Pith. sign in

REVIEW 3 major objections 6 minor 65 references

Stable diffusion unlearning needs a manifold-proximal anchor; cross-attention maps can synthesize one automatically.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-10 09:09 UTC pith:A33YJYT6

load-bearing objection Clean geometric diagnosis of why diffusion unlearning drifts off-manifold, plus a practical automatic anchor that improves seven baselines; the attention-to-geometry bridge is assumed rather than measured. the 3 major comments →

arxiv 2607.08337 v1 pith:A33YJYT6 submitted 2026-07-09 cs.LG stat.ML

AutoAnchor: Stable Diffusion Unlearning Using Cross-Attention as a Manifold Surrogate

Siyuan Wen , Jiahao Zeng , Ningning Ding This is my paper
classification cs.LG stat.ML
keywords diffusion unlearningmanifold hypothesiscross-attentionconcept erasureStable Diffusionanchor-based unlearningnormal-space drift
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Text-to-image diffusion models can be made to forget a concept, but the usual ways of choosing the update direction push the model off the low-dimensional manifold of valid images. The paper proves that any update lacking a nearby anchor on that manifold leaks almost all of its energy into the normal space, which produces fragile erasure and collateral damage to unrelated concepts. AutoAnchor builds the missing anchor in two automatic stages: it first gathers and filters candidate concepts, then optimizes a cross-attention consistency loss that acts as a cheap surrogate for manifold proximity. The resulting anchors give stronger target removal and better non-target utility, and they can be dropped into existing unlearning algorithms to improve them as well.

Core claim

Under the manifold hypothesis, unlearning updates without a manifold-proximal anchor concentrate almost all of their energy in the normal space and therefore leave the data manifold; a carefully constructed proximal anchor keeps the update nearly tangential, and a cross-attention consistency loss is a tractable surrogate that produces such anchors automatically.

What carries the argument

Cross-attention consistency loss: the expected Frobenius distance between the frozen U-Net’s cross-attention maps under the target embedding and under the candidate anchor embedding; minimizing it (inside a spherical semantic shell) is proved to bound the geometric normal-drift quantity ζ that Theorems 2 and 6 require for stability.

Load-bearing premise

The paper assumes that how far an update pushes a latent off the image manifold is controlled by how differently the target and the anchor light up the model’s cross-attention maps; if that link is weak, the surrogate no longer guarantees a stable anchor.

What would settle it

Construct a pair of embeddings whose cross-attention maps are nearly identical yet whose score residual still has a large normal component on the true data manifold; if such pairs routinely appear, the attention-geometry bridge fails and AutoAnchor’s stability claims collapse.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

Share X Bluesky LinkedIn Reddit HN

If this is right

  • Any diffusion unlearning method whose update direction is defined by an empty or purely semantic prompt will systematically leak energy off-manifold.
  • Existing anchor-based algorithms can be upgraded simply by replacing their hand-chosen anchors with AutoAnchor embeddings.
  • Concept removal and utility preservation need not trade off once the update is forced to stay nearly tangential.
  • The same attention-based surrogate can be reused for other latent-space editing tasks that require manifold-proximal directions.

Where Pith is reading between the lines

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

  • If attention maps are only a loose proxy, stronger geometric surrogates (local PCA of the score, estimated reach) may still be needed for high-curvature concepts.
  • The same normal-drift analysis likely applies to unlearning in other score-based or flow-based generative models that live on low-dimensional manifolds.
  • Adversarial re-learning attacks that succeed after AutoAnchor would indicate residual normal components that the current loss did not fully suppress.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper argues that diffusion unlearning is unstable because anchor-free updates and manually chosen semantic anchors induce large normal-space drift off the data manifold. Under high-dimensional concentration assumptions it proves that such updates concentrate almost all energy in the normal space (Theorems 1, 3), while a ζ-proximal anchor suppresses that drift (Theorems 2, 4–5). To construct such anchors it proposes AutoAnchor: Stage I automatically generates and filters LLM candidates; Stage II optimizes a cross-attention consistency loss LCA as a tractable surrogate for manifold proximity (Assumption 5 / Theorem 6). Empirically, AutoAnchor improves concept removal and non-target utility on three primary and four additional targets, and when plugged into seven prior methods yields average gains of roughly 6% on CLIP(U) and CLIP(R).

Significance. If the geometric account holds, the work supplies a unified explanation for several known failure modes of diffusion unlearning (catastrophic forgetting, fragile erasure, biased redirection) and a lightweight, automatic preprocessing step that improves both anchor-free and anchor-based baselines without redesigning their losses. The plug-and-play empirical results across seven methods and multiple concept categories are a concrete contribution. The formal random-walk stability comparison and the explicit ζ-proximal definition are useful organizing tools even if the attention–geometry bridge remains partly conjectural. The contribution is therefore of clear interest to the machine-unlearning and generative-modeling communities, provided the load-bearing surrogate claim is better substantiated.

major comments (3)
  1. Appendix A.7, Assumption 5 and Theorem 6: the claim that optimizing LCA yields a ζ-proximal anchor rests entirely on the untested Attention–Geometry Isomorphism (normal residual Lipschitz in Frobenius attention distance plus tolerance ν). The manuscript never reports an estimate of L_CA or ν, nor any correlation between LCA and a geometric proxy for normal drift (e.g., ||Δ_N||²/||Δ||², off-manifold distance of reverse trajectories, or score residual projected onto an estimated normal space). Without that measurement, Theorems 2 and 6 do not yet certify that AutoAnchor anchors are manifold-proximal; the observed CLIP/FID gains could arise from better semantic alternatives alone. A short empirical check of this bridge is load-bearing for the central theoretical claim.
  2. §4–§5 and Definition 1: the paper never measures the normal-energy fraction (or any related geometric quantity) for AutoAnchor versus empty-prompt or manual-anchor baselines. Table 2 shows that Stage-I semantic aggregation alone can degrade CLIP(U) while Stage-II LCA optimization recovers it, which is consistent with the story but does not directly test the normal-drift mechanism that Theorems 1–5 are written to explain. Reporting even a coarse proxy of ||Π_N(Δ)|| before and after optimization would substantially strengthen the link between theory and method.
  3. §5.2 and Table 1: when AutoAnchor is integrated into originally anchor-free methods (ESD, ResAlign, CCRT, tuneSD-AF), the paper replaces the unconditional term by the AutoAnchor embedding. The main text does not clearly state whether this changes the official loss formulation of those methods or only the conditioning embedding, nor whether hyper-parameters were re-tuned. Because the average “+6.30% / +6.65%” claim is a primary empirical selling point, the precise adaptation protocol should be specified so that the gains can be attributed to the anchor rather than to incidental loss changes.
minor comments (6)
  1. Figure 1 caption and body: the geodesic / Euclidean distinction is helpful, but the figure itself is dense; a short legend defining the three colored arrows would improve readability.
  2. Eq. (1) and surrounding text: Δ_AF and Δ_AB are written as noise-prediction differences; later the discrete update multiplies by a learning rate η (Theorems 3–4). Stating the discrete parameter-update step explicitly would avoid ambiguity.
  3. Table 1: Δ values ≤2% are grayed as “below error precision,” yet the abstract still quotes average gains that include those entries. Clarifying how averages are computed (with or without the gray cells) would help.
  4. §5.1: the clustering function f_cluster and the automatic choice of M via silhouette score are only fully described in Appendix B.6; a one-sentence pointer in the main text would help reproducibility.
  5. Appendix B.3–B.4: robustness to LLM choice and K is useful; stating the default (K, N, λ) used in the main tables in a single place would make the experimental protocol easier to follow.
  6. Typos / polish: “unrobust” appears repeatedly (prefer “non-robust”); “Weboldthe” in Table 1 caption; occasional missing spaces around citations.

Circularity Check

0 steps flagged

No circularity: geometric theorems follow from concentration under stated assumptions; the attention surrogate is an independent architectural hypothesis whose success is measured by external CLIP/FID metrics, not by construction.

full rationale

The derivation chain is self-contained and non-circular. Theorems 1–2 (and absolute-magnitude Theorems 3–4) are ordinary high-dimensional concentration statements (Lévy / chi-squared / Markov) applied to the isotropic-update Assumption 3 and the definition of a ζ-proximal anchor (Definition 1). Theorem 5 is a random-walk comparison that follows from those magnitude bounds. The only bridge from the tractable objective LCA to the geometric quantity ζ is Assumption 5 (Attention-Geometry Isomorphism) plus Proposition 1 / Theorem 6; that assumption is explicitly labeled a “strong” structural hypothesis and is not derived from the performance numbers that later appear in the tables. The empirical claims (CLIP(U)/CLIP(R)/FID improvements, including the 31 % figure) are obtained by running the two-stage procedure on held-out prompts and comparing against seven external baselines; none of those metrics is an algebraic rearrangement of LCA or of any fitted free parameter. There is no self-citation that carries the load of a uniqueness claim, no parameter fitted on a subset and then “predicted” on a closely related quantity, and no renaming of a known empirical pattern. The reader’s own circularity score of 2 and the skeptic’s attack correctly identify a correctness / validation gap (Assumption 5 is untested), but that gap is not circularity under the definitions used here. Score 0 is therefore the honest finding.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 2 invented entities

The central geometric claims rest on the classical manifold hypothesis plus four statistical assumptions about score errors and isotropy, plus one strong architectural bridging assumption that equates attention-map distance with normal-space drift. Free parameters are the usual optimization knobs plus the radii and regularization weight that keep the anchor inside a semantic shell. The only invented entities are the ζ-proximal-anchor definition and the attention-consistency loss itself; both are operationally defined inside the paper.

free parameters (5)
  • λ (regularization strength on L_reg)
    Balances the attention consistency term against the spherical-shell penalty; chosen by the authors and not derived.
  • r−, r+ (inner/outer radii of semantic shell)
    Set from Euclidean distances to cluster centroids of Stage-I candidates; directly control how close the optimized anchor may approach the target.
  • K (number of top candidate tokens)
    Controls size of the initial candidate pool; ablation shows performance is sensitive for K≤10.
  • α (utility-preservation weight in L_DU)
    Standard trade-off coefficient between erasure and retention losses.
  • N (number of LLM sentences)
    Determines diversity of the candidate set C0; fixed by authors.
axioms (5)
  • domain assumption Manifold hypothesis: valid images lie on a low-dimensional submanifold Mu of the ambient latent space (d*u ≪ d).
    Invoked throughout §4 and Appendix A; standard but unproved for the specific Stable Diffusion latent space.
  • domain assumption Assumption 2: score approximation error has zero mean and bounded normal-space variance σN².
    Used to bound absolute normal drift in Theorems 3–4.
  • domain assumption Assumption 3: normalized update vectors of anchor-free or biased-anchor methods are approximately isotropic.
    Supplies the concentration that yields the near-100 % normal-energy claim of Theorem 1.
  • ad hoc to paper Assumption 5 (Attention-Geometry Isomorphism): normal residual is Lipschitz in Frobenius attention distance plus tolerance ν.
    The sole link that converts the optimizable LCA loss into a guarantee on ζ (Theorem 6); not independently verified.
  • standard math Diffusion models learn the score function (ϵθ ∝ ∇ log p).
    Standard fact from Song et al. / Ho et al., used to equate noise-prediction differences with manifold updates.
invented entities (2)
  • ζ-proximal anchor no independent evidence
    purpose: Formal object whose normal-energy fraction is bounded by ζ², enabling the stability theorems.
    Defined in Definition 1; existence is guaranteed only after the attention optimization succeeds.
  • Cross-attention consistency loss LCA no independent evidence
    purpose: Tractable surrogate that replaces direct manifold projection.
    Introduced in Eq. (5); its geometric validity rests entirely on Assumption 5.

pith-pipeline@v1.1.0-grok45 · 37888 in / 3175 out tokens · 37063 ms · 2026-07-10T09:09:01.190240+00:00 · methodology

0 comments
Cite this review

Pith. "Pith review of AutoAnchor: Stable Diffusion Unlearning Using Cross-Attention as a Manifold Surrogate." pith.science (2026). https://pith.science/paper/A33YJYT6

@misc{pith2026260708337,
  author       = {Pith},
  title        = {Pith review of: AutoAnchor: Stable Diffusion Unlearning Using Cross-Attention as a Manifold Surrogate},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/A33YJYT6}},
  note         = {Machine review of arXiv:2607.08337}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Diffusion unlearning is essential for mitigating the generation of harmful or copyrighted content in text-to-image models. Current diffusion unlearning techniques determine the model update direction by either using alternatives of the target concept as an anchor or using empty prompts. The anchor-based method relies on manually and semantically-chosen anchors that risk biased unlearning, while the anchor-free method inherently suffers from unrobust unlearning due to unconstrained latent updates. In this work, we theoretically formalize such unstable diffusion unlearning issues under the manifold hypothesis and prove that lacking a manifold-proximal anchor inevitably induces significant normal-space drift that degrades unlearning performance. To achieve stable unlearning, we propose \mysysn, a two-stage framework that automatically synthesizes manifold-proximal anchors. However, direct geometric manifold optimization is computationally intractable. To address this challenge, \mysys introduces a novel cross-attention consistency loss which serves as a highly efficient surrogate of manifold proximity. Experimental results demonstrate that \mysys effectively achieves robust and unbiased unlearning across various state-of-the-art baselines, significantly improving targeted concept removal (by up to 31.04\% in CLIP score) and non-target utility (by up to 4.18\% in CLIP score). Moreover, \mysys can also be easily integrated into existing diffusion unlearning methods to enhance their unlearning performance (by 6.30\% for concept removal and 6.65\% for utility on average).

Figures

Figures reproduced from arXiv: 2607.08337 by Jiahao Zeng, Ningning Ding, Siyuan Wen.

Figure 1
Figure 1. Figure 1: Illustration of the data manifold and unlearning update directions. Without a manifold [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of AutoAnchor. Given a target concept [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Qualitative comparison of concept unlearning. For each target concept (Mickey Mouse, [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

65 extracted references · 65 canonical work pages · 5 internal anchors

  1. [1]

    Erasing more than intended? how concept erasure degrades the generation of non-target concepts

    Ibtihel Amara, Ahmed Imtiaz Humayun, Ivana Kajic, Zarana Parekh, Natalie Harris, Sarah Young, Chirag Nagpal, Najoung Kim, Junfeng He, Cristina Nader Vasconcelos, et al. Erasing more than intended? how concept erasure degrades the generation of non-target concepts. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 16420– 16430, 2025

    work page 2025

  2. [2]

    Intrinsic dimension of data representations in deep neural networks.Advances in Neural Information Processing Systems, 32, 2019

    Alessio Ansuini, Alessandro Laio, Jakob H Macke, and Davide Zoccolan. Intrinsic dimension of data representations in deep neural networks.Advances in Neural Information Processing Systems, 32, 2019

    work page 2019

  3. [3]

    Weighted sums of certain dependent random variables.Tohoku Mathematical Journal, Second Series, 19(3):357–367, 1967

    Kazuoki Azuma. Weighted sums of certain dependent random variables.Tohoku Mathematical Journal, Second Series, 19(3):357–367, 1967

    work page 1967

  4. [4]

    Cure: Concept unlearning via orthogonal representation editing in diffusion models

    Shristi Das Biswas, Arani Roy, and Kaushik Roy. Cure: Concept unlearning via orthogonal representation editing in diffusion models. InThe Thirty-ninth Annual Conference on Neural Information Processing Systems, 2025

    work page 2025

  5. [5]

    Cambridge University Press, 2020

    Avrim Blum, John Hopcroft, and Ravindran Kannan.Foundations of data science. Cambridge University Press, 2020

    work page 2020

  6. [6]

    Erasing Undesirable Concepts in Diffusion Models with Adversarial Preservation

    Anh Bui, Long Vuong, Khanh Doan, Trung Le, Paul Montague, Tamas Abraham, and Dinh Phung. Erasing undesirable concepts in diffusion models with adversarial preservation.arXiv preprint arXiv:2410.15618, 2024

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  7. [7]

    Distributions of angles in random packing on spheres.Journal of Machine Learning Research, 14(136):1837–1864, 2013

    T Tony Cai, Jianqing Fan, and Tiefeng Jiang. Distributions of angles in random packing on spheres.Journal of Machine Learning Research, 14(136):1837–1864, 2013

    work page 2013

  8. [8]

    Score approximation, estimation and distribution recovery of diffusion models on low-dimensional data

    Minshuo Chen, Kaixuan Huang, Tuo Zhao, and Mengdi Wang. Score approximation, estimation and distribution recovery of diffusion models on low-dimensional data. InInternational Conference on Machine Learning, pages 4672–4712. PMLR, 2023

    work page 2023

  9. [9]

    Improving diffusion models for inverse problems using manifold constraints.Advances in Neural Information Processing Systems, 35:25683–25696, 2022

    Hyungjin Chung, Byeongsu Sim, Dohoon Ryu, and Jong Chul Ye. Improving diffusion models for inverse problems using manifold constraints.Advances in Neural Information Processing Systems, 35:25683–25696, 2022

    work page 2022

  10. [10]

    SalUn: Empowering Machine Unlearning via Gradient-based Weight Saliency in Both Image Classification and Generation

    Chongyu Fan, Jiancheng Liu, Yihua Zhang, Eric Wong, Dennis Wei, and Sijia Liu. Salun: Empowering machine unlearning via gradient-based weight saliency in both image classification and generation.arXiv preprint arXiv:2310.12508, 2023

    work page internal anchor Pith review Pith/arXiv arXiv 2023

  11. [11]

    Curvature measures.Transactions of the American Mathematical Society, 93(3):418–491, 1959

    Herbert Federer. Curvature measures.Transactions of the American Mathematical Society, 93(3):418–491, 1959

    work page 1959

  12. [12]

    Testing the manifold hypothesis

    Charles Fefferman, Sanjoy Mitter, and Hariharan Narayanan. Testing the manifold hypothesis. Journal of the American Mathematical Society, 29(4):983–1049, 2016

    work page 2016

  13. [13]

    Erasing concepts from diffusion models

    Rohit Gandikota, Joanna Materzynska, Jaden Fiotto-Kaufman, and David Bau. Erasing concepts from diffusion models. InProceedings of the IEEE/CVF international conference on computer vision, pages 2426–2436, 2023

    work page 2023

  14. [14]

    The illusion of unlearning: The unstable nature of machine unlearning in text-to-image diffusion models

    Naveen George, Karthik Nandan Dasaraju, Rutheesh Reddy Chittepu, and Konda Reddy Mopuri. The illusion of unlearning: The unstable nature of machine unlearning in text-to-image diffusion models. InProceedings of the Computer Vision and Pattern Recognition Conference, pages 13393–13402, 2025

    work page 2025

  15. [15]

    Continuous Concepts Removal in Text-to-image Diffusion Models

    Tingxu Han, Weisong Sun, Yanrong Hu, Chunrong Fang, Yonglong Zhang, Shiqing Ma, Tao Zheng, Zhenyu Chen, and Zhenting Wang. Continuous concepts removal in text-to-image diffusion models.arXiv preprint arXiv:2412.00580, 2024

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  16. [16]

    Selective amnesia: A continual learning approach to forgetting in deep generative models.Advances in Neural Information Processing Systems, 36:17170–17194, 2023

    Alvin Heng and Harold Soh. Selective amnesia: A continual learning approach to forgetting in deep generative models.Advances in Neural Information Processing Systems, 36:17170–17194, 2023. 10

    work page 2023

  17. [17]

    Prompt-to-Prompt Image Editing with Cross Attention Control

    Amir Hertz, Ron Mokady, Jay Tenenbaum, Kfir Aberman, Yael Pritch, and Daniel Cohen-Or. Prompt-to-prompt image editing with cross attention control.arXiv preprint arXiv:2208.01626, 2022

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  18. [18]

    Denoising diffusion probabilistic models.Advances in neural information processing systems, 33:6840–6851, 2020

    Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models.Advances in neural information processing systems, 33:6840–6851, 2020

    work page 2020

  19. [19]

    All but one: Surgical concept erasing with model preservation in text-to-image diffusion models

    Seunghoo Hong, Juhun Lee, and Simon S Woo. All but one: Surgical concept erasing with model preservation in text-to-image diffusion models. InProceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages 21143–21151, 2024

    work page 2024

  20. [20]

    Manifold interpolating optimal-transport flows for trajectory inference.Advances in neural information processing systems, 35:29705–29718, 2022

    Guillaume Huguet, Daniel Sumner Magruder, Alexander Tong, Oluwadamilola Fasina, Manik Kuchroo, Guy Wolf, and Smita Krishnaswamy. Manifold interpolating optimal-transport flows for trajectory inference.Advances in neural information processing systems, 35:29705–29718, 2022

    work page 2022

  21. [21]

    Co-occurring associated retained concepts in diffusion unlearning

    Miso Kim, Georu Lee, Yunji Kim, Hoki Kim, Jinseong Park, and Woojin Lee. Co-occurring associated retained concepts in diffusion unlearning. InThe Fourteenth International Conference on Learning Representations, 2026

    work page 2026

  22. [22]

    Boosting alignment for post-unlearning text-to-image generative models.Advances in Neural Information Processing Systems, 37:85131–85154, 2024

    Myeongseob Ko, Henry Li, Zhun Wang, Jonathan Patsenker, Jiachen T Wang, Qinbin Li, Ming Jin, Dawn Song, and Ruoxi Jia. Boosting alignment for post-unlearning text-to-image generative models.Advances in Neural Information Processing Systems, 37:85131–85154, 2024

    work page 2024

  23. [23]

    Ablating concepts in text-to-image diffusion models

    Nupur Kumari, Bingliang Zhang, Sheng-Yu Wang, Eli Shechtman, Richard Zhang, and Jun-Yan Zhu. Ablating concepts in text-to-image diffusion models. InProceedings of the IEEE/CVF International Conference on Computer Vision, pages 22691–22702, 2023

    work page 2023

  24. [24]

    Diffusion Models already have a Semantic Latent Space

    Mingi Kwon, Jaeseok Jeong, and Youngjung Uh. Diffusion models already have a semantic latent space.arXiv preprint arXiv:2210.10960, 2022

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  25. [25]

    Adaptive estimation of a quadratic functional by model selection.Annals of statistics, pages 1302–1338, 2000

    Beatrice Laurent and Pascal Massart. Adaptive estimation of a quadratic functional by model selection.Annals of statistics, pages 1302–1338, 2000

    work page 2000

  26. [26]

    American Mathemati- cal Soc., 2001

    Michel Ledoux.The concentration of measure phenomenon, volume 89. American Mathemati- cal Soc., 2001

    work page 2001

  27. [27]

    Localized concept erasure for text-to- image diffusion models using training-free gated low-rank adaptation

    Byung Hyun Lee, Sungjin Lim, and Se Young Chun. Localized concept erasure for text-to- image diffusion models using training-free gated low-rank adaptation. InProceedings of the Computer Vision and Pattern Recognition Conference, pages 18596–18606, 2025

    work page 2025

  28. [28]

    Localized concept erasure in text-to-image diffusion models via high-level representation misdirection.arXiv preprint arXiv:2602.19631, 2026

    Uichan Lee, Jeonghyeon Kim, and Sangheum Hwang. Localized concept erasure in text-to-image diffusion models via high-level representation misdirection.arXiv preprint arXiv:2602.19631, 2026

    work page arXiv 2026

  29. [29]

    Towards resilient safety-driven unlearning for diffusion models against downstream fine-tuning

    Boheng Li, Renjie Gu, Junjie Wang, Leyi Qi, Yiming Li, Run Wang, Zhan Qin, and Tianwei Zhang. Towards resilient safety-driven unlearning for diffusion models against downstream fine-tuning. InThe Thirty-ninth Annual Conference on Neural Information Processing Systems, 2025

    work page 2025

  30. [30]

    Mace: Mass concept erasure in diffusion models

    Shilin Lu, Zilan Wang, Leyang Li, Yanzhu Liu, and Adams Wai-Kin Kong. Mace: Mass concept erasure in diffusion models. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6430–6440, 2024

    work page 2024

  31. [31]

    One-dimensional adapter to rule them all: Concepts diffusion models and erasing applications

    Mengyao Lyu, Yuhong Yang, Haiwen Hong, Hui Chen, Xuan Jin, Yuan He, Hui Xue, Jungong Han, and Guiguang Ding. One-dimensional adapter to rule them all: Concepts diffusion models and erasing applications. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 7559–7568, 2024

    work page 2024

  32. [32]

    Finding the homology of submanifolds with high confidence from random samples.Discrete & Computational Geometry, 39(1):419– 441, 2008

    Partha Niyogi, Stephen Smale, and Shmuel Weinberger. Finding the homology of submanifolds with high confidence from random samples.Discrete & Computational Geometry, 39(1):419– 441, 2008. 11

    work page 2008

  33. [33]

    Diffusion models are minimax optimal distribution estimators

    Kazusato Oko, Shunta Akiyama, and Taiji Suzuki. Diffusion models are minimax optimal distribution estimators. InInternational Conference on Machine Learning, pages 26517–26582. PMLR, 2023

    work page 2023

  34. [34]

    Leveraging catastrophic forgetting to develop safe diffusion models against malicious finetuning

    Jiadong Pan, Hongcheng Gao, Zongyu Wu, Taihang Hu, Li Su, Qingming Huang, and Liang Li. Leveraging catastrophic forgetting to develop safe diffusion models against malicious finetuning. Advances in Neural Information Processing Systems, 37:115208–115232, 2024

    work page 2024

  35. [35]

    Understanding the latent space of diffusion models through the lens of riemannian geometry.Advances in Neural Information Processing Systems, 36:24129–24142, 2023

    Yong-Hyun Park, Mingi Kwon, Jaewoong Choi, Junghyo Jo, and Youngjung Uh. Understanding the latent space of diffusion models through the lens of riemannian geometry.Advances in Neural Information Processing Systems, 36:24129–24142, 2023

    work page 2023

  36. [36]

    Direct unlearning optimization for robust and safe text-to-image models.Advances in Neural Information Processing Systems, 37:80244–80267, 2024

    Yong-Hyun Park, Sangdoo Yun, Jin-Hwa Kim, Junho Kim, Geonhui Jang, Yonghyun Jeong, Junghyo Jo, and Gayoung Lee. Direct unlearning optimization for robust and safe text-to-image models.Advances in Neural Information Processing Systems, 37:80244–80267, 2024

    work page 2024

  37. [37]

    Score-based generative models detect manifolds.Advances in Neural Information Processing Systems, 35:35852–35865, 2022

    Jakiw Pidstrigach. Score-based generative models detect manifolds.Advances in Neural Information Processing Systems, 35:35852–35865, 2022

    work page 2022

  38. [38]

    The intrinsic dimension of images and its impact on learning

    Phillip Pope, Chen Zhu, Ahmed Abdelkader, Micah Goldblum, and Tom Goldstein. The intrinsic dimension of images and its impact on learning. InInternational Conference on Learning Representations, 2021

    work page 2021

  39. [39]

    High- resolution image synthesis with latent diffusion models

    Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. High- resolution image synthesis with latent diffusion models. InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 10684–10695, 2022

    work page 2022

  40. [40]

    Silhouettes: a graphical aid to the interpretation and validation of cluster analysis.Journal of computational and applied mathematics, 20:53–65, 1987

    Peter J Rousseeuw. Silhouettes: a graphical aid to the interpretation and validation of cluster analysis.Journal of computational and applied mathematics, 20:53–65, 1987

    work page 1987

  41. [41]

    Efficient fine-tuning and concept suppression for pruned diffusion models

    Reza Shirkavand, Peiran Yu, Shangqian Gao, Gowthami Somepalli, Tom Goldstein, and Heng Huang. Efficient fine-tuning and concept suppression for pruned diffusion models. InPro- ceedings of the Computer Vision and Pattern Recognition Conference, pages 18619–18629, 2025

    work page 2025

  42. [42]

    Score-based generative modeling through stochastic differential equations

    Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score-based generative modeling through stochastic differential equations. In International Conference on Learning Representations, 2021

    work page 2021

  43. [43]

    Diffusion models encode the intrinsic dimension of data manifolds

    Jan Pawel Stanczuk, Georgios Batzolis, Teo Deveney, and Carola-Bibiane Schönlieb. Diffusion models encode the intrinsic dimension of data manifolds. InForty-first International Conference on Machine Learning, 2024

    work page 2024

  44. [44]

    Cambridge University Press, 2004

    J Michael Steele.The Cauchy-Schwarz master class: an introduction to the art of mathematical inequalities. Cambridge University Press, 2004

    work page 2004

  45. [45]

    What the daam: Interpreting stable diffusion using cross attention

    Raphael Tang, Linqing Liu, Akshat Pandey, Zhiying Jiang, Gefei Yang, Karun Kumar, Pontus Stenetorp, Jimmy Lin, and Ferhan Türe. What the daam: Interpreting stable diffusion using cross attention. InProceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), pages 5644–5659, 2023

    work page 2023

  46. [46]

    Fine-grained erasure in text-to-image diffusion-based foundation models

    Kartik Thakral, Tamar Glaser, Tal Hassner, Mayank Vatsa, and Richa Singh. Fine-grained erasure in text-to-image diffusion-based foundation models. InProceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9121–9130, 2025

    work page 2025

  47. [47]

    Mass concept erasure in diffusion models with concept hierarchy.arXiv preprint arXiv:2601.03305, 2026

    Jiahang Tu, Ye Li, Yiming Wu, Hanbin Zhao, Chao Zhang, and Hui Qian. Mass concept erasure in diffusion models with concept hierarchy.arXiv preprint arXiv:2601.03305, 2026

    work page arXiv 2026

  48. [48]

    Cambridge university press, 2018

    Roman Vershynin.High-dimensional probability: An introduction with applications in data science, volume 47. Cambridge university press, 2018

    work page 2018

  49. [49]

    Erasing undesirable influence in diffusion models

    Jing Wu, Trung Le, Munawar Hayat, and Mehrtash Harandi. Erasing undesirable influence in diffusion models. InProceedings of the Computer Vision and Pattern Recognition Conference, pages 28263–28273, 2025. 12

    work page 2025

  50. [50]

    Unlearning concepts in diffusion model via concept domain correction and concept preserving gradient

    Yongliang Wu, Shiji Zhou, Mingzhuo Yang, Lianzhe Wang, Heng Chang, Wenbo Zhu, Xinting Hu, Xiao Zhou, and Xu Yang. Unlearning concepts in diffusion model via concept domain correction and concept preserving gradient. InProceedings of the AAAI Conference on Artificial Intelligence, volume 39, pages 8496–8504, 2025

    work page 2025

  51. [51]

    Semantic surgery: Zero-shot concept erasure in diffusion models.arXiv preprint arXiv:2510.22851, 2025

    Lexiang Xiong, Chengyu Liu, Jingwen Ye, Yan Liu, and Yuecong Xu. Semantic surgery: Zero-shot concept erasure in diffusion models.arXiv preprint arXiv:2510.22851, 2025

    work page arXiv 2025

  52. [52]

    Forget-me- not: Learning to forget in text-to-image diffusion models

    Gong Zhang, Kai Wang, Xingqian Xu, Zhangyang Wang, and Humphrey Shi. Forget-me- not: Learning to forget in text-to-image diffusion models. InProceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 1755–1764, 2024

    work page 2024

  53. [53]

    Concept replacer: Replacing sensitive concepts in diffusion models via precision localization

    Lingyun Zhang, Yu Xie, Yanwei Fu, and Ping Chen. Concept replacer: Replacing sensitive concepts in diffusion models via precision localization. InProceedings of the Computer Vision and Pattern Recognition Conference, pages 8172–8181, 2025

    work page 2025

  54. [54]

    grumpy” as an example, which is used in ConAbl, the first anchor-based diffusion unlearning. We collect these manually chosen anchors (including “-

    Yimeng Zhang, Xin Chen, Jinghan Jia, Yihua Zhang, Chongyu Fan, Jiancheng Liu, Mingyi Hong, Ke Ding, and Sijia Liu. Defensive unlearning with adversarial training for robust concept erasure in diffusion models.Advances in neural information processing systems, 37:36748– 36776, 2024. 13 A Appendix of Theoretical Analysis This appendix provides the formal ju...

    work page arXiv 2024

  55. [55]

    He always dreamed of driving a Porsche down the Autobahn

    work page

  56. [56]

    She parked her brand new Porsche right in front of the restaurant

    work page

  57. [57]

    The vintage Porsche fetched a record price at the auction

    work page

  58. [58]

    You can tell it’s a Porsche just by the sound of its flat-six engine

    work page

  59. [59]

    They rented a sleek black Porsche for their weekend getaway to Napa

    work page

  60. [60]

    Maintenance on a classic Porsche can be quite expensive

    work page

  61. [61]

    He spent his entire bonus on a customized Porsche 911

    work page

  62. [62]

    Mickey Mouse

    The racing team unveiled their latest Porsche for the upcoming Le Mans. 26 Table 10: Ablation study (FID) on “Mickey Mouse” and “Nude”. Method FID↓ Orig *∆ ∗(%) +∆ +(%) Target Concept: Mickey Mouse ESD [13] 153.06 156.54 2.27↑148.75 2.82↓tuneSD-l [41] 185.96 188.31 1.26↑183.43 1.36↓ResAlign [29] 156.25 158.16 1.22↑157.27 0.65↑CCRT [15] 152.94 157.89 3.24↑...

    work page

  63. [63]

    Whenever a bright yellow Porsche drives by, heads inevitably turn

    work page

  64. [64]

    He always dreamed of driving a [MASK] down the Autobahn

    She carefully washed and waxed her father’s old Porsche on Sunday afternoon. For each sentence y(i) in this set S, we mask the concept word “Porsche” and predict the top M tokens with the highest probabilities from the LLM. The example of the first sentence is shown in the conversation context below. User: Predict the top 10 tokens for the masked word in ...

    work page

  65. [65]

    Porsche’ itself is also involved, thereby violatingR1. Such violation will be more pronounced in the case of descriptive target concepts,e.g., “grumpy

    Rolex, 7. automobile, 8. motorcycle, 9. vehicle, 10. truck ... ... Next, we aggregate the predicted tokens across all sentences and select the top K= 10 most frequently predicted tokens as the candidate set C0. In this case, the C0 for the Porsche concept is {car, Porsche, vehicle, Ferrari, BMW, motorcycle, Audi, Mercedes, truck, convertible}. It is obvio...

    work page