# Bigger Isn't Always Memorizing: Early Stopping Overparameterized Diffusion Models

arXiv: https://arxiv.org/abs/2505.16959 · HTML: https://mlsanity.com/paper/2505.16959/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 65 of its 81 references that are in the map.
- First posted on arXiv 22 May 2025.

## Placed in

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

## Builds on (most cited first, 30 of 65)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [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)
- [LAION-5B: An open large-scale dataset for training next generation image-text models](https://mlsanity.com/paper/2210.08402/) (2022)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [Structured Denoising Diffusion Models in Discrete State-Spaces](https://mlsanity.com/paper/2107.03006/) (2021)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [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)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Simplified and Generalized Masked Diffusion for Discrete Data](https://mlsanity.com/paper/2406.04329/) (2024)
- [Argmax Flows and Multinomial Diffusion: Learning Categorical Distributions](https://mlsanity.com/paper/2102.05379/) (2021)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [A Mean Field View of the Landscape of Two-Layers Neural Networks](https://mlsanity.com/paper/1804.06561/) (2018)
- [PixelCNN++: Improving the PixelCNN with Discretized Logistic Mixture Likelihood and Other Modifications](https://mlsanity.com/paper/1701.05517/) (2017)
- [High-dimensional dynamics of generalization error in neural networks](https://mlsanity.com/paper/1710.03667/) (2017)
- [Understanding and Mitigating Copying in Diffusion Models](https://mlsanity.com/paper/2305.20086/) (2023)
- [Feature Learning in Infinite-Width Neural Networks](https://mlsanity.com/paper/2011.14522/) (2020)
- [Generalization in diffusion models arises from geometry-adaptive harmonic representations](https://mlsanity.com/paper/2310.02557/) (2023)

## Built on by (most cited first, 25 of 25)

- [Why Diffusion Models Don't Memorize: The Role of Implicit Dynamical Regularization in Training](https://mlsanity.com/paper/2505.17638/) (2025)
- [On the Closed-Form of Flow Matching: Generalization Does Not Arise from Target Stochasticity](https://mlsanity.com/paper/2506.03719/) (2025)
- [Generalization Dynamics of Linear Diffusion Models](https://mlsanity.com/paper/2505.24769/) (2025)
- [The Generation Phases of Flow Matching: a Denoising Perspective](https://mlsanity.com/paper/2510.24830/) (2025)
- [Why Gaussian Diffusion Models Fail on Discrete Data and How to Prevent It?](https://mlsanity.com/paper/2604.02028/) (2026)
- [Biased Generalization in Diffusion Models](https://mlsanity.com/paper/2603.03469/) (2026)
- [Distinct mechanisms underlying in-context learning in transformers](https://mlsanity.com/paper/2604.12151/) (2026)
- [An exact information theory of generalization phase transitions in Bayesian diffusion models](https://mlsanity.com/paper/2607.08041/) (2026)
- [Generalization, memorization, and overfitting for diffusion models trained in the lazy high-dimensional regime](https://mlsanity.com/paper/2608.23938/) (2026)
- [Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Access](https://mlsanity.com/paper/2505.18344/) (2025)
- [Diffusion Models Memorize in Training -- and Generalize in Inference](https://mlsanity.com/paper/2603.13419/) (2026)
- [Understanding diffusion models requires rethinking (again) generalization](https://mlsanity.com/paper/2605.06077/) (2026)
- [The Interplay of Data Structure and Imbalance in the Learning Dynamics of Diffusion Models](https://mlsanity.com/paper/2605.06367/) (2026)
- [Learn from your own latents and not from tokens: A sample-complexity theory](https://mlsanity.com/paper/2605.27734/) (2026)
- [Sensitivity Analysis for Diffusion Models](https://mlsanity.com/paper/2509.23092/) (2025)
- [Early-stopping for Transformer model training](https://mlsanity.com/paper/2510.16074/) (2025)
- [MGD: Moment Guided Diffusion for Maximum Entropy Generation](https://mlsanity.com/paper/2602.17211/) (2026)
- [Memorisation, convergence and generalisation in generative models](https://mlsanity.com/paper/2605.21402/) (2026)
- [Diffusion Models Preferentially Memorize Prototypical Examples or: Why Does My Diffusion Model Love Slop?](https://mlsanity.com/paper/2605.30642/) (2026)
- [Evaluating the Representation Space of Diffusion Models via Self-Supervised Principles](https://mlsanity.com/paper/2606.09718/) (2026)
- [Double Descent and Malign Overfitting in Diffusion Models](https://mlsanity.com/paper/2609.26392/) (2026)
- [Latent Iterative Refinement Flow: A Geometric Constrained Approach for Few-Shot Generation](https://mlsanity.com/paper/2509.19903/) (2025)
- [Beyond Memorization: Selective Learning for Copyright-Safe Diffusion Model Training](https://mlsanity.com/paper/2512.11194/) (2025)
- [diffGHOST: Diffusion based Generative Hedged Oblivious Synthetic Trajectories](https://mlsanity.com/paper/2605.10647/) (2026)
- [Controlling Polar Exposure to Delay Memorization in Diffusion Models](https://mlsanity.com/paper/2610.02780/) (2026)

## Abstract (arXiv)

Diffusion probabilistic models have become a cornerstone of modern generative AI, yet the mechanisms underlying their generalization remain poorly understood. In fact, if these models were perfectly minimizing their training loss, they would just generate data belonging to their training set, i.e., memorize, as empirically found in the overparameterized regime. We revisit this view by showing that, in highly overparameterized diffusion models, generalization in natural data domains is progressively achieved during training before the onset of memorization. Our results, ranging from image to language diffusion models, systematically support the empirical law that memorization time is proportional to the dataset size. Generalization vs. memorization is then best understood as a competition between time scales. We show that this phenomenology is recovered in diffusion models learning a simple probabilistic context-free grammar with random rules, where generalization corresponds to the hierarchical acquisition of deeper grammar rules as training time grows, and the generalization cost of early stopping can be characterized. We summarize these results in a phase diagram. Overall, our results support that a principled early-stopping criterion - scaling with dataset size - can effectively optimize generalization while avoiding memorization, with direct implications for hyperparameter transfer and privacy-sensitive applications.