# Breakdown of Local Denoising as Semantic Speciation

arXiv: https://arxiv.org/abs/2609.38176 · HTML: https://mlsanity.com/paper/2609.38176/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 32 of its 43 references that are in the map.
- First posted on arXiv 29 Sep 2026.

## Builds on (most cited first, 30 of 32)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [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)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [ConvNeXt V2: Co-designing and Scaling ConvNets with Masked Autoencoders](https://mlsanity.com/paper/2301.00808/) (2023)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Perception Prioritized Training of Diffusion Models](https://mlsanity.com/paper/2204.00227/) (2022)
- [Dynamical Regimes of Diffusion Models](https://mlsanity.com/paper/2402.18491/) (2024)
- [An analytic theory of creativity in convolutional diffusion models](https://mlsanity.com/paper/2412.20292/) (2024)
- [A Phase Transition in Diffusion Models Reveals the Hierarchical Nature of Data](https://mlsanity.com/paper/2402.16991/) (2024)
- [Spontaneous Symmetry Breaking in Generative Diffusion Models](https://mlsanity.com/paper/2305.19693/) (2023)
- [Critical windows: non-asymptotic theory for feature emergence in diffusion models](https://mlsanity.com/paper/2403.01633/) (2024)
- [Towards a Mechanistic Explanation of Diffusion Model Generalization](https://mlsanity.com/paper/2411.19339/) (2024)
- [Memorization to Generalization: Emergence of Diffusion Models from Associative Memory](https://mlsanity.com/paper/2505.21777/) (2025)
- [Locality in Image Diffusion Models Emerges from Data Statistics](https://mlsanity.com/paper/2509.09672/) (2025)
- [Does Generation Require Memorization? Creative Diffusion Models using Ambient Diffusion](https://mlsanity.com/paper/2502.21278/) (2025)
- [Blink of an eye: a simple theory for feature localization in generative models](https://mlsanity.com/paper/2502.00921/) (2025)
- [A General Derivative Identity for the Conditional Mean Estimator in Gaussian Noise and Some Applications](https://mlsanity.com/paper/2104.01883/) (2021)
- [The Entropic Signature of Class Speciation in Diffusion Models](https://mlsanity.com/paper/2602.09651/) (2026)
- [Local Diffusion Models and Phases of Data Distributions](https://mlsanity.com/paper/2508.06614/) (2025)
- [Measuring Semantic Information Production in Generative Diffusion Models](https://mlsanity.com/paper/2506.10433/) (2025)
- [How Out-of-Equilibrium Phase Transitions can Seed Pattern Formation in Trained Diffusion Models](https://mlsanity.com/paper/2603.20092/) (2026)
- [MMG: Mutual Information Estimation via the MMSE Gap in Diffusion](https://mlsanity.com/paper/2509.20609/) (2025)
- [An exact information theory of generalization phase transitions in Bayesian diffusion models](https://mlsanity.com/paper/2607.08041/) (2026)
- [On the Separability of Information in Diffusion Models](https://mlsanity.com/paper/2509.23937/) (2025)

## Abstract (arXiv)

The dynamics of generative models exhibit two apparently distinct temporal windows: a speciation window, in which a sample commits to a semantic class, and a nonlocality window, in which local context windows become insufficient for generation. Motivated by evidence of their near-concurrence in a variety of frontier models, we investigate their relationship through the spatial distribution of semantic information. Under a "common cause" hypothesis, we prove that the nonlocality window must lie in the speciation window. This hypothesis postulates that semantic labels explain a fraction of the correlations between distant tokens, a condition that is natural for many real datasets. We further give conditions under which both windows shrink to a single limiting time as system size grows, defining a "phase transition", and verify this behavior analytically in Gaussian mixtures. Together, these results identify conditions under which semantic information explains the concurrence of speciation and nonlocality, connecting two complementary perspectives on the emergence of semantic structure in generative modeling.