# Understanding diffusion models requires rethinking (again) generalization

arXiv: https://arxiv.org/abs/2605.06077 · HTML: https://mlsanity.com/paper/2605.06077/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 52 of its 64 references that are in the map.
- First posted on arXiv 7 May 2026.

## Placed in

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

## Builds on (most cited first, 30 of 52)

- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [A Closer Look at Memorization in Deep Networks](https://mlsanity.com/paper/1706.05394/) (2017)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [The Perception-Distortion Tradeoff](https://mlsanity.com/paper/1711.06077/) (2017)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Gradient Descent on Neural Networks Typically Occurs at the Edge of Stability](https://mlsanity.com/paper/2103.00065/) (2021)
- [Diffusion Art or Digital Forgery? Investigating Data Replication in Diffusion Models](https://mlsanity.com/paper/2212.03860/) (2022)
- [Implicit Regularization in Matrix Factorization](https://mlsanity.com/paper/1705.09280/) (2017)
- [A note on the evaluation of generative models](https://mlsanity.com/paper/1511.01844/) (2015)
- [Implicit Bias of Gradient Descent for Wide Two-layer Neural Networks Trained with the Logistic Loss](https://mlsanity.com/paper/2002.04486/) (2020)
- [User-friendly introduction to PAC-Bayes bounds](https://mlsanity.com/paper/2110.11216/) (2021)
- [Nearly d-Linear Convergence Bounds for Diffusion Models via Stochastic Localization](https://mlsanity.com/paper/2308.03686/) (2023)
- [Understanding and Mitigating Copying in Diffusion Models](https://mlsanity.com/paper/2305.20086/) (2023)
- [Generalization in diffusion models arises from geometry-adaptive harmonic representations](https://mlsanity.com/paper/2310.02557/) (2023)
- [A Self-Supervised Descriptor for Image Copy Detection](https://mlsanity.com/paper/2202.10261/) (2022)
- [Diffusion Models are Minimax Optimal Distribution Estimators](https://mlsanity.com/paper/2303.01861/) (2023)
- [Dynamical Regimes of Diffusion Models](https://mlsanity.com/paper/2402.18491/) (2024)
- [On Memorization in Diffusion Models](https://mlsanity.com/paper/2310.02664/) (2023)
- [An analytic theory of creativity in convolutional diffusion models](https://mlsanity.com/paper/2412.20292/) (2024)
- [On Provable Copyright Protection for Generative Models](https://mlsanity.com/paper/2302.10870/) (2023)

## Built on by (most cited first, 2 of 2)

- [Edge Flow: A Tractable and Predictive Continuous-Time Model for Gradient Descent at the Edge of Stability](https://mlsanity.com/paper/2606.18080/) (2026)
- [Double Descent and Malign Overfitting in Diffusion Models](https://mlsanity.com/paper/2609.26392/) (2026)

## Abstract (arXiv)

This position paper argues that understanding generalization in diffusion models requires fundamentally new theoretical frameworks that go beyond both classical statistical learning theory and the benign overfitting paradigm developed for supervised learning. In diffusion models, unlike in supervised learning, memorization of training data and generalization to novel samples are incompatible: a model that has fully memorized its training set generates copies rather than novel data. Several theoretical explanations for why practical diffusion models nevertheless generalize have been proposed, based on capacity limitations, implicit regularization from optimization, or architectural inductive biases, but their interactions remain unclear. We argue that the field should pivot from explaining why the diffusion models do not memorize to investigating what the model actually learns during pre-memorization phase. To highlight our stance, we conduct empirical study of diffusion models trained on CIFAR-10, and we distill the findings into concrete open questions that we believe are key to improve understanding of generalization in diffusion models.