Models: A Controlled Benchmark](https://mlsanity.com/paper/2609.23055/) (2026)
- [Embedding Prediction Helps Image Generation](https://mlsanity.com/paper/2610.02203/) (2026)

## Abstract (arXiv)

Diffusion Transformers (DiTs) have achieved state-of-the-art (SOTA) performance in visual generative modeling, yet their training remains computationally prohibitive. While the recently proposed Momentum Orthogonalization (Muon) optimizer offers a promising alternative to AdamW, its direct application to DiTs yields suboptimal late-stage convergence. In this paper, we identify the root cause of this bottleneck: standard DiT architectures fuse functionally distinct weights (e.g., within AdaLN and QKV layers) into unified tensors for computational efficiency. Applying Muon to these fused tensors inadvertently induces implicit subspace coupling, which distorts update directions and degrades global optimization. To address this, we introduce Chunked Muon (CMuon), a simple yet highly effective strategy that partitions these matrices into independent sub-components prior to orthogonalization. Extensive experiments demonstrate that a 675M-parameter DiT trained with CMuon achieves a FID of 1.18 on ImageNet 256 in just 200 epochs. This represents more than a 2x training speedup over AdamW, while effectively overcoming the late-stage convergence plateaus of vanilla Muon.