# Local Mechanisms of Compositional Generalization in Conditional Diffusion

arXiv: https://arxiv.org/abs/2509.16447 · HTML: https://mlsanity.com/paper/2509.16447/

## 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 46 of its 56 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Placed in

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

## Builds on (most cited first, 30 of 46)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [SDXL: Improving Latent Diffusion Models for High-Resolution Image Synthesis](https://mlsanity.com/paper/2307.01952/) (2023)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Prompt-to-Prompt Image Editing with Cross Attention Control](https://mlsanity.com/paper/2208.01626/) (2022)
- [Generating Long Sequences with Sparse Transformers](https://mlsanity.com/paper/1904.10509/) (2019)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [GLIGEN: Open-Set Grounded Text-to-Image Generation](https://mlsanity.com/paper/2301.07093/) (2023)
- [Attend-and-Excite: Attention-Based Semantic Guidance for Text-to-Image Diffusion Models](https://mlsanity.com/paper/2301.13826/) (2023)
- [Compositional Visual Generation with Composable Diffusion Models](https://mlsanity.com/paper/2206.01714/) (2022)
- [Disentangling by Factorising](https://mlsanity.com/paper/1802.05983/) (2018)
- [Understanding the Effective Receptive Field in Deep Convolutional Neural Networks](https://mlsanity.com/paper/1701.04128/) (2017)
- [Analyzing and Improving the Training Dynamics of Diffusion Models](https://mlsanity.com/paper/2312.02696/) (2023)
- [BoxDiff: Text-to-Image Synthesis with Training-Free Box-Constrained Diffusion](https://mlsanity.com/paper/2307.10816/) (2023)
- [LayoutDiffusion: Controllable Diffusion Model for Layout-to-image Generation](https://mlsanity.com/paper/2303.17189/) (2023)
- [Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC](https://mlsanity.com/paper/2302.11552/) (2023)
- [Generalization in diffusion models arises from geometry-adaptive harmonic representations](https://mlsanity.com/paper/2310.02557/) (2023)
- [Composing Parameter-Efficient Modules with Arithmetic Operations](https://mlsanity.com/paper/2306.14870/) (2023)
- [A Length-Extrapolatable Transformer](https://mlsanity.com/paper/2212.10554/) (2022)
- [On Memorization in Diffusion Models](https://mlsanity.com/paper/2310.02664/) (2023)
- [Spatial Broadcast Decoder: A Simple Architecture for Learning Disentangled Representations in VAEs](https://mlsanity.com/paper/1901.07017/) (2019)

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

- [What Drives Compositional Generalization in Visual Generative Models? The Importance of Continuous Training Objectives](https://mlsanity.com/paper/2510.03075/) (2025)
- [An exact information theory of generalization phase transitions in Bayesian diffusion models](https://mlsanity.com/paper/2607.08041/) (2026)
- [When Do Diffusion Models learn to Generate Multiple Objects?](https://mlsanity.com/paper/2605.00273/) (2026)

## Abstract (arXiv)

Conditional diffusion models appear capable of compositional generalization, i.e., generating convincing samples for out-of-distribution combinations of conditioners, but the mechanisms underlying this ability remain unclear. To make this concrete, we study length generalization, the ability to generate images with more objects than seen during training. In a controlled CLEVR setting (Johnson et al., 2017), we find that length generalization is achievable in some cases but not others, suggesting that models only sometimes learn the underlying compositional structure. We then investigate locality as a structural mechanism for compositional generalization. Prior works proposed score locality as a mechanism for creativity in unconditional diffusion models (Kamb & Ganguli, 2024; Niedoba et al., 2024), but did not address flexible conditioning or compositional generalization. In this paper, we prove an exact equivalence between a specific compositional structure ("conditional projective composition") (Bradley et al., 2025) and scores with sparse dependencies on both pixels and conditioners ("local conditional scores"). This theory also extends to feature-space compositionality. We validate our theory empirically: CLEVR models that succeed at length generalization exhibit local conditional scores, while those that fail do not. Furthermore, we show that a causal intervention explicitly enforcing local conditional scores restores length generalization in a previously failing model. Finally, we investigate SDXL and find that in pixel-space, spatial locality is present but conditional-locality is mostly absent; however, we find quantitative evidence of local conditional scores in the network's learned feature-space.