# Does Generation Require Memorization? Creative Diffusion Models using Ambient Diffusion

arXiv: https://arxiv.org/abs/2502.21278 · HTML: https://mlsanity.com/paper/2502.21278/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 61 of its 71 references that are in the map.
- First posted on arXiv 28 Feb 2025.

## Placed in

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

## Builds on (most cited first, 30 of 61)

- [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)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (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)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Extracting Training Data from Diffusion Models](https://mlsanity.com/paper/2301.13188/) (2023)
- [What Neural Networks Memorize and Why: Discovering the Long Tail via Influence Estimation](https://mlsanity.com/paper/2008.03703/) (2020)
- [Does Learning Require Memorization? A Short Tale about a Long Tail](https://mlsanity.com/paper/1906.05271/) (2019)
- [Diffusion Art or Digital Forgery? Investigating Data Replication in Diffusion Models](https://mlsanity.com/paper/2212.03860/) (2022)
- [Information-theoretic analysis of generalization capability of learning algorithms](https://mlsanity.com/paper/1705.07809/) (2017)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Convergence of denoising diffusion models under the manifold hypothesis](https://mlsanity.com/paper/2208.05314/) (2022)
- [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)
- [Holistic Evaluation of Text-To-Image Models](https://mlsanity.com/paper/2311.04287/) (2023)
- [Reasoning About Generalization via Conditional Mutual Information](https://mlsanity.com/paper/2001.09122/) (2020)
- [Dynamical Regimes of Diffusion Models](https://mlsanity.com/paper/2402.18491/) (2024)
- [On Memorization in Diffusion Models](https://mlsanity.com/paper/2310.02664/) (2023)
- [Ambient Diffusion: Learning Clean Distributions from Corrupted Data](https://mlsanity.com/paper/2305.19256/) (2023)
- [When is Memorization of Irrelevant Training Data Necessary for High-Accuracy Learning?](https://mlsanity.com/paper/2012.06421/) (2020)
- [An analytic theory of creativity in convolutional diffusion models](https://mlsanity.com/paper/2412.20292/) (2024)
- [Soft Diffusion: Score Matching for General Corruptions](https://mlsanity.com/paper/2209.05442/) (2022)
- [How much does your data exploration overfit? Controlling bias via information usage](https://mlsanity.com/paper/1511.05219/) (2015)
- [Detecting, Explaining, and Mitigating Memorization in Diffusion Models](https://mlsanity.com/paper/2407.21720/) (2024)
- [RoentGen: Vision-Language Foundation Model for Chest X-ray Generation](https://mlsanity.com/paper/2211.12737/) (2022)
- [Position: Considerations for Differentially Private Learning with Large-Scale Public Pretraining](https://mlsanity.com/paper/2212.06470/) (2022)

## Built on by (most cited first, 17 of 17)

- [Why Diffusion Models Don't Memorize: The Role of Implicit Dynamical Regularization in Training](https://mlsanity.com/paper/2505.17638/) (2025)
- [Locality in Image Diffusion Models Emerges from Data Statistics](https://mlsanity.com/paper/2509.09672/) (2025)
- [Ambient Diffusion Omni: Training Good Models with Bad Data](https://mlsanity.com/paper/2506.10038/) (2025)
- [Selective Underfitting in Diffusion Models](https://mlsanity.com/paper/2510.01378/) (2025)
- [Diffusion Model's Generalization Can Be Characterized by Inductive Biases toward a Data-Dependent Ridge Manifold](https://mlsanity.com/paper/2602.06021/) (2026)
- [Ambient Dataloops: Generative Models for Dataset Refinement](https://mlsanity.com/paper/2601.15417/) (2026)
- [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)
- [Concurrence of Symmetry Breaking and Nonlocality Phase Transitions in Diffusion Models](https://mlsanity.com/paper/2605.04830/) (2026)
- [A Closer Look on Memorization in Tabular Diffusion Model: A Data-Centric Perspective](https://mlsanity.com/paper/2505.22322/) (2025)
- [GuessBench: Sensemaking Multimodal Creativity in the Wild](https://mlsanity.com/paper/2506.00814/) (2025)
- [Riemannian AmbientFlow: Towards Simultaneous Manifold Learning and Generative Modeling from Corrupted Data](https://mlsanity.com/paper/2601.18728/) (2026)
- [Is Memorization Helpful or Harmful? Prior Information Sets the Threshold](https://mlsanity.com/paper/2602.09405/) (2026)
- [Initialization is Half the Battle: Generating Diverse Images from a Guidance Potential Posterior](https://mlsanity.com/paper/2606.02453/) (2026)
- [Reducing information dependency does not cause training data privacy. Adversarially non-robust features do](https://mlsanity.com/paper/2607.12354/) (2026)
- [Breakdown of Local Denoising as Semantic Speciation](https://mlsanity.com/paper/2609.38176/) (2026)
- [From Modes to Memories: Characterizing the Scale-Space Dynamics of Diffusion Models](https://mlsanity.com/paper/2609.39648/) (2026)

## Abstract (arXiv)

There is strong empirical evidence that the state-of-the-art diffusion modeling paradigm leads to models that memorize the training set, especially when the training set is small. Prior methods to mitigate the memorization problem often lead to a decrease in image quality. Is it possible to obtain strong and creative generative models, i.e., models that achieve high generation quality and low memorization? Despite the current pessimistic landscape of results, we make significant progress in pushing the trade-off between fidelity and memorization. We first provide theoretical evidence that memorization in diffusion models is only necessary for denoising problems at low noise scales (usually used in generating high-frequency details). Using this theoretical insight, we propose a simple, principled method to train the diffusion models using noisy data at large noise scales. We show that our method significantly reduces memorization without decreasing the image quality, for both text-conditional and unconditional models and for a variety of data availability settings.