# Complexity-Balanced Diffusion Splitting

arXiv: https://arxiv.org/abs/2606.06477 · HTML: https://mlsanity.com/paper/2606.06477/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 34 references that are in the map.
- First posted on arXiv 4 Jun 2026.

## Builds on (most cited first, 23 of 23)

- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [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)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Qwen-Image Technical Report](https://mlsanity.com/paper/2508.02324/) (2025)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [eDiff-I: Text-to-Image Diffusion Models with an Ensemble of Expert Denoisers](https://mlsanity.com/paper/2211.01324/) (2022)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [How to train your neural ODE: the world of Jacobian and kinetic regularization](https://mlsanity.com/paper/2002.02798/) (2020)
- [RAPHAEL: Text-to-Image Generation via Large Mixture of Diffusion Paths](https://mlsanity.com/paper/2305.18295/) (2023)
- [ERNIE-ViLG 2.0: Improving Text-to-Image Diffusion Model with Knowledge-Enhanced Mixture-of-Denoising-Experts](https://mlsanity.com/paper/2210.15257/) (2022)
- [Learning Differential Equations that are Easy to Solve](https://mlsanity.com/paper/2007.04504/) (2020)
- [Scaling Laws For Diffusion Transformers](https://mlsanity.com/paper/2410.08184/) (2024)
- [Multi-Architecture Multi-Expert Diffusion Models](https://mlsanity.com/paper/2306.04990/) (2023)
- [Switch Diffusion Transformer: Synergizing Denoising Tasks with Sparse Mixture-of-Experts](https://mlsanity.com/paper/2403.09176/) (2024)
- [Denoising Task Routing for Diffusion Models](https://mlsanity.com/paper/2310.07138/) (2023)

## Built on by (most cited first, 1 of 1)

- [Geometry-Aware Time Reparameterization for Flow-Map Distillation](https://mlsanity.com/paper/2610.02427/) (2026)

## Abstract (arXiv)

Standard continuous-time generative models rely on monolithic architectures that must navigate vastly different signal regimes, from isotropic noise to intricate data distributions. While scaling model capacity improves performance, deploying a massive network uniformly across the entire generative timeline is inherently inefficient. In this work, we propose Complexity-Balanced Splitting (CBS), a principled framework for temporal capacity allocation that distributes the generative workload across multiple specialized sub-networks. Grounded in function approximation theory and de Boor's equidistribution principle, CBS partitions the diffusion timeline into segments of equal approximation burden, allocating more representational capacity to regions where the generative dynamics are more difficult to model. To estimate this local complexity, we introduce two complementary and tractable monitor functions: a spatial measure based on the flow's Dirichlet energy, and a geometric measure based on the acceleration of the sampling trajectories. Using a lightweight auxiliary model to estimate these complexity profiles, our approach eliminates the need for heuristic temporal splits or computationally expensive search procedures. Extensive evaluation across multiple architectures (SiT, JiT, and UNet) and datasets demonstrates that CBS consistently improves synthesis quality without increasing per-step inference cost. In particular, CBS improves FID by ~35% on SiT-XL with CFG relative to naive temporal partitioning. Project page is available at https://noamissachar.github.io/CBS/.