# Provable Separations between Memorization and Generalization in Diffusion Models

arXiv: https://arxiv.org/abs/2511.03202 · HTML: https://mlsanity.com/paper/2511.03202/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 32 of its 77 references that are in the map.
- First posted on arXiv 5 Nov 2025.

## Placed in

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

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

- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Generalization in diffusion models arises from geometry-adaptive harmonic representations](https://mlsanity.com/paper/2310.02557/) (2023)
- [Diff-TTS: A Denoising Diffusion Model for Text-to-Speech](https://mlsanity.com/paper/2104.01409/) (2021)
- [Symbolic Music Generation with Diffusion Models](https://mlsanity.com/paper/2103.16091/) (2021)
- [On Memorization in Diffusion Models](https://mlsanity.com/paper/2310.02664/) (2023)
- [Three Mechanisms of Weight Decay Regularization](https://mlsanity.com/paper/1810.12281/) (2018)
- [An analytic theory of creativity in convolutional diffusion models](https://mlsanity.com/paper/2412.20292/) (2024)
- [Differentially Private Diffusion Models Generate Useful Synthetic Images](https://mlsanity.com/paper/2302.13861/) (2023)
- [Why Diffusion Models Don't Memorize: The Role of Implicit Dynamical Regularization in Training](https://mlsanity.com/paper/2505.17638/) (2025)
- [Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory](https://mlsanity.com/paper/2403.11968/) (2024)
- [A Reproducible Extraction of Training Images from Diffusion Models](https://mlsanity.com/paper/2305.08694/) (2023)
- [Super Tickets in Pre-Trained Language Models: From Model Compression to Improving Generalization](https://mlsanity.com/paper/2105.12002/) (2021)
- [Efficient Diffusion Models for Vision: A Survey](https://mlsanity.com/paper/2210.09292/) (2022)
- [DiffusionShield: A Watermark for Copyright Protection against Generative Diffusion Models](https://mlsanity.com/paper/2306.04642/) (2023)
- [Towards a Mechanistic Explanation of Diffusion Model Generalization](https://mlsanity.com/paper/2411.19339/) (2024)
- [A Geometric Framework for Understanding Memorization in Generative Models](https://mlsanity.com/paper/2411.00113/) (2024)
- [The statistical thermodynamics of generative diffusion models: Phase transitions, symmetry breaking and critical instability](https://mlsanity.com/paper/2310.17467/) (2023)
- [Manifolds, Random Matrices and Spectral Gaps: The geometric phases of generative diffusion](https://mlsanity.com/paper/2410.05898/) (2024)
- [Locality in Image Diffusion Models Emerges from Data Statistics](https://mlsanity.com/paper/2509.09672/) (2025)
- [Generalization through variance: how noise shapes inductive biases in diffusion models](https://mlsanity.com/paper/2504.12532/) (2025)
- [On the Edge of Memorization in Diffusion Models](https://mlsanity.com/paper/2508.17689/) (2025)
- [Denoising Score Matching with Random Features: Insights on Diffusion Models from Precise Learning Curves](https://mlsanity.com/paper/2502.00336/) (2025)
- [Variational approximations using Fisher divergence](https://mlsanity.com/paper/1905.05284/) (2019)
- [Memorized Images in Diffusion Models share a Subspace that can be Located and Deleted](https://mlsanity.com/paper/2406.18566/) (2024)
- [Replication in Visual Diffusion Models: A Survey and Outlook](https://mlsanity.com/paper/2408.00001/) (2024)

## Built on by (most cited first, 14 of 14)

- [Generalization of Diffusion Models Arises with a Balanced Representation Space](https://mlsanity.com/paper/2512.20963/) (2025)
- [Diffusion Model's Generalization Can Be Characterized by Inductive Biases toward a Data-Dependent Ridge Manifold](https://mlsanity.com/paper/2602.06021/) (2026)
- [A Categorical Analysis of Large Language Models and Why LLMs Circumvent the Symbol Grounding Problem](https://mlsanity.com/paper/2512.09117/) (2025)
- [A Kinetic Energy Perspective of Flow Matching](https://mlsanity.com/paper/2602.07928/) (2026)
- [Benign Overfitting Does Not Occur in Diffusion Models](https://mlsanity.com/paper/2607.02671/) (2026)
- [Transport Novelty Distance: A Distributional Metric for Evaluating Material Generative Models](https://mlsanity.com/paper/2512.09514/) (2025)
- [On The Hidden Biases of Flow Matching Samplers](https://mlsanity.com/paper/2512.16768/) (2025)
- [Diffusion Models Memorize in Training -- and Generalize in Inference](https://mlsanity.com/paper/2603.13419/) (2026)
- [Manifold Generalization Provably Proceeds Memorization in Diffusion Models](https://mlsanity.com/paper/2603.23792/) (2026)
- [Memorization Control in Diffusion Models from Denoising-centric Perspective](https://mlsanity.com/paper/2601.21348/) (2026)
- [Adynamical systems view of training generativemodels and the memorization phenomenon](https://mlsanity.com/paper/2605.19483/) (2026)
- [Localizing Memorized Regions in Diffusion Models via Coordinate-Wise Curvature Differences](https://mlsanity.com/paper/2605.26756/) (2026)
- [A Theoretical Analysis of Memory and Overfitting Phenomena in Stochastic Interpolation Models](https://mlsanity.com/paper/2606.08554/) (2026)
- [Background Gradients Shape Memorization in Flow Matching](https://mlsanity.com/paper/2609.33210/) (2026)

## Abstract (arXiv)

Diffusion models have achieved remarkable success across diverse domains, but they remain vulnerable to memorization -- reproducing training data rather than generating novel outputs. This not only limits their creative potential but also raises concerns about privacy and safety. While empirical studies have explored mitigation strategies, theoretical understanding of memorization remains limited. We address this gap through developing a dual-separation result via two complementary perspectives: statistical estimation and network approximation. From the estimation side, we show that the ground-truth score function does not minimize the empirical denoising loss, creating a separation that drives memorization. From the approximation side, we prove that implementing the empirical score function requires network size to scale with sample size, spelling a separation compared to the more compact network representation of the ground-truth score function. Guided by these insights, we develop a pruning-based method that reduces memorization while maintaining generation quality in diffusion transformers.