# Local Coverage Governs Memorization in Diffusion Models

arXiv: https://arxiv.org/abs/2606.14390 · HTML: https://mlsanity.com/paper/2606.14390/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 21 of its 33 references that are in the map.
- First posted on arXiv 12 Jun 2026.

## Placed in

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

## Builds on (most cited first, 21 of 21)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [Diffusion Art or Digital Forgery? Investigating Data Replication in Diffusion Models](https://mlsanity.com/paper/2212.03860/) (2022)
- [Generalization in diffusion models arises from geometry-adaptive harmonic representations](https://mlsanity.com/paper/2310.02557/) (2023)
- [Score-Based Generative Models Detect Manifolds](https://mlsanity.com/paper/2206.01018/) (2022)
- [An analytic theory of creativity in convolutional diffusion models](https://mlsanity.com/paper/2412.20292/) (2024)
- [Detecting, Explaining, and Mitigating Memorization in Diffusion Models](https://mlsanity.com/paper/2407.21720/) (2024)
- [Why Diffusion Models Don't Memorize: The Role of Implicit Dynamical Regularization in Training](https://mlsanity.com/paper/2505.17638/) (2025)
- [In search of dispersed memories: Generative diffusion models are associative memory networks](https://mlsanity.com/paper/2309.17290/) (2023)
- [A Geometric Framework for Understanding Memorization in Generative Models](https://mlsanity.com/paper/2411.00113/) (2024)
- [A Good Score Does not Lead to A Good Generative Model](https://mlsanity.com/paper/2401.04856/) (2024)
- [Memorization to Generalization: Emergence of Diffusion Models from Associative Memory](https://mlsanity.com/paper/2505.21777/) (2025)
- [Losing dimensions: Geometric memorization in generative diffusion](https://mlsanity.com/paper/2410.08727/) (2024)
- [Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curves](https://mlsanity.com/paper/2502.00336/) (2025)
- [Taking a Big Step: Large Learning Rates in Denoising Score Matching Prevent Memorization](https://mlsanity.com/paper/2502.03435/) (2025)
- [Generalization of Diffusion Models Arises with a Balanced Representation Space](https://mlsanity.com/paper/2512.20963/) (2025)
- [A Random Matrix Theory Perspective on the Consistency of Diffusion Models](https://mlsanity.com/paper/2602.02908/) (2026)
- [Kernel Density Estimators in Large Dimensions](https://mlsanity.com/paper/2408.05807/) (2024)
- [A Closer Look on Memorization in Tabular Diffusion Model: A Data-Centric Perspective](https://mlsanity.com/paper/2505.22322/) (2025)
- [Memorisation, convergence and generalisation in generative models](https://mlsanity.com/paper/2605.21402/) (2026)

## Built on by (most cited first, 5 of 5)

- [Generalization, memorization, and overfitting for diffusion models trained in the lazy high-dimensional regime](https://mlsanity.com/paper/2608.23938/) (2026)
- [Recovering Weighted Tangent Geometry from a Single-Scale Score Field](https://mlsanity.com/paper/2608.22334/) (2026)
- [Mitigating Sequential Reappearance in Diffusion Data-Point Unlearning](https://mlsanity.com/paper/2609.25166/) (2026)
- [Background Gradients Shape Memorization in Flow Matching](https://mlsanity.com/paper/2609.33210/) (2026)
- [First Learn, Then Memorize: The Spectral Bias of Diffusion Models](https://mlsanity.com/paper/2609.35377/) (2026)

## Abstract (arXiv)

Memorization in diffusion models is often treated as a global property of the model or dataset. In practice, however, a single diffusion model can simultaneously generate both memorized and novel samples. Which training samples are most likely to be memorized? In this work, we show that memorization is governed by local data coverage. Leveraging the connection between diffusion models and kernel density estimation (KDE), we derive a theoretical criterion that predicts whether a point is memorized based on the density of training data in its neighborhood and the size of the training dataset. In the high-dimensional limit, this leads to a sharp, local transition: regions of low coverage are dominated by isolated training samples, which are memorized, while dense regions support interpolation and generalization. We validate these predictions empirically, showing that memorization increases with local sparsity and that diffusion models exhibit a coexistence of memorized and novel samples within the same model. Extending this framework to multi-class settings, we further show that classes with higher intra-class sparsity (and thus lower local coverage) are more strongly memorized. Our results provide a local view of memorization in diffusion models, explaining when and where memorization occurs in terms of data geometry.