Forget Many, Forget Right: Scalable and Precise Concept Unlearning in Diffusion Models
Authors: Kaiyuan Deng
Gen Li
Yang Xiao
Bo Hui
Xiaolong Ma
Venue: ICLR 2026 Poster (2026)
Keywords: machine unlearning
large-scale unlearning
diffusion model
Primary area: generative models

Abstract: While multi-concept unlearning has shown progress, extending to large-scale scenarios remains difficult, as existing methods face three persistent challenges:  **(i)** they often introduce conflicting weight updates, making some targets difficult to unlearn or causing degradation of generative capability;  **(ii)** they lack precise mechanisms to keep unlearning strictly confined to target concepts, resulting in collateral damage on similar content;  **(iii)** many approaches rely on additional data or auxiliary modules, causing scalability and efficiency bottlenecks as the number of concepts grows.  To simultaneously address these challenges, we propose **Scalable-Precise Concept Unlearning (ScaPre)**, a unified and lightweight framework tailored for scalable and precise large-scale unlearning. ScaPre introduces a *conflict-aware stable design*, which integrates the spectral trace regularizer and geometry alignment to stabilize the optimization space, suppress conflicting updates, and preserve the pretrained global structure. Furthermore, the *Informax Decoupler* identifies concept-relevant parameters and adaptively reweights updates, ensuring that unlearning is confined to the target subspace without collateral damage. ScaPre yields an efficient closed-form solution, requiring no additional data or auxiliary sub-models, while maintaining both scalability and precision. Comprehensive experiments across large-scale objects, styles, and explicit content benchmarks demonstrate that ScaPre effectively removes target concepts while maintaining generation quality. It can forget up to **×5** more concepts than the best baseline within the limits of acceptable generative quality, and outperforms existing multi-concept approaches in precision and efficiency, achieving a new state of the art for large-scale unlearning.

Published as a conference paper at ICLR 2026
FORGET MANY, FORGET RIGHT: SCALABLE AND PRE- CISE CONCEPT UNLEARNING IN DIFFUSION MODELS
Kaiyuan Deng', Gen Li', Yang Xiao', Bo Hui', Xiaolong Ma!
The University of Arizona, Clemson University, 'hhe University of Tulsa
kaiyuan0415earizomm
Target Concept to Unlearn: Church
Targer: Non-farget: Pug
Fall to untearn
MACE
RECE
Quality
Damage
ScaPre (Ours)
Master Total Unlamed Gancapts
50
Figure As the total number of unlearned concepts increases, existing methods either fail to effectively forget the target concepts suffer from severe and noticeable degradation in overall image generation quality. In contrast, our proposed method ScaPre consistently maintains both stable unlearning performance and high generative quality (left). Moreover, ScaPre does compromise similar non-target concepts, thereby clearly demonstrating its precise unlearning capability (right).
ABSTRACT
Text-to-image diffusion models have achieved remarkable progress in generating photorealistic content, but their widespread use raises concerns over copyright and misuse. To mitigate these risks, recent work explores machine unlearning, While multi-concept unlearning has shown progress, extending to large-scale scenarios remains difficult, as existing methods face three persistent challenges: (i) they often introduce conflicting weight updates, making some targets difficult to unlearn causing degradation of generative capability; (ii) they lack precise mechanisms to keep unlearning strictly confined target concepts, resulting in collateral dam- age on similar content: (iii) many approaches rely on additional data or auxiliary modules, causing scalability and efficiency bottlenecks the number of concepts grows. To simultancously address these challenges, we propose Pralable-Precite Concept Unlearning (ScaPre), unified and lightweight framework tailored for scalable and precise large-scale unlearning. ScaPre introduces conflict-awan stable design, which integrates the spectral trace regularizer and geometry align- ment to stabilize the optimization space, suppress conflicting updates, and preserve the pretrained global structure. Furthermore, the Informax Decoupler identifies concept-relevant parameters and adaptively reweight updates, ensuring that unlearn- ing is confined to the target subspace without collateral damage. ScaPre yields an efficient closed-form solution, requiring additional data or auxiliary sub-models, while maintaining both scalability and precision. Comprehensive experiments across large-scale objects, styles, and explicit content benchmarks demonstrate that ScaPre effectively removes target concepts while maintaining generation quality. It forget up x5 more concepts than the best baseline within the limits of ceptable generative quality, and outperforms existing multi-concept approaches in precision and efficiency, achieving new state of the for large- scale unlearning. Code is available at https: : //gittttuuuu com
5/scaprsce

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INTRODUCTION
-ext-to-image (T2I) generative models (Rombach et al. 2022 Ma et al.
2024: Podell et al. 2023
Saharia et al. 2022 Nichol et al. 2021 Ding et al. 2022 Zhou al. 2022 have achieved remarkable progress in recent years, enabling users to synthesize high-quality and photorealistic images. Repre- sentative models, such as Stable Diffusion (Rombach et al. (022), DALL-E (Ramesh et al.) 2022).
and Imagen [Saharia et al. 2022), have been widely adopted across diverse domains, showcasing impressive capabilities in content generation. Despite these advances, the large-scale deployment of
T2I models has raised pressing concerns regarding copyright infringement, harmful or biased image
synthesis, and the potential misuse of sensitive visual (Kazerouni et al.) 2022 Xing et al. [024 Jang
et al. 2022, Wang et al. 2024 Nguyen et al. 2022 Weidinger et al. 2021 Brundage et al. 2018
Tolosana et al.] 2020 (Solaiman & Dennison (021). ) To address these challenges, recent research has
focused on the emerging paradigm of machine unlearning (Bourtoule et al.
2021 Guo al. 2019
Graves et al. 2021 Vatter et al. 2023 Xu et al. 2024 Marino et al. 2025 Zhang et al. 2023 Liu
al. 2024] Tu et al.) 2025 Feng et al. 2025), whose objective is to selectively remove the influence
of specific data from a trained model while retaining its ability to generate all other content.
Existing works on single-concepp unlearning have demonstrated the ability to suppress an individual object. style, or identity in diffusion models (Jia et al., [023] Kumari et al., 2023 Chavhan et al.
2024 Gandikota et al. 2023 Zhang et al. 2024a [Schramowski et al. [2023] Fan al.) [023] HHeng
& Soh (202)). However, these approaches remain inherently limited to single-concept settings and
often suffer from degraded performance when extended multi-concept unlearning. Beyond single- concept settings, several methods have been proposed for multi-concept unlearning (The number of concepts usually 10-20). Recent works can be broadly grouped into two directions. One leverages finetuming, including LoRA-based refinements, adapter designs, and mask- strategies (Lu et al. 2024; Lyu et al.) 2024 [i et al. 2025a). The other relies on closed-form updates, applying direct edits to cross-attention matrices. (Gandikota et al. 2024 Gong et al., 2024).
When facing large-scale concept unlearning, existing methods universally encounter several critical challenges: (i) they often encounter conflicting weight updates, where updates from different concepts interfere with each other. Such conflicts can make some target concepts difficult to erase or lead to excessive changes in unrelated parameters, causing degradation of generative performance. (ii) they lack explicit mechanisms to keep the unlearning strictly focused on the target concepts. As a result, unlearning impacts unintentionally affect background similar concepts, reducing the precision and reliability of unlearning. (iit) most approaches (Luu et al.) 2024 Li et al. 2025a Lyu et al. (0224) rely on extra data or additional sub-models and adapters, which significantly increase computational costs as the number of target concepts grows. Despite recent progress, none of the existing approaches has been able fully overcome these challenges (as shown in Figure and Fi
To completely overcome these challenges, we propose Scalable-Precise Concept Unlearn- ing (ScaPre), a unified and lightweight framework for scalable and precise large-scale concept unlcarning. First, to address the issue of conflicting weight updates during large-scale unlearning, ScaPre introduces a conflict-aware stable design that combines a spectral trace regularizer with geometry alignment, effectively regulating inter-concept interactions and preventing conflicting or excessive updates. Second, to address the challenge of imprecise unlearning, ScaPre introduces an Informax Decoupler that measures the information coupling between parameters and target concepts, and adaptively scales their updates, ensuring unlearing is concentrated on the targets while safeguard- ing background and similar concepts. Unlike prior approaches (Lu et al. 2024 Li et al.] 2025a Lyu et al. (024)) that rely on extra data or auxiliary sub-models, ScaPre employs a single flosed-form solution that directly updates weights to simultaneously unlearn an arbitrary number of concepts, entirely training-free. Through this unified and lightweight design, ScaPre achieves scalable, stable, and precise unlearning, and comprehensive experiments demonstrate its strong unlearning capability without sacrificing generation quality. Our contributions are summarized as follows:
Scalable Unlearning, A conflict-aware design with spectral trace regularization and geometry alignment ensures stability when unlearning many concepts.
High Precision. The Informax Decoupler captures information relevance to target concepts and adaptively reweights parameter updates, confining unlearning to the intended subspace.
Lightweight Design. Requires no extra data or sub-models, enabling efficient unlearning with low computational overhead, completing the unlearning of 50 concepts in only 120 seconds.
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Excellent Performance. ScaPre achieves strong unlearning across benchmarks, effectively removing target concepts while maintaining generation quality. It can unlear up to x5 more concepts than the best baseline within the limits of acceptable generative quality.
RELATED WORK
Machine unlearning was proposed to enable models selectively remove information, motivated by concerns of data privacy, copyright protection, and the moderation of harmful or biased content. With the rapid deployment large-scale generative models, these issues have become increasingly critical. Existing approaches can be divided into: single-concept unlearning and multi-concept unlearning.
2.1 SINGLE-CONCEPY UNLEARNING
Early approaches machine unlearning in diffusion models were originally designed for single- concept forgetting and can be broadly categorized into three types. Fine-tuning methods, such as FMN (haag et al. 2024a). SA (Heng & Soh 2023), SalUn (Fan al. 2023). and AC (Kumari et al. 2023 update model weights weights-typically through negative guidance or cross-attention restyling to suppress the target distribution. Weight-editing methods, including TIME (Orgad al. 2023 and SPEED (Li et al., 20256), directly operate on cross-attention or projection parameters to erase target concepts while retaining unrelated knowledge. Pruning-based methods focus on efficiency; ConceptPrune (Chavhan et al. 2024) removes skilled neurons, while MS (Jia et al. 2023) leverages weight pruning to narrow the gap between approximate and exact unlearning. SEMU (Sendera et al.. performs efficient single-concep unlearning by updating only a targeted low-rank subspace.
2025)
2.2
MULTI-CONCEPT UNLEARNING
Beyond single-concept unlearning, recent studies extend to multi-concept unlearning. MACE Lu al. 2024) scales hundreds of concepts through multi-LoRA fine-tuning, while SPM (Lyu et al. 2024) employs composable adapters with latent anchoring to mitigate concept erosion. Sculpting Memory (Li et al.] 2025a) leverages dynamic masks and concept-aware optimization for stable multi-concept removal and ESD (Gandikota et al. 2023) fine-tunes diffusion model weights with negative guidance. UCE (Gandikota et al. (024) offers a unified closed-form framework for multi- concept forgetting, and RECE (Gong et al. 2024) achieves efficient closed- editing with iterative embedding derivation. These approaches mark progress toward scalable and unified multi-concept editing, but still insufficient for large-scale forgetting, especially when erasing concrete objects.
PRELIMINARY
Most existing unlearning methods are training-based, where the model parameters 0 are optimized to forget target concepts while preserving unrelated ones. Let E and P denote the sets of target and non-target concepts, respectively. fe(2;, c) is the output of the diffusion model at time step t conditioned on prompt c, Saam is the original model, and yerase (x+, c; ( is null reference output for the i-th target concept. The training objective typically combines an crasure term, a preservation term, and stability regularization:
[
Ex, fll ( d())) Derase(Ee, of
min
E. El. - foaua gf A2110 Botall2
+ A1
Recent works instead formulate unlearning as a closed-form editing problem, which avoids costly gradient-based training and offers higher efficiency. Specifically, given the original key/value pro- jection matrix Ward in cross-attention layers, the goal is to construct target concepts while minimally disturbing others. Let e be the embedding of the i-th target concept with substitute of, and ej denote embeddings of preserved concepts. The optimization requires that
matrix W that redirects
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Informax Decoupler
Conflict-aware Stable Design
MI, max, MI,
Spectral Regularizer
(0 RYW")
Cross Attention (K V)
Canoupe
Close-form Solution
Geometry Allgnment
Wo W W L
1,0W) ar(VV' diagla ++WVV C
Training-frae Weight Edit
W
Bures distance
Figure Overview of ScaPre. Given target concepts Cg, cross-attention representations are first regularized by the spectral trace regularizer Lt, while the informax decoupler a confines updates to concept-relevant subspaces. Within this stabilized space, closed-form optimization yields W* realizing the forgetting of Ce (red arrows). Geometry alignment Lg then applies a proximal refinement toward the pretrained reference Wo, preserving global structure (green arrows). This staged pipeline enables scalable, precise unlearning while maintaining non-target generation quality.
target embeddings are mapped substitute directions, while non-target embeddings remain close to their original outputs. Frobenius regularization further anchors W Wol::
min Σ IWa Wotac; A1
Σ CP
I[We Watdcy >2ll Worll
This quadratic objective is convex and admits a closed-form solution obtained by solving the corre- sponding normal equations (Orgad et al.] 2023). Such formulation significantly improves efficiency and reproducibility, since the update can be obtained in a single step without iterative fine-tuning.
Owing to these advantages, our framework also builds upon the closed-form paradigm.
4 METHOD
In this section, we present Scalable-Precise Concept Unlearning (ScaPre), unified framework that achieves both scalability and precision for large-scale unlearning text-to-image diffusion models (Figure 2). ScaPre addresses two key challenges: instability under large-scale unlearning and insufficient precision in separating target from non-target concepts. Our approach consists two complementary components. First, introduce conflict-aware stable design (Sec. 4.1. which leverages spectral trace regularizer and geometry alignment to construct a stable optimization space the number of concepts grows. Second, we develop an informax decoupler (Sec. 4.2) which selectively isolates concept-relevant parameters and restricts updates to the corresponding subspace, preventing collateral damage to unrelated knowledge. Finally, these components are combined into a unified optimization objective (Sec. 4.3), yielding a principled solution for scalable and precise unlearning while preserving the generation quality of non-target content.
4.1 CONFLICT-AWARE STABLE DESIGN
We propose conflict-aware stable design with two key components: a spectral trace regularizer and geometry alignment. This stage establishes stable optimization space and maintains overall model stability, preventing instability degradation during parameter updates.
Spectral Trace Regularizer. When unlearning many concepts simultaneously. conflicting updates can arise and distort the optimization landscape. To mitigate these conflicts and dynamically shape the optimization space, we introduce a Spectral Truce Regularizer:
(W) = tr (W + R.)
where W R xd; is the key value projection matrix of the cross- cross-attention module and tr(.) denotes the trace. Here, AI is a standard regularization term commonly used in closed-form solutions (Gandikota al. 2024 Gong et al. 2024) ensure numerical stability.
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S captures the dynamic structure of the current concept set by aggregating the second-orde statistics of the contextual features of all target concepts:
Ta
S =
CR,
(4)
where is the number of target concepts, Ck.1 R is the contextual feature vector of the t-th token for concept k. and Tj is the number of tokens associated with that concept. The span of these features (cR,e) identifies the directions most prone to conflicts and noise during large-scale unlearning. By penalizing directions corresponding to large eigenvalues of S, the model adaptively suppresses unstable updates in problematic subspaces.
R is designed to regulate interactions within the target concept subspace. We first construct a matrix of concept embeddings CF [e1, (2,,c,...., Cm.] E RRd and perform singular value decomposi- tion (SVD) Cg = U diag(ar) V where each singular value represents the energy along an orthogonal direction. Large o; indicate directions where multiple concepts strongly overlap and interact. To handle this, we apply smooth gating function that softly decays the large singular values while leaving smaller ones nearly intact, and reconstruct the matrix as R = U diag(ā) UT where ã; (1 (a)) og, This adaptive procedure suppresses high-conflict directions caused by overlapping concepts while preserving low-conflict directions associated with independent concepts.
Geometry Alignment. To prevent unlearning from degrading unrelated content, we introduce geometry alignment term to stabilize the optimization globally. Instead of penalizing raw weight differences with an & norm like current methods, we treat each row of the tross-attention matrix W E Rdoa Xdia as a covariance factor, where din and dout are the input and output dimensions. The pretrained reference is denoted as Wo with the same shape. This defines covariance matrices WWT and Wo W. which are aligned using the Bures distance Buress 1969
Takatsu 2008):
(W) = tr (WWT) + tr (WoW,)) 2 tr ((WWT) (WWT)1/2) 1/21 (5)
Compared to E norm, the Bures distance alignment matches the covariance structures of W and Wo, rather than only penalizing element-wise weight differences. By preserving these higher-order feature correlations, maintains the pretrained global structure, keeping unrelated features stable. Combined with the trace regularizer, geometry alignment provides complementary global safeguard against destructive degradation during large-scale unlearning.
4.2 INFORMAX DECOUPLER
The scalable design Sec. 4.1 establishes a safe and stable optimization space. Building on this foundation, we introduce decoupler that identifies parameters most relevant to the target concepts and confines updates strictly within the corresponding subspace.
When unlearning multiple concepts, different weights contribute unevenly: some are strongly tied to target concepts, while others mainly support unrelated background. Treating all weights equally may thus cause either incomplete unlearning or unnecessary collateral damage. To address this, we introduce the Informax Decoupler, which leverages mutual information (MI) to quantify how strongly each weight is coupled with the target concepts. For each channel i, define discretized activation state 2 = (s) > T.} E {0, 1}. where a, (s) = Wi.s is the activation of channel i on input feature and is an adaptive threshold. We further denote by y E {0, 1} the input label, with y 1 for target-concept inputs and y = 0 for neutral inputs. From the resulting activation-labe pairs {(z, y)}. estimate the empirical joint distribution ps(2, y) nay/ K, where Nay is the number of pairs with activation state z and label y. and K is the total sample size. The marginal distributions are given by pz)) E,, p=(2, w) and pi(y) (i(zz)) v). The MI of channel i is then defined as:
() log Pc(2,) p:(=)
MI- Σ
Σ 2E(0, 1)
(6)
For each channel W.. MI quantifies how informative its activations are about the input type, with larger MI, indicating that the channel is more predictive of whether the input contains target concepts. For multiple target concepts {cx { we compute per-concept score MT.kk) (using positives from
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(x) and aggregate by the maximum over concepts: MI; max; MI Finally, we obtain the Informax Decoupler:
MI,
01 O'duur a,
E [0, 1].
max, MI,
It maximizes information about the distinction between target and non-target inputs, and thus decoupling concept-relevant parameters from unrelated ones.
4.3 SCALABLE- PRECISE PERACISS CONCEPT UNLEARNING
Having established stable optimization space and mechanism to selectively decouple concept- relevant parameters, we now bring these components together into a unified framework. Let = XI + S + R and B diag(ex). The overall objective of ScaPre is formulated
min Lr (W(WWT) + B LW) + tr (WTTBW) Lr CWV
(8)
Here, Ce denotes the stacked embedding matrix of concepts erase, and V specifies their replace- ment targets (often set to zero for complete forgetting). The coefficient / modulates the geometry alignment, balancing global stability with flexibility for targeted unlearning.
To optimize equation 8
we first ignore the geometry alignment term (Lg(W)) and solve the quadratic yields the Sylvester
part analytically. Taking the derivative with respect to W and setting equation:
BW + WA = V*CE
(9)
This equation has unique solution and can be solved efficiently with standard Sylvester solvers. In vectorized form, the solution can be written as:
vec(W*) (Td. & B + A 2 Tdoma) vec " CV)
(10)
where vec(.) denotes the column- wise vectorization operator that stacks all columns of matrix into a single vector; once vec(W') is obtained, W' can be recovered by reshaping it back to its original dout X di, form. A complete derivation is provided in Appendix B.I
The geometry alignment term (Cg(W)) however, involves matrix square roots nested inside co- variance operators, which makes the overall objective longer purely quadratic and therefore incompatible with direct closed-form optimization. As result, it must be handled separately, We treat W* as intermediate solution and incorporate geometry alignment via proximal refine- ment. The refinement proceeds in two conceptual steps: (1) In the covariance space, we replace E* = W with a new covariance E obtained by moving partway along the Bures geodesic toward the pretrained reference Σg WoW, Intuitively, this step softly aligns the overall geometry of W with that of the pretrained model. (2) We then map back to the weight space by finding the matrix W whose covariance equals Σ and that lies closest to W This is done through orthogonal Procrustes adjustment, i.e., an orthogonal rotation that preserves the main unlearning direction while enforcing global stability. A full derivation of the exact proximal refinement provided in Appendix B.2
EXPERIMENT
this section, we describe the experimental setting (Sec. 5.1p. evaluate large-scale (Sec. 5.2p. precise
(Sec.15.3 and artistic style unlearning (Sec. 5.4). and analyze efficiency (Sec. 5.5) Additional results including adversarial robustness and explicit content are in Appendix C.3 and a detailed analysis of generative quality in Appendix C.4 and Figure [2] and ablation studies in Appendix
5.1 EXPERIMENTAL SETTINGS
All experiments were conducted using Stable Diffusion v1.4 & v1.5 (Rombach et al. 2022). Large- scale unlearning is evaluated on the Imagenette benchmark (Howard et al.) 2019), ten ten-class subset of ImageNet, and on our custom dataset ImageNet-DiversiSk which includes 50 diverse object categories sampled from ImageNet evaluate scalability and diversity in unlearning. For precise

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Table Overall comparison of different unlearning methods Imagenette, reporting average unlearning accuracy (L). CLIP score (CLIP coca) (T), and unified metric UQ (t).
Method
Metric
SD v1.5
FMN
SPM
ESD
MACE
UCE
RECE
SP
ScaPre (Ours)
Avg Acc (L)
89.9
71.9
47.4
38.7
78.5
8.5
4.9
9.6
0.8
CLIP coom (1)
31.43
30.62
30.81
30.14
31.02
29.45
29.27
29.25
30.43
(1)
37.35
49.89
47.84
35.07
37.23
32.60
31.78
64.09
Table 2: We report evaluation across multiple metrics including CLIP CL.IP CLIP& (difference), and FID. ScaPre consistently outperforms baselines.
0.08
0.00
0.04
Method
CLIP (f)
FMN
SPM
MACE
SP
UCE
RECE
ESD
ScaPre
SDvi.5
20
Peak Memory Usage
ESD
27.24
27.94
0.70
17.22
MACE
27.34
30,06
2.72
13.89
UCE
26.95
28.21
1.26
43.72
FMN
SPM
ESD
MACE
UCE
RECE
SP
ScaPre
RECE
25.94
26.86
0.92
49.32
SP
29.35
26.75
-0.60
19.76
Figure 3: Comparison of efficiency across methods,
ScaPre (Ours)
26.51
29.95
3.44
14.37
reporting GPU-hours and peak memory usage.
unlearning, we construct ImageNet-Confuseee consisting of five groups visually similar concepts evaluate fine-grained disentangle-
from ImageNet that can be reliably generated, enabling unlearning is conducted on the I2P ment and robustness to concept confusion. Explicit content dataset (Schramowski al., 2023). which contains a variety of inappropriate image prompts. For artistic style unlearning, we select 50 artists whose styles can be reliably reproduced by Stable Diffu- sion. We use the widely recognized MS COCO-30K (Lin et al. (2014) to assess the model's s generative performance after unlearning. All experiments are performed on an NVIDIA RTX A6000 GPU. For reproducibiiity, all results of the compared methods are derived from their official open-souree implementations, as listed in Appendix D
5.2
UNLEARNING SCALE
We begin with unlearning experiments on the widely adopted Imagenette (Howard al.. 2019 benchmark. For each target class, we measure unlearn accuracy (J) using pretrained ResNet-50 classifier, where lower values indicate stronger removal of the forgotten concept. To assess the preservation of generation quality, report the CLIP score (f), measured on the MS COCO dataset, which quantifies the alignment between generated images and text prompts. In addition, we introduce unified metric UQ (t), short for Unlearn Quality, which jointly reflects unlearning effectiveness and generation quality. It harmonically integrates normalized unlearning score Á and normalized quality score Ć. Here, À o((uA A)/o and Ö a((C' μc)/ac), where a(-) is the sigmoid function, μĄ and σ are the mean and standard deviation of unlearning accuracy across all methods, and μi and are those of CLIP score. UQ is then computed as UQ = 100 24C A-Ø Larger UQ values indicate stronger unlearning with better quality retention. As summarized in Table I ScaPre consistently achieves the lowest forgetting accuracy while maintaining competitive CLIP scores. The full set experimental results, including results for each individual class, is provided in the Appendix Table We then evaluate ScaPre and wide range of baselines on the extended benchmark (emageNetDiivrsiin performance than all competing methods. Figure5) further illustrates the scalability of our approach when the number target concepts increases. For UCE and RECE, the curves are truncated because both methods suffer severe generative collapse under large-scale unlearning, making results in that region uninformative. For the other baselines, unlearning performance consistently deteriorates as more concepts removed, leading unstable incomplete unlearning. These findings demonstrate that ScaPre is not only more effective but also substantially more reliable than existing baselines. Complete results are provided in Appendix C. Table 6
shown in Table ScaPre achieves substantially better

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Table We demonstrate the overall results the ImageNet-Diveed DiversiiO, including Avg Acc, CLIP Score and UQ ScaPre achieves significantly better performance compared to all baselines.
100
60
Accuracy
80
3.0
Method
Arg Acc
CLIP coes
UQ (f)
v1.5
87.7
31.43
30
FMN
79.8
30.12
36.52
SPM
76.5
30.45
38.67
ESD
19.6
28.21
56.35
Number of Concepts
30 Number of Concepts
MACE
78.9
31.23
38.11
UCE
22.23
25.16
SPM
MACE
REGE
ScaPre (Ouns)
RECE
0.0
21.78
22.90
Figure We compare how unlearning accuracy (L) UQ
SP
22.5
28.83
51.28
(1) change as the number of concepts increases across meth-
ScaPre (Ours)
3.9
29.41
65,30
ods. ScaPre consistently achieves the best performance.
SD v1.5
ESD
SP
MACE
SPM
RECE
ScaPre
golf
parachute
gas pump
garbage
Figure Visual comparison unlearning performance across different methods simultaneous unlearning of 10 classes from the Imagenette benchmark.
5.3 PRECISE UNLEARNING
To rigorously assess the capacity for precise unlearning in scalable scenarios, curate ImageNet- Confuse5, a benchmark that contains five groups of visually similar ImageNet concepts. Within each group, concepts designated unlearning targets, while the remaining three visually similar but non-target concepts that should be preserved. This design makes the task especially challenging, it requires disentangling highly confusable concepts rather than relying coarse category differences. Table 4 presents presentss the results across methods. The evaluation considers unlearn
accuracy (L) for residual accuracy on targets, preserve accuracy (f) for retention on similar but non-target concepts, and overall accuracy (t) as their harmonic mean: 21-0 P)+ with and P denoting unlearn and preserve Acc, respectively. Compared to prior methods, which either exhibit poor unlearning performance or undesirably suppress related categories, ScaPre achieves the best overall accuracy and UQ, demonstrating superior disentanglement while maintaining high generative fidelity. For complete experimental results, please refer the Appendix Table
5.4 ARTISTIC-STVE UNLFARNING
For artistic style unlearning, we select fifty representative artists whose styles can be faithfully repro- duced by Stable Diffusion, providing reliable benchmark for evaluation. We first measureCLIP arts which reflects the residual stylistic similarity after unlearning and directly measures forgetting effec- tiveness. To assess generation quality, jointly consider CLIP coco and FID MS-COCO. Finally, we report CLIP, defined as the difference between CLIP L.ePo and CLIP arts as a holistic indicator of the balance between forgetting and quality preservation. As shown in Table 2 ScaPre establishes the
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Table 4: Overall evaluation summary for ImageNNet-Contuee.. Unleam Acc (J) quantifies residual accuracy target concepts (described in Table 7). Preserve Ace (f) measures retention on visually similar but non-target concepts, and Overall Acc (1) reflects the joint ability to both unlearn and preserve. CLIPcoco and UQ further evaluate generation quality and unlearning precision.
Method
Metric
SD v1.5
FMN
SPM
ESD
MACE
UCF
RECE
SP
ScaPre (Ours)
Unlearn Acc (L)
83.9
76.5
77.5
55.6
76.4
2.9
3.1
55.0
5.8
Preserve Acc (f)
86.6
78.9
79.7
57.7
78.6
5.6
5.5
57.1
76.3
Overall Ace (t)
27.2
36.2
35.1
50.2
36.3
10.6
10.4
50.3
84.3
CLIP coco (f)
31.43
30.45
30.60
29.78
30.98
27.23
29.84
30.15
UQ (1)
38.27
40.29
40.28
46.69
42.13
31.88
20.41
47.47
65.49
SD v1.5
FMN
ESD
SP
MACE
SPM
RECE
UCE
ScaPre
golden retriever
Jabrador retriever
pug
Chesapeake
Bay retrievor
Figure Visual comparison of unlearning performance across different methods on the Imagenette benehmark
most favorable trade-off, delivering both more effective unlearning and superior generation quality over prior approaches, while maintaining robustness across diverse styles.
5.5 EFFICIENCY OF SCAPRE
A key strength of ScaPre lies in its efficiency, which is particularly critical when scaling unlearning methods to large numbers of concepts and real-world deployments. As illustrated in Figure ( (We have provided specific data in the Appendix Table 11). most existing approaches suffer from substantial computational overhead, often demanding both Tong training time and large memory consumption, yet their overall performance still lags behind. In contrast, ScaPre maintains lightweight profile with minimal execution time and memory usage, completing the unlearning of 50 concepts within only 120 seconds. Although methods such as UCE and RECE also exhibit low runtime and memory costs, their unlearning effectiveness and generative quality fall far short of ScaPre. Taken together, ScaPre establishes a uniquely favorable trade-off, combining scalability, precision, and efficiency in way that prior approaches do not achieve.
6 CONCLUSION
In this work, we introduced ScaPre, the first closed-form framework specifically designed for large- scale concept unlearning diffusion models. By combining conflict-aware stable design with an informax decoupler, ScaPre enables stable optimization, precise disentanglement, and highly efficient computation. Our closed-form formulation eliminates the need for fine-tuning and auxiliary modules, achieving scalability to a large number of concepts with minimal overhead. Extensive experiments across objects, styles, and explicit content benchmarks demonstrate both superior unlearning efficacy and consistently high generative fidelity. We believe ScaPre establishes a new and effective paradigm for reliable large-scale unlearning, offering a principled and forward-looking direction for future research in safe and controllable generative modeling.

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7 ETHICS STATEMENT
This work does not involve human subjects, personally identifiable data, or private information. We therefore believe this work does raise ethical concerns.
REPRODUCIBILITY STATEMENT
We have made every effort to ensure that the results presented in this paper are reproducible. A detailed description of the complete algorithmic workflow is provided, and the full derivations are included in the Appendix to facilitate faithful implementation of the entire method. All generative models and baseline methods used in this study based publicly available open-source code, ensuring consistency and reproducibility of the evaluations. We will release the full code repository in the near future.
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A LLM USAGE STATEMENT
Large language models (LLMs) were employed solely for polishing the manuscript, including refining clarity and checking/correcting grammatical errors and typos. LLMs did not contribute to the generation of substantive ideas, analyses, or results. All scientific content, interpretations, and conclusions are entirely the authors' own.
B DETAILED DERIVATIONS FOR SCAPRE
We provide detailed derivations for the optimization steps in ScaPre. We first present the closed-form solution of the quadratic part of the objective (ignoring geometry alignment), and then describe the proximal refinement procedure used to incorporate Bures alignment. For clarity, all variables, operators, and dimensions are explicitly stated once and used consistently.
B.
CLOSED-FORM SOLUTION OF QUADRATIC PART
We start from the quadratic component of Eq. equation g ignoring the geometry alignment (Bures distance) term:
S(W) ir (WAWT) tr (WWBWT) - (W"M,",
(11)
where:
W Roo :du;; weight matrix being updated (cross-attention).
A AI S R E Rd Xdin; input-side stabilizer (symmetric, typically A > 0).
B diag(a) (a) E Redu xdow; output-side channel weighting from the Informax Decoupler (symmetric, = 0).
M = V I Xddin; with CE E Iid the stacked embeddings of the concepts to erase, and V E Xm their replacement targets (often zero).
Using standard matrix calculus for symmetric A, B, the first-order optimality condition (after cancel- ing a common factor) simplifies to the Sylvester equation:
BW + WA = M.
(12)
Equation equation 12 has a unique solution the spectra satisfy oBB) n (-o(A)) Ø. In our setting, A >- 0 and B z 0, hence uniqueness holds.
Using vec (Bc (Lam. B) vec(W) and vec(WA] (AT Idaa vec(W), we obtain
(Iain @ B+A & Idous) vec = vec(M).
Thus,
vec(W*) [dim B+ Idams) ) voo(M).
(13)
Here vec(-) stacks matrix columns; once vec(W*) is obtained, W is recovered by reshaping to dout x din-
Let A QA B QBARQT be eigendecomppsitionn. Define X Q M
QBMQA Then
AgX + XAA = M,
which decouples element-wise:
Me
X1J AB + AA.
Finally,
W' QBXQT
In our case, B diag(a) is already diagonal (Q = I), so only a single eigendecomposition of needed, followed by element-wise division and trck-transformation.
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B.2 PROXIMAL REFINEMENT FOR GEOMETRY ALIGNMENT
We now detail the treatment of the geometry alignment (Bures distance) term:
Cg(W) tr( tr( 2 2 (WWWT))/WWWV (WWT)u/2))
(14)
where Wu Rous xdu the pretrained reference and WWT, W. R xdout are the induced covariances.
Because of nested matrix square roots, jointly optimizing equation IT and equation 14 in one closed form is infeasible; we therefore apply proximal refinement after solving the quadratic part.
Compute W via Eq. equation 13 (or the spectral method) and form
Mx = W*W* Rdoot Xdout,
Let Mi Wo Interpolate toward Mg along the Bures geodesic with weight 3 E [0, 1]: Σx ((1 -11-11111)) (1-- /2
This is geometry-awar interpolation on the PSD cone, not a naive Euclidean average.
Find W such that WWT T = Σ and W is as close as possible to W*.
Proceed by orthogonal Procrustes:
1. Eigendecompose n = UAUT, take UA2/2
2. Solve minqr Q= I|W - U l|..
3. With K W UK V (SVD), the optimum is Q" = UK
4. Set W UA
This preserves the interpolated covariance while staying closest to W* up to an orthogonal rotation.
C ADDITIONAL EXPERIMENTAL RESULTS
C.1 UNLEARNING AT SCALE AND PRECISE UNLEARNING
We provide per-concept unlearning results for all benchmarks reported in the main paper, including the 50-class 1naeeset-Diversi500 Table 6). Imagenette Table 5), and ImageNet- Across nearly all concepts, ScaPre attains the lowest unlearn accuracy while maintaining competitive CLIP scores and the highest UQ indicating effective removal of target concepts without degrading generation quality. On visually confusable groups, ScaPre yields the best overall accuracy by jointly unlearning targets and preserving similar non-targets, highlighting its precision.
(Table 7).
We also provide comprehensive visual results to complement the quantitative analysis. As shown in Figure g and Figure [0, under large-scale unlearning condition, existing methods either fail to fully unlearn the target concepts severely degrade the generative ability of the model. In contrast, ScaPre delivers consistently high-quality and stable generations while achieving precise removal of the target concepts, even in large-scale settings. As shown in Figure D. the results demonstrate that fine-tuning- a large number of concepts. In contrast, UCE and RÉCE severely disrupt similar but non- target concepts, thereby compromising precision. Our proposed ScaPre, however, achieves precise unlearning of the target concepts while preserving the integrity of closely related non-target concepts, highlighting its effectiveness and reliability in large-scale unlcarning scenarios. For artistic styles unlearning. as shown Figure all existing baselines fail to achieve effective unlearning, whereas ScaPre successfully removes the target styles while preserving high generation quality. We also compare ScaPre with representative baselines that exhibit relatively strong multi-concepl unlearning capabilities. As the number of target concepts increases (as shown in Figure 12). these baselines suffer drastic decline in generative quality, quickly falling below an acceptable range. In contrast, method maintains consistently high generative fidelity even when unlearning up to 50 concepts. This demonstrates that, under comparable quality requirements, ScaPre can successfully forget more than five times the number of concepts compared to prior baselines.
approaches fail to satisfy unlearning requirements when scaled
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Table 5: Comparison of different unlearning methods on Imagenette benchmark, We report unlearning accu- racy (1), CLIP score (1) and UQ (t).
Method
Imagenette classes
SD v1.5
FMN
SPM
ESD
MACE
UCE
RECE
SP
ScaPre (Ours)
parachute
92.8
90.6
74.5
6.5
88.9
8.3
3.0
0.2
0.0
golf ball
97.6
92.5
93.2
13.4
94.9
7.7
4.2
12.2
0.0
garbage truck
79.2
54.1
31.4
28.7
15.3
43.2
cassette player
15.2
3.7
4.9
2.2
1.1
6.1
church
77.3
66.9
61.6
19.6
13.4
21.3
tench
97.9
79.0
43.7
64.7
84.5
5.1
1.0
2.2
0.0
English springer
97.6
85.8
67.5
79.5
92.7
0.9
2.0
1.2
0.0
French horn
97.9
87.1
17.1
57.5
96.1
3.7
2.1
0.3
0.0
chain saw
77.9
43.4
32.5
12.0
73.2
4.8
3.1
4.1
0.0
gas pump
94.2
69.4
20.7
55.2
83,5
5.3
4.2
5.2
0.0
Avg Ace (L)
89.9
47.4
38.7
78.5
8.5
4.9
9.6
CLIP coco (f)
31.43
30.62
30.81
30.14
31.02
29.45
29.27
29.25
30.43
UQ (1)
37.35
49.89
47.84
35.07
37.23
32.60
31.78
64.09
SD v1.5
FMN
ESD
SP
MACE
SPM
RECE
UCE
ScaPre
Leonardo da Vinci
Vincent van Gogh
Claude
Monet
Figure Visual comparison of unlcarning performance across different methods on 50 artistic styles; results for three representative styles are shown.
ESD
ScaPre
player
chainsaw
church
French
English springer
Figure Visual comparison unlearning performance across different methods simultaneous unlearning of 10 classes from the Imagenette benchmark.
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Table 6: Unlearning results on 50 classes from the extended benchmark (ImageNet-Diversi50)) We report
unlearning accuracy (%)(L). CLIP score (1) and UQ (1). ScaPre consistently outperforms existing methods.
Method
Classes
SD v1.5
FMN
SPM
ESD
MACE
UCE
RECE
SP
ScuPre (Ours)
tabby
76.8
61.7
55.2
60.7
25.3
1.7
Labrador retriever
85.2
83.0
82.0
21.7
82.4
0
0
24.7
0.8
tiger
98.2
96.0
95.0
24.5
95.4
0
0
26.5
9.2
lion
98.3
93.5
91.5
27.8
92.5
0
0
31.8
3.3
African elephant
71.7
71.5
71.4
29.3
71.7
34.3
1.7
sports car
95.8
93.4
92.5
21.8
92.8
22.8
17.5
convertible
96.7
87.2
82.6
18.3
86.2
0
21.3
3.3
school bus
97.2
93.7
92.0
19.2
92.7
0
23.2
1.2
airliner
96.7
93.5
91.3
34.7
92.5
36.7
7.5
mountain bike
97.5
92.1
89.5
42.7
minivan
75.8
68.7
67.7
24.5
1.7
pickup
92.5
83.5
79.7
16.7
82.5
17.7
7.5
motor scooter
87.5
85.1
84.2
30.2
84.5
32.2
9.2
folding chair
96.3
91.3
89.2
19.5
90.3
22.5
3.3
rocking chair
91.9
32.7
desk
76.7
64.2
16.7
67.0
4.2
dining table
93.3
90.0
88.3
39.5
89.0
40.5
19.2
table lamp
78.3
77.0
76.4
9.5
76.7
11.5
5.0
acoustic guitar
95.2
87.1
83.7
23.5
86.1
27.5
5.0
grand piano
85.0
84.7
84.2
21.5
84.5
25.2
3.4
violin
97.5
88.0
84.3
15.8
87.0
15.8
0.8
cornet
76.7
68.4
64.8
19.7
67.4
19.7
5.1
sax
87.5
83.3
81.7
12.0
82.3
14.0
3.4
cellular telephone
64.8
49.9
42.5
17.0
48.9
20.0
4.8
reflex camera
95.8
91.0
15.2
laptop
31.1
21.7
10.3
30.1
television
72.5
53.0
44.3
16.0
52.0
18.0
2.5
computer keyboard
65.0
57.1
54.2
15.8
56.1
17.8
3.8
Granny Smith
85.0
76.6
73.0
12.4
75.6
15.4
6.1
orange
84.5
76.7
73.3
75.7
18.8
5.8
banana
94.2
87.2
84.2
19.8
86.2
strawberry
90.8
89.0
87.8
14.3
88.1
15.3
1.7
broccoli
97.2
92.7
90.2
12.0
91.7
14.0
4.2
cauliflower
98.2
94.9
93.4
18.5
93.9
21.5
2.5
cowboy hat
79.2
72.1
69.2
17.7
running shoe
93.3
87.8
85.3
50.2
86.8
51.2
1.7
sweatshirt
85.8
80.1
78.0
20.2
79.1
0
22.2
1.8
jean
69.9
25.6
12.8
7.0
24.6
9.0
1.4
trench coat
96.3
91.9
88.3
29.3
90.9
33.3
8.3
pizza
95.0
75.8
21.8
hotdog
93.3
88.0
86.2
15.8
87.0
16.8
3.2
cheeseburger
93.5
89.2
87.5
14.2
88.2
15.2
0.0
ice cream burrito
91.7
83.7
79.8
13.8
82.7
16.8
0.8
97.5
90.0
87.5
12.6
89.0
15.6
0.0
mashed potato
85.0
76.7
72.8
75.7
23.9
traffic light
89.2
85.8
83.3
10.2
84.8
11.2
0.7
backpack
90.8
80.3
76.5
11.8
79.3
0
0
13.8
0.8
umbrella
94.2
85.6
81.2
29.7
84.6
0
32.7
2.9
bookease
80.8
62.1
54.8
25.2
61.1
29.2
7.5
bottle
84.2
75.1
71.0
74.1
17.5
Avg Ace (1)
87.7
79.8
76.5
19.6
78.9
0.0
0.0
22.5
3,9
CLIP coco (t)
31.43
30.12
30.45
28.21
31.23
22.23
21.78
28.23
29.41
UQ (1)
36.52
38.67
56.35
38.11
51.28
65.30
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Table 7: Evaluation ImageNet-Confussee comprising five groups of visually similar ImageNet concepts. Uunlearn accuracy (%)(L quantifies the residual accuracy on target (hlue) concepts, and preserve accuracy (t) assesses retention on visually similar but non non-target concepts. overall accuracy (f) evaluates the joint ability of unlcariing target concepts and preserving other similar concepts.
Method
Image Imaof-ee-Confuues classes
SD v1.5
FMN
SPM
ESD
MACE
UCE
RECE
SP
ScaPre (Ours)
golden retriever
82.0
84.0
83.0
5.0
5.3
61.5
7.5
labrador retriever
80.8
74.8
74.6
56.8
73.6
5.8
6.1
56.1
5.0
german shepherd
78.3
71.3
71.0
49.3
69.9
3.3
3.1
48.7
76.8
Chesapeake Bay retriever pug
93.3
85.3
87.3
67.3
86.3
8.3
8.0
66.8
89.2
90.0
84.0
83.8
63.0
82.8
6.7
62.3
tabby
86.7
79.7
81.6
58.7
80.7
11.7
12.0
58.0
23.3
tiger
80.0
72.0
71.8
5.0
52.4
9.2
persian cat
85.0
78.0
80.2
566.0
79.2"
5.3
3.7
55.77
80.2
Siamese cat
79.2
72.2
72.0
52.2
71.0
4.2
4.0
51.6
76.2
Egyptian cat
95.0
87.0
86.8
65.0
85.8
3.3
3.1
64.4
91.7
orange
81.7
74.7
77.0
$2.7
75.9
0.0
0.1
52.1
2.5
lemon
92.5
85.5
85.3
63.5
84.1
0.0
0.1
62.9
0.8
pomegranate
85.0
77.0
76.8
$7.0
75.6
0.0
0.1
$6.3
75.8
fig
80.8
72.8
74.8
51.8
73.8
0.0
0.1
51.1
75.7
Granny Smith
93.3
85.3
85.1
63.3
83.9
1.7
1.5
62.7
76.2
yawl
74.2
66.2
68.4
67.4
0.0
43.6
lifeboat
84.2
77.2
77.0
55.2
75.8
0.0
0.1
54.6
2.5
speedboat
83.3
75.3
75.2
55..3
74.1
0.0
0.7
53.7
69.2
catamaran
50.8
5.8
50.2
77.4
schooner
81.7
73.7
76.0
51.7
74.9
10.0
10.3
51.1
78.3
ball
85.0
77.0
79.2
55.0
78.2
1.7
54.4
2.5
volleyball
76.2
76.0
74.8
0.0
54.6
tennis ball
86.7
78.7
78.5
$7.77
77.3
2.5
2.3
57.0
62.5
rugby ball
92.5
84.5
86.8
62.5
85.7
9.2
9.0
61.9
71.7
ping-pong ball
86.2
84.8
25.8
63.7
60.8
Unlearn Ace (3)
83.9
76.5
77.5
55.6
76.4
2.9
3.1
55.0
5,8
Preserve Ace
86.6
78.9
78.6
5.6
5.5
57.1
76.3
Overall Acc (f)
27.2
36.2
35.1
50.2
36.3
10.6
10.4
50.3
84.3
CLIP coco (1)
31.43
30.45
30.60
29.78
30.98
28.04
27.23
29.84
30.15
UQ (1)
38.27
40.29
40.28
46.69
42.13
31.88
20.41
47.47
65.49
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SD v1.5
FMN
ESD
SP
MACE
SPM
RECE
UCE
ScaPre
tabby
persian cat
cat
RAPA
schooner
Figure Visual comparison of unlearning performance across different methods the ImageNet- SeNNfuue benchmark. The underlined classes denote target concepts to be unleamed, while the underleldd classes represent visually similar but non-target concepts.
SD v1.5
FMN
ESD
SP
MACE
SPM
RECE
UCE
ScaPre
cheese
burger
television
COTP
SOHIOS DSAATER
umbrella
wafer bottle
Figure 10: Visual comparison unlearning performance across different methods when simultaneously unlearning 50 classes from the ImageNet-Divenn Diversss0 benchmark.
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Table 8: Results of NudeNet detection using Stable Diffusion v1.4 the I2P dataset. "(F)" denotes female, and
"(M)" denotes male.
NodeNet Detection
Metric
Method
Armpits
Belly
Buttocks
Feet
Breasts (F)
Genitalia (F)
Breasts (M)
Genitalia (M)
Trtal
FID J
CLIP
FMN
47
120
23
163
17
21
448
13.54
30.43
153
180
298
14.13
UCE
29
62
7
29
35
5
11
4
182
14.07
30.85
SPM
51
69
8
70
5
10
229
13.81
31.24
MACE
17
19
2
16
2
9
111
13,42
29.41
15
20
12
ScaPre
10
15
2
54
13.95
30.88
v1.
170
Table 9: Results of NudeNet detection using Stable Diffusion v1.5 on the 12P dataset. "(F)" denotes female, and "(M)" denotes male.
NudeNet Detection
Metric
Method
Armpits
Belly
Buttocks
Genitalia
Genitalia
FID
FMN
132
186
27
30
147
28
60
17
627
13.17
30.07
AC
162
194
39
304
19
64
8
861
13.88
31,62
UCE
54
5
52
15
14
200
13.92
31.23
ESD
139
162
31
32
252
16
42
14
688
14.12
31.11
MACE
40
10
6
12
18
11
14
16
127
12.89
29.18
14
13
10
15
14
13.74
30.79
ScaPre
6
12
5
56
13.53
31.37
SD
137
151
34
283
24
42
18
718
13.93
31,42
C.2 EXPLICIT CONTENT UNLEARNING
We evaluate Explicit concept unlearning on the I2P ("Inappropriate Image Prompts") benchmark, which includes 4,703 real-world prompts prone generating inappropriate content. Evaluation is conducted using three metrics: (1) NudeNet detection counts for unlearning effectiveness, (2)
FID for visual quality, and (3) CLIP score for semantic consistency. NudeNet (Bedapudi] 2019)
is lightweight nudity detector that classifies and localizes NSFW regions, and following prior work (Schramowski et al. 2023 Lu al. 2024). we mark a region inappropriate only if the detection confidence exceeds 0.6. As shown in Tables X and ScaPre achieves the most effective reduction of inappropriate content while maintaining both semantic consistency and visual fidelity, demonstrating clear advantages over prior methods the 12P benchmark.
C.3 ROBUSTNESS OF SCAPRE
We summarize the robustness evaluation against three representative attacks and highlight ScaPre's advantages. Ring-A-Bell (Tai al. 2023) is black-box attack that crafts prompts to bypass safety filters and indirectly trigger undesired content. MMA (Yang et al., (024) black-box multimodal adversary that jointly perturbs text and image inputs to evade built-in safeguards. In contrast, UnlearnDiffAtk (Zhang et al. 2024b) is a white-box attack that directly manipulates model internals to recover previously erased concepts, representing a more severe threat model given full access model parameters. Against this diverse set of attacks, our method demonstrates substantially improved resilience compared prior approaches (as shown in Table TOp: ScaPre not only more effectively prevents adversarial re-triggering of erased concepts under black-box probing, but also better resists white-box attempts to recover forgotten concepts, while preserving generation quality and semantic consistency. These results indicate that the conflict-aware stable design together with the Informax Decoupler yields a practical balance between robustness and fidelity in adversarial settings.
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Table 10: Evaluation of robustness under three types of adversarial attacks.
GPU hours and memory con- sumption unlearning methods.
Table 11:
Method
Ring A Bell
MMA
UnleamDifAAAk J
Method
GPU Hours
Memory (GB) +
FMN
5.6
17.4
97.9
FMN
1.43
19.41
SPM
18.1
97.2
SPM
21.20
20.04
ESD
60.8
87.3
76.1
ESD
0.0917
13.09
MACT
18.5
96.8
MACE
1.94
10.43
UCF
74.2
77.3
93.2
UCE
0.0167
6.82
RECE
79.4
91.3
68.5
RECE
0.0350
8.23
SP
ScaPre (Ours)
84.5
94.6
60.9
ScaPre
0.0317
6.54
Table 12: Overall generative quality results on the ImageNet-Divvrsi500 benchmark. ScaPre achieves significantly better performance compared to all baselines.
Method
SD v1.5
FMN
SPM
ESD
MACE
UCE
RECE
SP
ScaPre (Ours)
Avg Acc (1)
87.7
79.8
76.5
19.6
78.9
0.0
0.0
22.5
3.9
CLIP coco (f)
31.43
30.12
30.45
28.21
31.23
22.23
21.78
28.83
29.41
FID (L)
13.92
14.82
15.29
18.12
17.73
56.81
62.57
14.94
17.18
UQ. (1)
34.69
37.58
39.62
56.05
39.17
26.88
24.66
57.83
65,30
UQ (t)
33.69
37.43
38.96
59.61
37.90
27.14
22.09
58.38
66.94
C.4
EVALUATION OF GENERATIVE QUALITY PRESERVATION
To more comprehensively reflect the trade-off between unlearning effectiveness and generative quality, we udopt the unified metric UQ, defined as
2ÁČ
UQ = 100
A A
where À is the normalized forgetting score and Ö is the normalized quality score. We compute two concrete variants: (i) UQ.. where C' corresponds to the CLIP score, jointly assessing unlearning accuracy and semantic alignment; and (ii) UQ₁, where C' -FII (since lower FID is better), jointly assessing unlearning accuracy and quality of images, As reported in Table 12 ScaPre achieves the highest values on both metrics, clearly surpassing all baselines. These results highlight that ScaPre not only enforces large-scale unlearning but also preserves generative quality: FID remains nearly unaffected, and although CLIP alignment slightly decreases, remains competitive. The consistently superior unified scores confirm ScaPre the only method achieving balanced and reliable trade-off between forgetting effectiveness and generative quality, Since U UQe and UQ, yield similar overall trends, in the main text we primarily report UQ computed with CLIP scores for clarity and consistency.
C.5 ABLATION STUDY
The ablation study examines the influence of different components in our framework. As shown in Figure IT] we first compare the effect of the Spectral Trace Regularizer and Geometry Aligument. The left side contains two subplots: the first reflects the generative quality, while the second shows the unlearning performance. With these components enabled (red), the model largely preserves generative quality and the forgetting ability is only minimally affected. In contrast, without them (blue), the model degradation: although the forgetting accuracy trivially reaches zero, such a result meaningless since generative capacity has already been destroyed. This highlights the critical role of these modules in maintaining stability under large-scale unlearning.
On the right, the comparison focuses on the Informax decoupler. Models with this component (red) achieve better preservation of unrelated concepts and reduced collateral unlearning, while those without it (blue) show weaker disentanglement control and tend to disrupt similar non-target concepts. As shown, each module plays a complementary role in balancing scalability and precision in large-scale unlearning.
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31
Unleam Accuracy (%)
Preserve Accuracy (%)
80
CLIP Soore
30
70
29
60
28
0
20 Number of Conoepts
10
50
10
20
50
5
15 Number Concepts
10
25
Number Concepts
Figure 11: Ablation study results. Left: CLIP Score (generative quality). Middle: Unlearn Accuracy. Right: Preserve Accuracy. lines indicate models with corresponding component enabled, and blue lines indicate models without it.
Clip Score (t)
30
Method
60
Method
ScaPre
ScaPre
28
UCE
3
UCE
26
RECE
40
RECE
FID
24
20
22
10
20
30
40
50
10
20
30
40
50
Number of Concepts
Number of Concepts
Figure 12: Comparison of generative quality (CLIP score f and FID 1) the number of unlearned concepts increases.
C.6 EXTENDED ABLATIONS
This section provides additional ablation studies on all four components of ScaPre, including the spectral trace regularizer (S and R), the Informax decoupler, and the geometry alignment module. These experiments examine the contribution of each component to forgetting precision and generative quality. As shown in Table [3]add Table 14] removing any component leads to a clear reduction in unlearning performance or preservation of non-target concepts, while the full ScaPre configuration consistently achieves the best balance between the two objectives.
Table 13: Ablation on preservation accuracy across different concept counts.
Table 14: Ablation on generative fidelity across differ- ent concept counts.
Variant
5
50
Variant
20
Full ScaPre
85.42
83.17
76.28
72.11
Full ScaPre
31.04
30.45
30.24
29.41
-oo S
83.76
80.92
69.35
63.87
No
30.97
30.41
29.90
28.60
No R
82.94
81.23
71.48
62.59
No R
31.01
30.38
29.70
28.80
No Geometry
83.21
79.64
68.72
60.43
No Informax
30.94
30.15
29.44
27.61
No Informax
82.64
79.83
60.37
55.18
No Geometry
30.96
30.43
29.80
28.40
C.7 ROBUSTNESS THE UQ METRIC UNDER ALTERNATIVE NORMALIZATIONS
To assess the robustness of the unified quality (UQ) metric, recompute UQ using normalization schemes: min max normalization and rank-based normalization. Tables [5] and Tables (6) results for multi-concept unlearning. In all scenarios, ScaPre consistently achieves
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the highest UQ scores among comparable methods, indicating that its performance advantage is not sensitive to the choice of normalization.
1. MIN-MAX NORMALIZATION
We first evaluate UQ using min-max normalization scheme. For metrics where lower values indicate better forgetting performance, we normalize each method's 's score by mapping it linearly to the interval [0, 1] based on the best and worst values observed across all methods:
Amax A
minmax
Amax Amin
Conversely, for metrics where higher values are preferable, we apply the standard min-max scaling:
C Cimn
Cmmimmax
Cmax Cmin
The unified quality score is then computed as the harmonic mean of the normalized forgetting and fidelity metries:
2A minmmx Cmminmax
UQ
A Aminmax
C'ninmax
2. RANK-BASED NORMALIZATION
We also report UQ under a rank-based normalization scheme, which evaluates relative performance independent of absolute metric scales. For lower-better metries, each method is assigned rank from 1 (best) to (worst), and the corresponding normalized score is defined as:
rank (A)
rank
Similarly, higher-better metrics are normalized using:
rank(C) -1
Crank
N -
As in the min-max case, the final unified quality score is given by the harmonic mean of the normalized forgetting and fidelity terms:
UQ
Arank + Crank"
Table 15: Comparison different unlearning methods on Imagenette under min- min- normalization
Table 16: Comparison of different unlearning methods on Imagenette under rank-based normalization
Method
Avg Acc (1)
CLIPcoco (f)
UQ (Min-max)
Method
Avg Acc (1)
Cl.PPcoco (f)
UQ (Rank-based)
VD
89.9
31.43
FMN
71.9
30.62
0.153
FMN
71.9
30.62
0.232
SPM
47.4
30.81
0.551
SPM
47.4
30,81
0.636
38.7
30.14
0.508
38.7
30.14
0,533
MACE
78.5
31,02
0.000
MACE
78.5
31,02
0.000
UCE
RECE
4.9
29.27
0.022
RECE
29.27
0.000
0.000
SP
9.6
29.25
0.000
ScaPre (Ours)
0.8
30.43
0.800
(Ours)
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D OPEN SOURCE CODE REFERENCE LIST
To ensure fair and reproducible comparison, we evaluate our approach against the most comparable state-of-the-art unlearning and concept editing methods. Their official open-source implementations are listed below, and all baseline results in this paper are obtained using these repositories with recommended settings unless otherwise noted:
FMN: htt.:torr./gggiiio..cc////////rr SPM http::///gghhubbooooo///o2211313
ESD: /btp://ttce/cttta.ccooooooooaaaa MACE: |MM,0:11110////aaaooo..1101/1111 UCE: innfiee--ooeept-elliing https//gthhb..mm//oottaaaaaaaaa
RECE: REC5:///LL5////t/oooooo/o/ooooon
24


Reviews:
[{"review_id": "WbddLG1MTd", "reviewer": "Reviewer_RFw7", "summary": "The paper addresses a challenge of large-scale concept unlearning in text-to-image diffusion models. While existing approaches can remove individual concepts, they struggle when scaling to multiple concepts simultaneously, facing issues with conflicting weight updates, imprecise unlearning boundaries, and computational scalability bottlenecks.", "questions": "see Weaknesses section", "limitations": "", "rating": 4, "confidence": 2, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The paper is well-structured and easy to follow\n2. While the majority of other algorithms fine-tune the the entire model weights\n3. Addresses fundamental challenges through theoretically grounded components\n4. Comparison with other methods on a large-scale multi-concept unlearning (up to 50 concepts)\n5. Extensive appendix with math proofs and detailed results", "weaknesses": "1. No comparison with parameter efficient Unlearning methods (e.g., SEMU https://arxiv.org/abs/2502.07587)\n2. It would be beneficial to have the data from figure 3 in a from of a table in the appendix\n3. Based on the theoretical foundation the method should also work on other SOTA models (e.g., SDXL, Stable Diffusion 3.5, FLUX.1-dev, Qwen-Image); however, no experimental confirmation is presented in the paper", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "h8CIrZLzF3", "reviewer": "Reviewer_zBcc", "summary": "To address the challenges of conflicting weight updates, collateral damage to non-target concepts, and reliance on extra data in large-scale concept unlearning for text-to-image diffusion models, this paper proposes ScaPre (Scalable-Precise Concept Unlearning), a unified lightweight framework aiming for scalable and precise unlearning.\nScaPre integrates a conflict-aware stable design (spectral trace regularizer + geometry alignment) and an Informax Decoupler, achieving an efficient closed-form solution without extra data/sub-models; experiments show it can unlearn up to 5× more concepts than the best baseline while maintaining high generation quality.", "questions": "See weakness.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper innovatively combines a conflict-aware stable design and an Informax Decoupler, which effectively solves the core problems of instability in large-scale unlearning and imprecise separation of target/non-target concepts, making up for the shortcomings of existing methods in large-scale scenarios.\n\nScaPre adopts a closed-form solution, ensuring high efficiency (unlearning 50 concepts in 120 seconds) and reproducibility without extra data or auxiliary modules; meanwhile, its experiments cover objects, styles, and explicit content benchmarks, with comprehensive and convincing results.", "weaknesses": "1. Experimental benchmarks are mostly ImageNet-derived datasets (e.g., Imagenette, ImageNet-Diversi50), lacking evaluations on more complex and diverse real-world scenarios (e.g., dynamic concepts, cross-modal associated concepts), making it hard to verify the method’s practical generalization.\n\n2. It is suggested to explore ScaPre’s adaptability and performance changes on larger diffusion models (e.g., Stable Diffusion XL). \n\n3. It is suggested that the authors enhance and enrich the elaboration of the overview figure in this paper, as the current description of this figure is too simplistic, omits many details, and makes it difficult for readers to understand.\n\n4. In the proposed Imagenette benchmark, it is not explicitly specified what prompts are used for evaluation and whether these prompts are merely category names; thus, it is suggested that the authors use more complex prompts to evaluate the impact of prompts on the experimental results.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "sVUPXrqCzG", "reviewer": "Reviewer_VrCc", "summary": "The paper proposes ScaPre, a closed-form framework for scalable and precise concept unlearning in text-to-image diffusion models.\nIt addresses three challenges in large-scale unlearning: conflicting weight updates, imprecise forgetting causing collateral damage, and inefficiency from auxiliary modules.", "questions": "Please introduce A and B in the main text when first used in Eq. (8), aligning with Appendix B.1 notation.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The empirical validation is good, for example, ScaPre achieves the lowest unlearning accuracy on Imagenette while maintaining high CLIPcoco, outperforming other baselines.\n\n2. The algorithm is innovative and lightweight. The closed-form solution avoids iterative fine-tuning, and geometry alignment via Bures distance preserves global covariance structure better than L2 regularization. Also, the Informax Decoupler is reasonable.\n\n3. The benchmark construction. ImageNet-Confuse5 explicitly tests disentanglement of visually similar concepts (e.g., dog breeds), a realistic and challenging setting absent in prior work.", "weaknesses": "1.  Some notation is ambiguous. For example, The symbol W is used for both the updated matrix and intermediate solution W⋆ without distinction in Sec. 4.3 (see Eq. (8)–(10)). In Appendix B.1, Eq. (11) redefines the objective with A = λI + S+R and B = diag(α), but these symbols are not introduced in the main text, breaking continuity.\n\n2. Random seeds, data splits for ImageNet-Diversi50/ImageNet-Confuse5, and prompt selection criteria are omitted (see Sec. 5.1), hindering replication.\n\n3. Fig. 3 reports GPU-hours and memory but omits per-concept scaling trends (e.g., time vs. number of concepts), critical for “scalable” claims (see Sec. 5.5).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "gVhWqdZe38", "reviewer": "Reviewer_4a91", "summary": "The paper proposes ScaPre, a training‑free, closed‑form framework to erase many target concepts from text‑to‑image diffusion models while preserving quality on non‑targets. It stabilizes multi‑concept edits via a spectral trace regularizer (second‑order target statistics plus an SVD‑based overlap regulator), improves precision with a mutual‑information–guided \"Informax Decoupler\", and preserves global structure through Bures‑geometry alignment; the quadratic part reduces to a Sylvester system solved in one shot. On Stable Diffusion v1.4/1.5, ScaPre achieves state‑of‑the‑art large‑scale forgetting, e.g., Imagenette residual accuracy 0.8 (Table 1), Diversi50 3.9 (Table 3), Confuse5 overall 84.3 (Table 4), and unlearns 50 concepts in $\\sim$120 s on an A6000 (Fig. 3), while claiming up to x5 more concepts than baselines.", "questions": "- How are \"target\" and especially \"neutral\" inputs instantiated for MI estimation without extra data? What sample size/thresholding is used, and how stable are channel scores across layers?\n\n- Which cross‑attention layers/branches (K vs. V) are edited, and how does performance vary layerwise?\n\n- Can you show results on SDXL/DiT to illustrate architectural generality or required modifications to S and R?\n\n- Do you test robustness to synonyms/negation/compositional prompts or other circumventions (e.g., multilingual)? A breakdown would substantiate \"precise\" forgetting.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "- Conflict‑aware spectral trace regularizer + SVD overlap control; MI‑guided channel reweighting; Bures‑alignment for geometry‑aware stability.\n\n- Convex quadratic core with unique Sylvester solution; clear derivations and proximal mapping.\n\n- Best residual accuracy/UQ on Imagenette, Diversi50, and Confuse5 with robust visuals.\n\n- 50‑concept unlearning in $\\sim$120s; low memory/time vs. baselines (Fig. 3).", "weaknesses": "- Construction of \"target/neutral\" inputs, threshold choice, and variance of MI estimates need clarification.\n\n- Heavy use of classifier‑based \"unlearn accuracy\" and CLIP; limited human/adversarial prompt evaluation.\n\n- Results limited to SD v1.4/1.5; unclear portability to SDXL/DiT architectures.\n\n- Deeper, main‑text ablations of S vs. R vs. Informax vs. geometry step and sensitivity of UQ's normalization would strengthen claims.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)