# From Global to Factor-Wise Expert Composition in Discrete Diffusion Models

arXiv: https://arxiv.org/abs/2607.11758 · HTML: https://mlsanity.com/paper/2607.11758/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 29 of its 37 references that are in the map.
- First posted on arXiv 13 Jul 2026.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [Large Language Diffusion Models](https://mlsanity.com/paper/2502.09992/) (2025)
- [Simple and Effective Masked Diffusion Language Models](https://mlsanity.com/paper/2406.07524/) (2024)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [Train for the Worst, Plan for the Best: Understanding Token Ordering in Masked Diffusions](https://mlsanity.com/paper/2502.06768/) (2025)
- [Beyond Autoregression: Discrete Diffusion for Complex Reasoning and Planning](https://mlsanity.com/paper/2410.14157/) (2024)
- [DiffCollage: Parallel Generation of Large Content with Diffusion Models](https://mlsanity.com/paper/2303.17076/) (2023)
- [Feynman-Kac Correctors in Diffusion: Annealing, Guidance, and Product of Experts](https://mlsanity.com/paper/2503.02819/) (2025)
- [Generative Skill Chaining: Long-Horizon Skill Planning with Diffusion Models](https://mlsanity.com/paper/2401.03360/) (2023)
- [LLMs and the Abstraction and Reasoning Corpus: Successes, Failures, and the Importance of Object-based Representations](https://mlsanity.com/paper/2305.18354/) (2023)
- [Compositional Diffusion-Based Continuous Constraint Solvers](https://mlsanity.com/paper/2309.00966/) (2023)
- [The Superposition of Diffusion Models Using the Ito Density Estimator](https://mlsanity.com/paper/2412.17762/) (2024)
- [Self-Improving Language Models for Evolutionary Program Synthesis: A Case Study on ARC-AGI](https://mlsanity.com/paper/2507.14172/) (2025)
- [Addressing the Abstraction and Reasoning Corpus via Procedural Example Generation](https://mlsanity.com/paper/2404.07353/) (2024)
- [Graphs, Constraints, and Search for the Abstraction and Reasoning Corpus](https://mlsanity.com/paper/2210.09880/) (2022)
- [ARC Is a Vision Problem!](https://mlsanity.com/paper/2511.14761/) (2025)
- [Neural-guided, Bidirectional Program Search for Abstraction and Reasoning](https://mlsanity.com/paper/2110.11536/) (2021)
- [Product of Experts with LLMs: Boosting Performance on ARC Is a Matter of Perspective](https://mlsanity.com/paper/2505.07859/) (2025)
- [RNE: plug-and-play diffusion inference-time control and energy-based training](https://mlsanity.com/paper/2506.05668/) (2025)
- [Generative Factor Chaining: Coordinated Manipulation with Diffusion-based Factor Graph](https://mlsanity.com/paper/2409.16275/) (2024)
- [Tackling the Abstraction and Reasoning Corpus with Vision Transformers: the Importance of 2D Representation, Positions, and Objects](https://mlsanity.com/paper/2410.06405/) (2024)
- ["Set It Up!": Functional Object Arrangement with Compositional Generative Models](https://mlsanity.com/paper/2405.11928/) (2024)
- [Tiny Recursive Models on ARC-AGI-1: Inductive Biases, Identity Conditioning, and Test-Time Compute](https://mlsanity.com/paper/2512.11847/) (2025)
- [Relational decomposition for program synthesis](https://mlsanity.com/paper/2408.12212/) (2024)
- [Adapting Diffusion Models for Improved Prompt Compliance and Controllable Image Synthesis](https://mlsanity.com/paper/2410.21638/) (2024)
- [Compositional-ARC: Assessing Systematic Generalization in Abstract Spatial Reasoning](https://mlsanity.com/paper/2504.01445/) (2025)
- [ARC-AGI Without Pretraining](https://mlsanity.com/paper/2512.06104/) (2025)

## Abstract (arXiv)

Discrete diffusion models offer a powerful framework for solving complex reasoning tasks, particularly through compositional generation, which combines multiple pre-trained experts to generalize beyond their individual training data. Recent theoretical corrections introduce time-dependent mixing weights to better align composed diffusion dynamics with the intended target. However, these methods are fundamentally limited by working on a per-sample basis, treating each generated state monolithically and ignoring the potential spatial or functional specializations of different experts. In this work, we address this limitation by proposing FactorDiff - a factor-wise composition framework for diffusion models. We posit that samples can be further decomposed into smaller factors, and propose a sampling process that dynamically routes each factor to the most relevant expert. We instantiate this framework with spatial/pixel-level compositions and validate it on the ARC-AGI benchmark, demonstrating that simple factor-specific routing consistently outperforms complex global scalar weighting schemes on tasks that require logical consistency and spatial disentanglement.