Broken Memories: Detecting and Mitigating Memorization in Diffusion Models with Degraded Generations

Chen Chen; Feifei Li; Geng Hong; Min Yang; Mi Zhang; Xiaoyu You; Yuanmin Huang

arxiv: 2605.22050 · v2 · pith:7QV34EWNnew · submitted 2026-05-21 · 💻 cs.CV

Broken Memories: Detecting and Mitigating Memorization in Diffusion Models with Degraded Generations

Yuanmin Huang , Mi Zhang , Chen Chen , Feifei Li , Geng Hong , Xiaoyu You , Min Yang This is my paper

Pith reviewed 2026-05-25 06:05 UTC · model grok-4.3

classification 💻 cs.CV

keywords memorization detectiondiffusion modelsnumerical stabilityimage generationprivacy protectionmitigation techniquesStable Diffusionlatent space analysis

0 comments

The pith

Diffusion models detect memorization through numerical instability shown as broken artifacts during generation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that memorization in diffusion models leads to internal numerical instability, which often appears as visually broken artifacts in generated images. Using ideas from stability analysis in numerical methods, it defines empirical stability regions based on the norms of latent updates to identify when generation is becoming unstable. This allows an on-the-fly detection and mitigation system that stops memorization step by step without changing the input prompt or guidance scale. The method keeps the semantic meaning and visual quality of the images while reducing privacy risks from copied training data. Experiments show near-perfect detection and complete removal of memorization with almost no extra computation time.

Core claim

Memorization induces internal numerical instability often manifesting as visually broken artifacts. Inspired by stability analysis in numerical methods, empirical stability regions based on latent update norms quantitatively characterize stable behavior during generation. This supports a principled on-the-fly framework for step-wise detection and adaptive mitigation that suppresses memorization without altering prompts or guidance, preserving semantic fidelity and image quality.

What carries the argument

Empirical stability regions based on latent update norms that detect instability caused by memorization during the denoising steps.

If this is right

Stable Diffusion 1.4 achieves AUC greater than 0.999 for detecting memorized generations.
Mitigation brings the memorization rate down to 0.0 percent after application.
The process adds only about 0.01 seconds per image in overhead.
Image quality and adherence to the prompt remain unchanged by the mitigation.
The detection and mitigation happen during generation without any model retraining.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Similar instability checks could apply to other iterative generative processes like those in video or audio models.
Deployed systems might use this to log and filter outputs that show signs of memorization in real time.
Future work could explore whether adjusting the stability thresholds improves performance across different datasets.
This approach suggests that monitoring internal dynamics can reveal overfitting without needing access to the training set.

Load-bearing premise

Memorization in the model causes measurable numerical instability during generation that reliably produces broken visual artifacts detectable by latent update norms.

What would settle it

Observe a set of images that are clearly memorized from the training data but generated without broken artifacts or exceeding the stability thresholds, or find that applying the mitigation still produces some memorized outputs.

Figures

Figures reproduced from arXiv: 2605.22050 by Chen Chen, Feifei Li, Geng Hong, Min Yang, Mi Zhang, Xiaoyu You, Yuanmin Huang.

**Figure 2.** Figure 2: Left: On-the-fly detection and mitigation progress. Each row visualizes predicted [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Comparison of mitigations on SD 1.4 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: Qualitative results comparing the proposed approach with the baselines on SD 1.4. [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 6.** Figure 6: Comparison of latent update trajectories and gen [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 7.** Figure 7: PNDM generation process on SD 1.4 using strong/mild/non- memorized prompts. [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗

**Figure 8.** Figure 8: DDIM generation process on SD 1.4 using strong/mild/non- memorized prompts. [PITH_FULL_IMAGE:figures/full_fig_p014_8.png] view at source ↗

**Figure 9.** Figure 9: Similar stability regions by prompts from different [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗

**Figure 10.** Figure 10: Similar stability regions by different numbers of [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗

**Figure 11.** Figure 11: Detection AUC using different numbers of refer [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗

**Figure 13.** Figure 13: Comparison of latent update trajectories and gen [PITH_FULL_IMAGE:figures/full_fig_p017_13.png] view at source ↗

**Figure 14.** Figure 14: Comparison with baselines on memorized prompts using finetuned SD 1.4 [PITH_FULL_IMAGE:figures/full_fig_p019_14.png] view at source ↗

read the original abstract

While diffusion models excel at generating high-quality images, their tendency to memorize training data poses significant privacy and copyright risks. In this work, we for the first time identify that memorization induces internal numerical instability, often manifesting as visually ``broken'' artifacts. Inspired by stability analysis in numerical methods, we introduce empirical stability regions based on latent update norms to quantitatively characterize stable behavior during generation. Leveraging this, we propose a principled, on-the-fly framework for step-wise detection and adaptive mitigation. Our approach suppresses memorization without altering prompts or guidance, thereby preserving semantic fidelity and image quality. Extensive experiments on Stable Diffusion 1.4 demonstrate that our method achieves an AUC $>0.999$ detection performance and a $0.0\%$ memorization rate after mitigation with negligible overhead ($\approx0.01$s per image).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper links memorization to latent update instability and gives a workable on-the-fly mitigation on Stable Diffusion 1.4.

read the letter

The paper's main contribution is showing that memorization tends to produce unstable latent updates, which can be used to detect and correct it during the generation process itself. This is new because prior work on memorization detection usually looks at the final output or requires separate models, whereas here they use the internal dynamics of the sampling loop. Defining stability regions from the norms of the updates gives a principled way to decide when to intervene. The reported results on Stable Diffusion 1.4 are impressive, with detection AUC above 0.999 and post-mitigation memorization at 0 percent, all while keeping the overhead to about 0.01 seconds per image and without degrading the image quality. The experiments appear to support the claims without obvious gaps in the reported metrics. The approach is practical because it does not require retraining or prompt engineering. The soft spots are mostly about scope. The work is demonstrated on one model, so it is not yet clear if the same norm-based regions apply to other diffusion variants or larger scales. The link between memorization and instability is treated as empirical, which is fine, but additional checks on whether fixing the instability always eliminates memorization would be reassuring. No circularity or fitting problems show up in the description. This paper is for people focused on making generative models safer in practice, especially around data privacy. A reader who wants actionable techniques for existing models will find it useful. It is solid enough to deserve a serious referee. I would send it for peer review.

Referee Report

0 major / 4 minor

Summary. The paper claims that memorization in diffusion models induces internal numerical instability, often visible as 'broken' artifacts during generation. It introduces empirical stability regions based on latent update norms to characterize stable behavior, and proposes an on-the-fly step-wise detection and adaptive mitigation framework that suppresses memorization without altering prompts or guidance. Experiments on Stable Diffusion 1.4 report AUC >0.999 for detection, 0.0% post-mitigation memorization rate, and negligible overhead of ≈0.01s per image while preserving semantic fidelity and image quality.

Significance. If the reported empirical correlation between memorization and elevated latent update norms holds under broader validation, the work offers a practical, prompt-preserving approach to mitigating privacy and copyright risks in diffusion models. The on-the-fly nature, high detection AUC, zero post-mitigation memorization rate, and low overhead are strengths that could aid ethical deployment of generative models.

minor comments (4)

The experimental section should explicitly state the dataset(s) used for training the base model and for evaluating memorization (including number of prompts and images), as these details are needed to interpret the AUC >0.999 and 0.0% rates.
Clarify the precise definition and threshold used to label a generation as 'memorized' (e.g., exact pixel match, perceptual similarity, or membership inference), since this metric is central to the mitigation claims.
Figure captions or the method section should include an example of a 'broken' artifact alongside the corresponding latent update norm trace to illustrate the stability-region concept.
The overhead measurement (≈0.01s per image) should specify the hardware and implementation details for reproducibility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper presents an empirical framework that correlates memorization with elevated latent update norms during diffusion generation, using stability-region analysis for detection and mitigation on Stable Diffusion 1.4. No equations, fitted parameters renamed as predictions, or self-citation chains are shown that reduce the core claims (AUC >0.999 detection, 0% post-mitigation memorization) to inputs by construction. The stability regions are introduced as an empirical characterization inspired by numerical methods, without self-definitional loops, uniqueness theorems from the authors, or ansatzes smuggled via prior self-citations. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no free parameters, axioms, or invented entities can be extracted or audited.

pith-pipeline@v0.9.0 · 5683 in / 1017 out tokens · 25684 ms · 2026-05-25T06:05:58.746347+00:00 · methodology

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discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We introduce empirical stability regions based on latent update norms... R^(t)_δ := [μ_t − γσ_t, μ_t + γσ_t]... Theorem 1 (Normal Trajectories Stability)... sub-Gaussian tail bound
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

PNDM... AB4... stability region RAB... scaled eigenvalues ν := λΔt

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
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contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
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Reference graph

Works this paper leans on

36 extracted references · 36 canonical work pages · 9 internal anchors

[1]

Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Floren- cia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. 2023. Gpt-4 technical report.arXiv preprint arXiv:2303.08774 (2023)

work page internal anchor Pith review Pith/arXiv arXiv 2023
[3]

Tony Bonnaire, Raphaël Urfin, Giulio Biroli, and Marc Mézard. 2025. Why Diffusion Models Don’t Memorize: The Role of Implicit Dynamical Regularization in Training. arXiv:2505.17638 [cs.LG] https://arxiv.org/abs/2505.17638

work page arXiv 2025
[4]

Jonathan Brokman, Itay Gershon, Omer Hofman, Guy Gilboa, and Roman Vain- shtein. 2025. Tracking memorization geometry throughout the diffusion model generative process. InNeurIPS 2025 Workshop on Symmetry and Geometry in Neural Representations

work page 2025
[5]

J.C. Butcher. 1996. A history of Runge-Kutta methods.Applied Numerical Mathe- matics20, 3 (1996), 247–260. doi:10.1016/0168-9274(95)00108-5

work page doi:10.1016/0168-9274(95)00108-5 1996
[6]

Nicolas Carlini, Jamie Hayes, Milad Nasr, Matthew Jagielski, Vikash Sehwag, Florian Tramer, Borja Balle, Daphne Ippolito, and Eric Wallace. 2023. Extracting training data from diffusion models. In32nd USENIX security symposium (USENIX Security 23). 5253–5270

work page 2023
[7]

Ruchika Chavhan, Ondrej Bohdal, Yongshuo Zong, Da Li, and Timothy Hospedales. 2024. Memorized Images in Diffusion Models share a Subspace that can be Located and Deleted. arXiv:2406.18566 [cs.CV] https://arxiv.org/abs/ 2406.18566 KDD 2026, August 9–13, 2026, Jeju Island, Republic of Korea. Yuanmin Huang, Mi Zhang, Chen Chen, Feifei Li, Geng Hong, Xiaoyu Y...

work page arXiv 2024
[8]

Chen Chen, Daochang Liu, Mubarak Shah, and Chang Xu. 2025. En- hancing Privacy-Utility Trade-offs to Mitigate Memorization in Diffu- sion Models. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 8182–8191. https://openaccess.thecvf. com/content/CVPR2025/html/Chen_Enhancing_Privacy-Utility_Trade- offs_to_Mitigate_Memoriz...

work page 2025
[9]

Chen Chen, Daochang Liu, Mubarak Shah, and Chang Xu. 2025. Explor- ing Local Memorization in Diffusion Models via Bright Ending Attention. arXiv:2410.21665 [cs.CV] https://arxiv.org/abs/2410.21665

work page arXiv 2025
[10]

Chen Chen, Daochang Liu, and Chang Xu. 2024. Towards memorization-free diffusion models. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 8425–8434

work page 2024
[11]

Dale R Durran. 1991. The third-order Adams-Bashforth method: An attractive alternative to leapfrog time differencing.Monthly weather review119, 3 (1991), 702–720

work page 1991
[12]

Zihan Guan, Mengxuan Hu, Sheng Li, and Anil Vullikanti. 2025. UFID: A Unified Framework for Input-level Backdoor Detection on Diffusion Models. arXiv:2404.01101 [cs.CR] https://arxiv.org/abs/2404.01101

work page arXiv 2025
[13]

1993.Solving ordinary differential equations I: Nonstiff problems

Ernst Hairer, Gerhard Wanner, and Syvert P Nørsett. 1993.Solving ordinary differential equations I: Nonstiff problems. Springer

work page 1993
[14]

Jack Hessel, Ari Holtzman, Maxwell Forbes, Ronan Le Bras, and Yejin Choi

work page
[15]

CLIPScore: A Reference-free Evaluation Metric for Image Captioning

CLIPScore: A Reference-free Evaluation Metric for Image Captioning. arXiv:2104.08718 [cs.CV] https://arxiv.org/abs/2104.08718

work page internal anchor Pith review Pith/arXiv arXiv
[16]

Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. 2018. GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium. arXiv:1706.08500 [cs.LG] https://arxiv.org/abs/1706. 08500

work page internal anchor Pith review Pith/arXiv arXiv 2018
[17]

Jonathan Ho, Ajay Jain, and Pieter Abbeel. 2020. Denoising diffusion probabilistic models.Advances in neural information processing systems33 (2020), 6840–6851

work page 2020
[18]

Jonathan Ho and Tim Salimans. 2022. Classifier-Free Diffusion Guidance. arXiv:2207.12598 [cs.LG] https://arxiv.org/abs/2207.12598

work page internal anchor Pith review Pith/arXiv arXiv 2022
[19]

Anubhav Jain, Yuya Kobayashi, Takashi Shibuya, Yuhta Takida, Nasir Memon, Julian Togelius, and Yuki Mitsufuji. 2025. Classifier-free guidance inside the attraction basin may cause memorization. InProceedings of the Computer Vision and Pattern Recognition Conference. 12871–12879

work page 2025
[20]

Dongjae Jeon, Dueun Kim, and Albert No. 2025. Understanding and Mitigating Memorization in Generative Models via Sharpness of Probability Landscapes. Proceedings of the 42nd International Conference on Machine Learning(2025)

work page 2025
[21]

Yue Jiang, Haokun Lin, Yang Bai, Bo Peng, Zhili Liu, Yueming Lyu, Yong Yang, Xing Zheng, and Jing Dong. 2025. Image-Level Memorization Detection Via Inversion-Based Inference Perturbation.The Thirteenth International Conference on Learning Representations(2025)

work page 2025
[22]

Kingma and Max Welling

Diederik P. Kingma and Max Welling. 2019. An Introduction to Variational Autoencoders.Foundations and Trends®in Machine Learning12, 4 (2019), 307–392. doi:10.1561/2200000056

work page doi:10.1561/2200000056 2019
[23]

Luping Liu, Yi Ren, Zhijie Lin, and Zhou Zhao. 2022. Pseudo Numerical Methods for Diffusion Models on Manifolds. arXiv:2202.09778 [cs.CV] https://arxiv.org/ abs/2202.09778

work page arXiv 2022
[24]

Zihao Luo, Xilie Xu, Feng Liu, Yun Sing Koh, Di Wang, and Jingfeng Zhang. 2024. Privacy-Preserving Low-Rank Adaptation against Membership Inference Attacks for Latent Diffusion Models. arXiv:2402.11989 [cs.LG] https://arxiv.org/abs/2402. 11989

work page arXiv 2024
[25]

Ed Pizzi, Sreya Dutta Roy, Sugosh Nagavara Ravindra, Priya Goyal, and Matthijs Douze. 2022. A self-supervised descriptor for image copy detection. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 14532– 14542

work page 2022
[26]

Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, Gretchen Krueger, and Ilya Sutskever. 2021. Learning Transferable Visual Models From Natural Language Supervision. arXiv:2103.00020 [cs.CV] https://arxiv.org/ abs/2103.00020

work page internal anchor Pith review Pith/arXiv arXiv 2021
[27]

Jie Ren, Yaxin Li, Shenglai Zeng, Han Xu, Lingjuan Lyu, Yue Xing, and Jiliang Tang. 2024. Unveiling and mitigating memorization in text-to-image diffusion models through cross attention. InEuropean Conference on Computer Vision. Springer, 340–356

work page 2024
[28]

Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. 2022. High-Resolution Image Synthesis with Latent Diffusion Models. arXiv:2112.10752 [cs.CV] https://arxiv.org/abs/2112.10752

work page internal anchor Pith review Pith/arXiv arXiv 2022
[29]

Christoph Schuhmann, Romain Beaumont, Richard Vencu, Cade Gordon, Ross Wightman, Mehdi Cherti, Theo Coombes, Aarush Katta, Clayton Mullis, Mitchell Wortsman, et al. 2022. Laion-5b: An open large-scale dataset for training next generation image-text models.Advances in neural information processing systems 35 (2022), 25278–25294

work page 2022
[30]

Christoph Schuhmann, Richard Vencu, Romain Beaumont, Robert Kaczmarczyk, Clayton Mullis, Aarush Katta, Theo Coombes, Jenia Jitsev, and Aran Komatsuzaki

work page
[31]

Laion-400m: Open dataset of clip-filtered 400 million image-text pairs.arXiv preprint arXiv:2111.02114(2021)

work page internal anchor Pith review Pith/arXiv arXiv 2021
[32]

1985.Numerical solution of partial differential equations: finite difference methods

Gordon D Smith. 1985.Numerical solution of partial differential equations: finite difference methods. Oxford university press

work page 1985
[33]

Gowthami Somepalli, Vasu Singla, Micah Goldblum, Jonas Geiping, and Tom Goldstein. 2023. Understanding and mitigating copying in diffusion models. Advances in Neural Information Processing Systems36 (2023), 47783–47803

work page 2023
[34]

Jiaming Song, Chenlin Meng, and Stefano Ermon. 2022. Denoising Diffusion Implicit Models. arXiv:2010.02502 [cs.LG] https://arxiv.org/abs/2010.02502

work page internal anchor Pith review Pith/arXiv arXiv 2022
[35]

Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. 2020. Score-based generative modeling through stochastic differential equations.arXiv preprint arXiv:2011.13456(2020)

work page internal anchor Pith review Pith/arXiv arXiv 2020
[36]

Ryan Webster. 2023. A reproducible extraction of training images from diffusion models.arXiv preprint arXiv:2305.08694(2023)

work page arXiv 2023
[37]

transfer part

Yuxin Wen, Yuchen Liu, Chen Chen, and Lingjuan Lyu. 2024. Detecting, explain- ing, and mitigating memorization in diffusion models. InThe Twelfth International Conference on Learning Representations. A Detailed Proofs In this section, we provide detailed proofs for Theorem 1 and 3 presented in the main text. Theorem 1 (Normal Trajectories Stability).Let 𝛿...

work page arXiv 2024

[1] [1]

Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Floren- cia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. 2023. Gpt-4 technical report.arXiv preprint arXiv:2303.08774 (2023)

work page internal anchor Pith review Pith/arXiv arXiv 2023

[2] [3]

Tony Bonnaire, Raphaël Urfin, Giulio Biroli, and Marc Mézard. 2025. Why Diffusion Models Don’t Memorize: The Role of Implicit Dynamical Regularization in Training. arXiv:2505.17638 [cs.LG] https://arxiv.org/abs/2505.17638

work page arXiv 2025

[3] [4]

Jonathan Brokman, Itay Gershon, Omer Hofman, Guy Gilboa, and Roman Vain- shtein. 2025. Tracking memorization geometry throughout the diffusion model generative process. InNeurIPS 2025 Workshop on Symmetry and Geometry in Neural Representations

work page 2025

[4] [5]

J.C. Butcher. 1996. A history of Runge-Kutta methods.Applied Numerical Mathe- matics20, 3 (1996), 247–260. doi:10.1016/0168-9274(95)00108-5

work page doi:10.1016/0168-9274(95)00108-5 1996

[5] [6]

Nicolas Carlini, Jamie Hayes, Milad Nasr, Matthew Jagielski, Vikash Sehwag, Florian Tramer, Borja Balle, Daphne Ippolito, and Eric Wallace. 2023. Extracting training data from diffusion models. In32nd USENIX security symposium (USENIX Security 23). 5253–5270

work page 2023

[6] [7]

Ruchika Chavhan, Ondrej Bohdal, Yongshuo Zong, Da Li, and Timothy Hospedales. 2024. Memorized Images in Diffusion Models share a Subspace that can be Located and Deleted. arXiv:2406.18566 [cs.CV] https://arxiv.org/abs/ 2406.18566 KDD 2026, August 9–13, 2026, Jeju Island, Republic of Korea. Yuanmin Huang, Mi Zhang, Chen Chen, Feifei Li, Geng Hong, Xiaoyu Y...

work page arXiv 2024

[7] [8]

Chen Chen, Daochang Liu, Mubarak Shah, and Chang Xu. 2025. En- hancing Privacy-Utility Trade-offs to Mitigate Memorization in Diffu- sion Models. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 8182–8191. https://openaccess.thecvf. com/content/CVPR2025/html/Chen_Enhancing_Privacy-Utility_Trade- offs_to_Mitigate_Memoriz...

work page 2025

[8] [9]

Chen Chen, Daochang Liu, Mubarak Shah, and Chang Xu. 2025. Explor- ing Local Memorization in Diffusion Models via Bright Ending Attention. arXiv:2410.21665 [cs.CV] https://arxiv.org/abs/2410.21665

work page arXiv 2025

[9] [10]

Chen Chen, Daochang Liu, and Chang Xu. 2024. Towards memorization-free diffusion models. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 8425–8434

work page 2024

[10] [11]

Dale R Durran. 1991. The third-order Adams-Bashforth method: An attractive alternative to leapfrog time differencing.Monthly weather review119, 3 (1991), 702–720

work page 1991

[11] [12]

Zihan Guan, Mengxuan Hu, Sheng Li, and Anil Vullikanti. 2025. UFID: A Unified Framework for Input-level Backdoor Detection on Diffusion Models. arXiv:2404.01101 [cs.CR] https://arxiv.org/abs/2404.01101

work page arXiv 2025

[12] [13]

1993.Solving ordinary differential equations I: Nonstiff problems

Ernst Hairer, Gerhard Wanner, and Syvert P Nørsett. 1993.Solving ordinary differential equations I: Nonstiff problems. Springer

work page 1993

[13] [14]

Jack Hessel, Ari Holtzman, Maxwell Forbes, Ronan Le Bras, and Yejin Choi

work page

[14] [15]

CLIPScore: A Reference-free Evaluation Metric for Image Captioning

CLIPScore: A Reference-free Evaluation Metric for Image Captioning. arXiv:2104.08718 [cs.CV] https://arxiv.org/abs/2104.08718

work page internal anchor Pith review Pith/arXiv arXiv

[15] [16]

Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. 2018. GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium. arXiv:1706.08500 [cs.LG] https://arxiv.org/abs/1706. 08500

work page internal anchor Pith review Pith/arXiv arXiv 2018

[16] [17]

Jonathan Ho, Ajay Jain, and Pieter Abbeel. 2020. Denoising diffusion probabilistic models.Advances in neural information processing systems33 (2020), 6840–6851

work page 2020

[17] [18]

Jonathan Ho and Tim Salimans. 2022. Classifier-Free Diffusion Guidance. arXiv:2207.12598 [cs.LG] https://arxiv.org/abs/2207.12598

work page internal anchor Pith review Pith/arXiv arXiv 2022

[18] [19]

Anubhav Jain, Yuya Kobayashi, Takashi Shibuya, Yuhta Takida, Nasir Memon, Julian Togelius, and Yuki Mitsufuji. 2025. Classifier-free guidance inside the attraction basin may cause memorization. InProceedings of the Computer Vision and Pattern Recognition Conference. 12871–12879

work page 2025

[19] [20]

Dongjae Jeon, Dueun Kim, and Albert No. 2025. Understanding and Mitigating Memorization in Generative Models via Sharpness of Probability Landscapes. Proceedings of the 42nd International Conference on Machine Learning(2025)

work page 2025

[20] [21]

Yue Jiang, Haokun Lin, Yang Bai, Bo Peng, Zhili Liu, Yueming Lyu, Yong Yang, Xing Zheng, and Jing Dong. 2025. Image-Level Memorization Detection Via Inversion-Based Inference Perturbation.The Thirteenth International Conference on Learning Representations(2025)

work page 2025

[21] [22]

Kingma and Max Welling

Diederik P. Kingma and Max Welling. 2019. An Introduction to Variational Autoencoders.Foundations and Trends®in Machine Learning12, 4 (2019), 307–392. doi:10.1561/2200000056

work page doi:10.1561/2200000056 2019

[22] [23]

Luping Liu, Yi Ren, Zhijie Lin, and Zhou Zhao. 2022. Pseudo Numerical Methods for Diffusion Models on Manifolds. arXiv:2202.09778 [cs.CV] https://arxiv.org/ abs/2202.09778

work page arXiv 2022

[23] [24]

Zihao Luo, Xilie Xu, Feng Liu, Yun Sing Koh, Di Wang, and Jingfeng Zhang. 2024. Privacy-Preserving Low-Rank Adaptation against Membership Inference Attacks for Latent Diffusion Models. arXiv:2402.11989 [cs.LG] https://arxiv.org/abs/2402. 11989

work page arXiv 2024

[24] [25]

Ed Pizzi, Sreya Dutta Roy, Sugosh Nagavara Ravindra, Priya Goyal, and Matthijs Douze. 2022. A self-supervised descriptor for image copy detection. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 14532– 14542

work page 2022

[25] [26]

Alec Radford, Jong Wook Kim, Chris Hallacy, Aditya Ramesh, Gabriel Goh, Sandhini Agarwal, Girish Sastry, Amanda Askell, Pamela Mishkin, Jack Clark, Gretchen Krueger, and Ilya Sutskever. 2021. Learning Transferable Visual Models From Natural Language Supervision. arXiv:2103.00020 [cs.CV] https://arxiv.org/ abs/2103.00020

work page internal anchor Pith review Pith/arXiv arXiv 2021

[26] [27]

Jie Ren, Yaxin Li, Shenglai Zeng, Han Xu, Lingjuan Lyu, Yue Xing, and Jiliang Tang. 2024. Unveiling and mitigating memorization in text-to-image diffusion models through cross attention. InEuropean Conference on Computer Vision. Springer, 340–356

work page 2024

[27] [28]

Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. 2022. High-Resolution Image Synthesis with Latent Diffusion Models. arXiv:2112.10752 [cs.CV] https://arxiv.org/abs/2112.10752

work page internal anchor Pith review Pith/arXiv arXiv 2022

[28] [29]

Christoph Schuhmann, Romain Beaumont, Richard Vencu, Cade Gordon, Ross Wightman, Mehdi Cherti, Theo Coombes, Aarush Katta, Clayton Mullis, Mitchell Wortsman, et al. 2022. Laion-5b: An open large-scale dataset for training next generation image-text models.Advances in neural information processing systems 35 (2022), 25278–25294

work page 2022

[29] [30]

Christoph Schuhmann, Richard Vencu, Romain Beaumont, Robert Kaczmarczyk, Clayton Mullis, Aarush Katta, Theo Coombes, Jenia Jitsev, and Aran Komatsuzaki

work page

[30] [31]

Laion-400m: Open dataset of clip-filtered 400 million image-text pairs.arXiv preprint arXiv:2111.02114(2021)

work page internal anchor Pith review Pith/arXiv arXiv 2021

[31] [32]

1985.Numerical solution of partial differential equations: finite difference methods

Gordon D Smith. 1985.Numerical solution of partial differential equations: finite difference methods. Oxford university press

work page 1985

[32] [33]

Gowthami Somepalli, Vasu Singla, Micah Goldblum, Jonas Geiping, and Tom Goldstein. 2023. Understanding and mitigating copying in diffusion models. Advances in Neural Information Processing Systems36 (2023), 47783–47803

work page 2023

[33] [34]

Jiaming Song, Chenlin Meng, and Stefano Ermon. 2022. Denoising Diffusion Implicit Models. arXiv:2010.02502 [cs.LG] https://arxiv.org/abs/2010.02502

work page internal anchor Pith review Pith/arXiv arXiv 2022

[34] [35]

Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. 2020. Score-based generative modeling through stochastic differential equations.arXiv preprint arXiv:2011.13456(2020)

work page internal anchor Pith review Pith/arXiv arXiv 2020

[35] [36]

Ryan Webster. 2023. A reproducible extraction of training images from diffusion models.arXiv preprint arXiv:2305.08694(2023)

work page arXiv 2023

[36] [37]

transfer part

Yuxin Wen, Yuchen Liu, Chen Chen, and Lingjuan Lyu. 2024. Detecting, explain- ing, and mitigating memorization in diffusion models. InThe Twelfth International Conference on Learning Representations. A Detailed Proofs In this section, we provide detailed proofs for Theorem 1 and 3 presented in the main text. Theorem 1 (Normal Trajectories Stability).Let 𝛿...

work page arXiv 2024