FAST: Foreground‑aware Diffusion with Accelerated Sampling Trajectory for Segmentation‑oriented Anomaly Synthesis
Authors: Xichen Xu
Yanshu Wang
Jinbao Wang
XiaoNing Lei
Guoyang Xie
GUANNAN JIANG
Zhichao Lu
Venue: NeurIPS 2025 poster ()
Keywords: Anomaly synthesis
anomaly segmentation
Primary area: applications
TL;DR: Segmentation-oriented Industrial Anomalies Synthesis

Abstract: Industrial anomaly segmentation relies heavily on pixel-level annotations, yet real-world anomalies are often scarce, diverse, and costly to label. Segmentation-oriented industrial anomaly synthesis (SIAS) has emerged as a promising alternative; however, existing methods struggle to balance sampling efficiency and generation quality. Moreover, most approaches treat all spatial regions uniformly, overlooking the distinct statistical differences between anomaly and background areas. This uniform treatment hinders the synthesis of controllable, structure-specific anomalies tailored for segmentation tasks. In this paper, we propose FAST, a foreground-aware diffusion framework featuring two novel modules: the Anomaly-Informed Accelerated Sampling (AIAS) and the Foreground-Aware Reconstruction Module (FARM). AIAS is a training-free sampling algorithm specifically designed for segmentation-oriented industrial anomaly synthesis, which accelerates the reverse process through coarse-to-fine aggregation and enables the synthesis of state-of-the-art segmentation-oriented anomalies in as few as 10 steps. Meanwhile, FARM adaptively adjusts the anomaly-aware noise within the masked foreground regions at each sampling step, preserving localized anomaly signals throughout the denoising trajectory. Extensive experiments on multiple industrial benchmarks demonstrate that FAST consistently outperforms existing anomaly synthesis methods in downstream segmentation tasks. We release the code in https://github.com/Chhro123/fast-foreground-aware-anomaly-synthesis.

FAST: Foreground-aware Diffusion with Accelerated Sampling Trajectory for Segmentation-oriented Anomaly Synthesis
Xichen Xu Yanshu Wang' Jinbao Wang² Xiaoning Lei²
Guoyang Xie Guanman Jiang"* Zhichao Lu
Global Institute of Future Technology, Shanghai Jiao Tong University, Shanghai, China School of Artificial Intelligence, Shenzhen University, Shenzhen, China Depaatment of Intelligent Manufacturing, CATL, Ningde, China 'Department Computer Science, City University of Hong Kong, Hong Kong, China isaac_ maaa__aag@sjjuu edu. wangjbeszu, edu. cn zhichao lu@cityu.edu, edu. hk
neptune 23330s edu, en
1eixm010cat1.com com jianggnccatl.cm com guoyang xie0ieee. org
Abstract
Industrial anomaly segmentation relies heavily on pixel-level annotations, yet real-world anomalies are often scarce, diverse, and costly to label. Segmentation- oriented industrial anomaly synthesis (SIAS) has emerged as promising alter- native; however, existing methods struggle balance sampling efficiency and generation quality. Moreover, most approaches treat all spatial regions uniformly, overlooking the distinct statistical differences between anomaly and background cas. This uniform treatment hinders the synthesis of controllable, sppccfc anomalies tailored for segmentation tasks. In this paper, propose FAST, foreground-awar diffusion framework featuring two novel modules: the Anomaly- Informed Accelerated Sampling (AIAS) and the Foreground-Awen Awarre Reconstruction Module (FARM). AIAS is a training-free sampling algorithm specifically designed for segmenntation-oriente industrial anomaly synthesis, which accelerates the reverse process through coarse-to-fine aggregation and enables the synthesis of state-of-the-art cegmentation-oriented anomalies in few 10 steps. Mean- while, FARM adaptively adjusts the anomaly- aware noise within the masked foreground regions at each sampling step, preserving localized anomaly signals throughout the denoising trajectory. Extensive experiments on multiple industrial benchmarks demonstrate that FAST consistently outperforms existing anomaly syn- thesis methods in downstream segmentation tasks. We release the code in https: //github com/ Chwhhhhhhhaaaeeee ooooo aware- anomaly-symnnta syythhsssss
1 Introduction
Motivation. Industrial anomaly segmentation plays vital role in modern manufacturing, aiming to localize abnormal regions at the pixel level. Unlike traditional anomaly detection, which typically performs binary classification at the image or region level, anomaly segmentation requires more fine-grained and precise localization of abnormal patterns. However, real-world anomalies are inherently scarce, diverse, and non-repeatable, making it difficult to collect data that fully captures the range of possible abnormal types. Moreover, acquiring high-quality pixel-level annotations is labor-intensive and costly, especially industrial scenarios. address these limitations, recent studies have increasingly explored the use of synthetic anomalies to expand the training data space and improve downstream performance.
Conresponding authors.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Limitations. Despite recent advances, current anomaly synthesis methods face three fundamental limitations that hinder their effectiveness for segmentation tasks [35]. (i) Lack of controllability. Most existing methods provide limited control over the structure, location, or extent of synthesized
anomalies. This limitation particularly evident in GAN-based approaches [22, 41, 6]. These methods typically adopt one-shot generation paradigm, offering little flexibility in specifying where and how anomalies should appear. (ii) Neglect of segmentation-relevant properties. Training- methods such as patch replacement or texture corruption [16, 40] may produce visible anomalies, but the synthesized patterns often lack the structural consistency and complexity of real-world industrial anomalies, which critical for improving segmentation performance. (iii) Uniform treatment of spatial regions and inefficiency. Although recent diffusion- methods [11, 14, 26] have mitigated the above issues, they still treat all spatial regions uniformly during both forward and reverse processes, without explicitly modeling the distinct statistical properties of anomaly regions [43, 38]. This absence of region-aware modeling prevents the model from preserving abnormal regions throughout the synthesis trajectory. Moreover, these models typically require hundreds to thousands of denoising steps [12, 27], resulting in significant computational cost, especially for the real-world production line changeover. While recent training-free methods [17] aim accelerate sampling, they fail to incorporate anomaly-aware cues, making them less effective industrial anomaly synthesis (SIAS). These limitations motivate the need
for segmentation-orieni for SIAS models that support controllable anomaly synthesis, explicit modeling of anomaly regions, and efficient, tusk-aligned sampling strategies.
FAST. To address these issues, we propose FAST, novel foreground- aware diffusion framework with two complementary modules: Anomaly-Informed Accelerated Sampling (AIAS) and the Foreground- Aware Reconstruction Module (FARM). (i) AIAS is a training-free sampling strategy that reduces the number of denoising steps by up to 99% (from 1000 to as few as 10), resulting in over 100x speedup for SIAS tasks. Despite this drastic acceleration, FAST achieves an average mloU of 76. 76.72% and accuracy of 83.97% on MVTec-AD, outperforming all prior state-of-the-art methods. (ii) FARM explicitly models abnormal regions by reconstructing pseudo-clean anomalies and generating unomaly-awer aware noise at each step in both the forward and reverse processes. Incorporating FARM boosts performance from 65.33% 76.72% in mIoU (t11.39), and from 71.24% to 83.97% in accuracy (1 (117733) demonstrating its critical role in enhancing anomaly salience. Detailed results are provided in Sec. 4.3. Together, AIAS and FARM enable FAST generate controllable and segmentationnaligneed anomalies that significantly improve downstream performance.
Contributions. In summary, our contributions three-fold: (1) To mitigate the inefficiency and se- mantic misalignment of existing diffusion sampling, we introduce a training-free Anomaly-Infornon Accelerated Sampling (AIAS) strategy that aggregates multiple denoising steps into small number of coarse-to- fine analytical updates. (2) To address the lack of persistent anomaly-region representation. Reconstruction Module (FARM) that reconstructs pseudo-clent clean
we propose a Foreground- anomalies and reintegrates anomaly- aware noise at each step. (3) To support segmentation -oriente industrial anomaly synthesis, we design FAST, a controllable and efficient model. Extensive ex- periments on MVTec- AD and BTAD datasets demonstrate that it significantly outperforms existing methods in downstream segmentation tasks.
2 Related work
Industrial Anomaly Synthesis. Industrial anomaly synthesis aims to mitigate the scarcity of labeled abnormal samples in real-world inspection scenarios. Existing methods can be categorized into hand- crafted and DL-based approaches. Hand-crafted methods typically apply triniin-frree manipulations to normal images, such as patch pasting [23, 25] or external texture blending [40, 36, 44] from sources like DTD [4], but they suffer from distributional deviation and limited realism. Deep learning- based methods alleviate these limitations by learning from real anomaly patterns. GAN-base methods [7, 32] can synthesize visually realistic anomalies but lack fine- fine-grained controllability over anomaly shape and location. Diffusion-based methods [7, 15, 37, 10] offer stronger generative capacity via large-scale pretrained models, yet treat all regions uniformly and lack explicit control over anomaly localization, which is essential for segmentation. To this end, we propose FAST, which integrates foreground-aware reconstruction and efficient, segmentation-orienter anomaly synthesis into a unified diffusion framework.
Acceleration of Discrete- Time Diffusion Models. Diffusion models can be categorized into continuous-time and discrete-time frameworks. Continuous formulations [18, 19, 46] adopt SDE/ODE- parameterizations and leverage high-order solvers for efficient sampling. In contrast,

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standard DDPMs [12] model discrete-timg Markov chain with fixed variance schedules and require thousands of iterative denoising steps. While continuous- solvers achieve notable speedups. they rely on continuously parameterized noise or score functions, which requires reformulating training objectives or interface discrete-time models. Therefore, various acceleration techniques have been developed specifically for discrete-time diffusion. Some methods modify the generative process to reduce steps: DDGAN [33] integrates GAN-based decoding, TLDM [45] and ES-DDPM [20] truncate the forward process, and Blurring Diffusion Models [13] operate in the frequency domain. However, these methods require retraining and show limited generalization. In contrast, training-fre approaches such DDIM [27]. PLMS [17], and GGDM [30] accelerate sampling without model modification. Yet, they treat all spatial regions uniformly and lack task speccficc guidance essential for SIAS. Recent work like CUT [28] introduces external prompts for localized control for anomalies, but at the cost of multiple iterations per sampling step. In comparison, FAST proposes a novel training-free strategy that aggregates multiple denoising steps into coarse-to-fine segments while injecting mask-aware structural guidance, enabling efficient SIAS.
decoupling has been widely em- ployed in industrial anomaly synthesis to enhance spatial precision and suppress irrelevant background interference. The core idea is to isolate defect-related regions from normal contexts, thereby improv- ing downstream performance and synthesis controllability. Most methods such as PRN [42] and DCDGANc [31] perform explicit two-stage compositions, which first generate abnormal foregrounds and then blend them with normal backgrounds under soft mask constraints, but often suffer from boundary inconsistencies. Recent studies have introduced implicit separation; for instance, FCIS [29] enlarges the
srrgrruund-bcckrronn Decoupling.
distance via contrastive learning, while BDG [3] incorporates masked attention and regularization within the denoiser to disentangle the influence of anomalies from the surrounding background. Although both BDG and FAST involve diffusion-basse synthesis with certain forms of prreground-backgrouun decoupling, they pursue different research objectives through fundamentally distinct methodologies. FAST is regmentation-orientte anomaly synthesis framework that emphasizes pixel-wise structural alignment and contextual consistency, whereas BDG primarily targets robust anomaly detection. Technically, AIAS in FAST analytically aggre- gates multiple DDPM reverse transitions into a few closed-form. coarse-to -terse-t--fieee updates, forming a deterministic and training- free sampler (c.g., + 2t-1) whose coefficients are precomputed under the original variance schedule, without any variance--onttrolinng parameters like DDIM [27]. In contrast, BDG depends on DDIM inversion (e.g., It-1 Xς)) to maintain background features, which requires inversion consistency and retraining with regularization losses. These two mechanisms are fundamentally distinct and not directly interchangeable. Furthermore, the FARM module in FAST functions as an external foreground-recowe recostructtttttion pathway that injects anomaly-aware noise via masks across timesteps to preserve anomaly salience throughout the sampling trajectory, whereas BDG employs masks merely as internal attention gates to localize edits within the denoiser. Essen- tially, BDG modifies the attention dynamics inside the denoiser to limit interference, while FARM operates outside the denoiser as reconstruction based enhancement module. These conceptual and algorithmic distinctions, together with different experiments and evaluation (segmentation-orine mloU/Acc vs. detection-oriented AUROC/AP) demonstrate that FAST and BDG follow independent research lines and remain technically and theoretically original.
3
Methods
Xt
St
Xo
Forward Process
Foreground-aware Reconstruction
Forward diffsion
New Xt,
Reverse sample
M
AIAS
Update
g(x,, Xe,y Xo)
Foregrond process both directions
IDDM
Reverse Process
Figure 1: Illustration of a single forward reverse process in FAST. AIAS accelerates sampling by aggregating multiple denoising steps into a small number of coarse-to-fint segments, achieving up to 100x speedup while preserving semantic alignment under anomaly mask guidance. FARM extracts anomaly-only content from the noisy latent x, at each timestep and transforms it into anomaly-aware noise by re-applying forward diffusion.
3

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EAST for Anomaly Segmentation. The proposed FAST framework is built upon the LDM [24] of T steps. For notational simplicity, we denote the encoded latent of the original image as 20. and its predicted reconstruction from the network as Zp. We define It, as the noisy latent at timestep 4s. and &t as the FARM-adjusted, anomaly-aware latent at the same step. Let M E {0. H} denote the binary anomaly mask, and [/., (.e] represent a coarse-to-fine segment in AIAS, where te < t.- Fig. illustrates a single forward-reverse process at step f.. In the forward phase, noise is added up to timestep las yielding noisy latent 2t,- FARM (F& in Algorithm 1) then predicts pscudo-clean anomaly latent ai' and adds noise to it up to timestep ta to obtain an anomaly-aware latent ft,, which aims to match the observed Ft, in masked regions during training. In the corresponding reverse process, we divide the full denoising process into 5 segments, each spanning [tz. te]. Within each segment, AIAS approximates the posterior transition using: ( Tt,, Tu). This formulation aggregates multiple DDPM steps into a single numerical update. FARM is also applied to refine Tt., ensuring the preservation of anomaly cues throughout the reverse process. More details can be in Algorithms and 2n addition, for the textual conditioning component of LDM, we follow the configuration of Anomaly Diffusion [15]; more implementation details can be found there.
Algorithm FAST Training
Algorithm 2 FAST Sampling
(Details shown in Supplementary Material A.4)
1: repeat
2: To g(zg), M, and weights A1. X2
1: Initialize AT -N(0,))
3: ts ~ Uniform( (1..... ,T).....))).ee
2:
for each segment (Lx: te] from T - 0 do
4: It, = vār, +V--au Ct
3:
? = co( 1.))
5:
ft, = Vār, Folr, + VI ōz,
4:
δo = Jai, (It, v1 - Ōt,
6: Take gradient descent step
5:
AIAS:
Voll l| fale--o(ft,, co( 14)1
Xt. = Fola(xr. I te:
+ (M@ xn
6: end for return 20
7: until converged
3.1 Chomaly-Informet Accelerated Sampling
The standard DDPM allows us to directly compute the marginal distribution of z, given clean sample zo and additive noise e. Therefore, the one-step posterior distribution x,-1 can be expressed as:
q( 21, mu) = -V + B, oiI), where the coefficients are derived from the variance schedule as follows:
A. vā,-13
-
1- ār- Br:
B- 1 ..
Cte
and 0; = 1 Br, Oq II's (ks. All are closed-form coefficients derived from a predefined noise schedule. In practice, the true sample is not accessible during inference, and is typically replaced by a model prediction do obtained via denoising estimation. Equation thus serves as the foundation for approximate posterior sampling, provided that ao is sufficiently accurate estimate of the ground truth zz--
Theoretically, if we assume to = Tp holds exactly (i.e., the prediction perfectly matches the ground- truth image), then the entire reverse process becomes fully deterministic and analytically tractable, with the only source of stochasticity being the injected noise at each step. In this idealized setting, the reverse sampling trajectory fully governed by closed-fomm ffrm probabilistic transitions. This forms the basis for Lemma. 1 (For brevity, the full proof is provided in the Supplementary Material A.1). Lemma (Gausaa-Gaussian closure). Let ]
Rdd satisfy the recursion
Ik-1- = Ck Ig + dk + Eki Ek ~ Ex),
Ex LI Ex+1.....
(2)
where Cg Rxd dy E Rd, and Σg Rddd are deterministic. Then, for every integer m with 1 < m S k, Fk-m m is again an affine Gaussian functttoo of Ix:
Cg
II C i=0
I
+
III
Ck- da-i + (m)
(3)
mm)

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where
x = ((
(I. j=1
(m) ~ N((0 )
While the ideal condition 2.- = zo rarely holds in practice, the following properties justify the use of Co in the multi-step formulation:
(i) The training objective of standard DDPM is explicitly designed to minimize the discrep- ancy between the predicted noise and the true noise. Consequently, the denoising model co(#,, t) implicitly learns reconstruct a close approximation of zg through the reverse reparameterization formula.
(ii) Both empirical observations and theoretical analyses suggest that åg varies slowly with respect to at large diffusion steps. That is, for segment [ta, te] with t, >> te and moderate length (e.g., f - te < T), we (Te, t,) ss 2p (2,, t) for all t E [fs,, te]. due to the temporal smoothness of model predictions in the doise-dominated regime.
Therefore, it reasonable treat in as fixed within a short temporal window. Under this assump- tion, multiple single-step reverse transitions can be analytically composed into a single multi-step Ilfine-Gaussian kernel. This approximation and Lemma. I form the basis for Theorem 2, which characterizes the closed- reverse process from t, to te (For brevity, the full proof is provided in the Supplementary Material ).2)
Lemma 2 (Closed-form reverse from t. + te). Fix indices 0 S te < t, S T, and let the single- step coefficients (A,, oi) be defined as in Eq. 12. Then the aggregated reverse kernel over to > te is affine- -Gaussian
St. = =TT, It, + E): 80 + Eto.
where
2
4
Bi, E
A By, Et, ~ 0, i=
Σ
Σ 1=
By
of
i=t+1
j=++1
j=i-1
Therefore, it can be observed that in the limited segments (e.g., tu - fe), there are the three scalars (II;; Ei, Et),, allowing us to precompute them once and re-use them during sampling. Lemma. enables theoretical computation of posterior transitions between any two timesteps t, and f.. allowing multi-step sampling in a manner distinct from DDIM. However, while the -aauss-a transition provides an efficient coarse approximation for the reverse path It,, It. the approximation may introduce residual artifacts in parctice. It is caused by the strong noise attenuation and the fixed tn assumption. Moreover, since 2; inherently entangles both the foreground and the background content, direct sampling through the affine-Gaussian kernel will ignore the critical spatial structure discrepancies for SIAS.
To better preserve anomaly-localizer information while ensuring smooth global composition, we explicitly decompose the clean sample ze into two disjoint components:
X x x
(5)
where xi" is the anomaly-only region (masked by M). and x bg is the background. The background is independently forward-diffusee
X
bg g(x, X. x)
(6)
while the anomaly foreground is refined by the learned FARM module (introduced later in Sec. 3.2), and merged with the background through spatial masking:
FARM(X..)
X1, = Mox + (1-
This foreground aware fusion ensures consistent noise levels between anomalous and normal regions at each step. preserving local anomaly salience while maintaining global visual coherence. In practice, we also introduce final fine-grained refinement stage using standard DDPM posterior sampling for small / (e.g., L = or = 2) to restore the alignment between the coarse trajectory and the ground-truth posterior, and enhance fine-scale texture fidelity. The complete sampling algorithm summarized in Algorithm 3.
5

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3.2 Foreground-Aware Reconstruction Module
As discussed above, conventional dif- fusion models treat all spatial regions uniformly, which limits their abil- ity to synthesize localized anoma- stops lies. To address this, we propose the Foreground-Awar Awarre Reconstruc- tion Module (FARM), which recon- structs clean anomaly-only content from noisy latent inputs under both temporal and spatial guidance. As lustrated in Fig. 2, FARM adopts an encoder-decoder architecture. The en- coder fenc extracts deep representa- tions from the noisy latent 2,,, while the decoder fdee progressively upsam- ples and integrates the binary mask M multiple resolutions, ensuring spatial alignment with anomaly regions throughout the hierarchy.
Sinusoidal embedding
Signeid
Linear Projection
Cooeon Oilitonn
fene
dec
Resion
Figure 2: The architecture of FARM. Given noisy latent at, and mask M,, the encoder fene extracts features Re,, which is also modulated by brcckrouud-adaptiie soft mask M and related timestep embedding Tr.- The decoder fdee then reconstructs the anomaly-only latent 4 which is forward- diffused to produce anomaly-aware noise.
To encode temporal context, we initialize sinusoidal timestep embeddings Tr, Id and project them into latent space via a learned linear layer. These embeddings are added to the encoder output, modulating feature responses based on the current noise level and allowing the decoder to reconstruct temporally consistent structures.
In addition, to modulate background activation, we introduce background- soft mask:
M = Ma + -1 ((bg(TT,))
(8)
where Ma is downsampled binary mask aligned with encoder resolution, and fig is lightweight MLP. This design allows FARM to suppress irrelevant background features while adapting to the current timestep. The encoded feature computed as:
2t, = M [xnc(Xt,) + Proj(Tr.):
and decoded into an anomaly-only latent: 4.00 = fdec(ze,
To inject anomaly-awan noise into the sampling trajectory, the reconstructed anomaly is forward- diffused:
Cie -I Ci e, c0,,
(10)
and replaces the original noise in masked regions:
fr (1 M) X4, + M 22
(11)
During training, FARM is supervised to ensure that the reconstructed anomalies match the masked regions of the noisy inputs. During inference, temporal and spatial guidance together enable FARM to introduce localized and temporally coherent anomaly signals into the reverse trajectory, ensuring alignment with the global generative process while enhancing fine-grained control.
4
Experiments
4.1 Implementation Details.
Datasets. We evaluate FAST on two widely-used industrial anomaly segmentation benchmarks: MVTec-AD [1] and BTAD [21]. For each anomaly class, we synthesize image-mask pairs using normal images, binary masks, and text prompts describing anomaly semantics. A total of 500 samples are generated for each anomaly type within class, with approximately one-third used for training and the remainder reserved for evaluation. This design ensures sufficient structural diversity while maintaining training efficiency. Mask Generation Strategy. Our mask synthesis consists of two complementary components: (i) geometric augmentation of real anomaly masks via operations like rotation and flipping (ii) synthesis of new masks using a Latent Diffusion Model (L.M) pre- trained on real anomaly mask examples, which follows the protocol of AnomalyDiffusion [15]. All

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synthesized masks undergo manual screening to guarantee visual realism, structural diversity, and consistency with typical industrial abnormal structures. Evaluation Metries. We report performance using mean intersection over union (mloU) and pixel-wise accuracy (Acc), following standard practice in anomaly segmentation. Baselines. FAST is compared against six representative anomaly synthesis approaches: CutPaste [16], ARA [40], GLASS [2], the GAN-based SOTA method DFMGAN [8], and diffusion- SOTA models Anomaly Diffusion [15] and RealNet [43]. To simulate realistic deployment scenarios, we pair all generation methods with lightweight segmentation networks, including Segformer [34], BiSeNet V2 [39], and STDC [9]. As our method adopts the same prompt-driven synthesis setup as AnomalyDiffusion [15], we omit the details here for brevity. Full specifications of the textual configuration, as well as other implementation details, including dataset preprocessing, sampling schedules, loss weights, and hyperparameter settings, are provided in the Supplementary Materials A.5.
4.2 Comparison Studies
Table 1: Evaluation of pixel-level segmentation accuracy on extended MVTec data using real-time Segformer. Detailed per-category results for other real-time segmentation model, such as BiseNet V2 and STDC are reported in Supplementary Material A.6.
Category
CaiPasie
DRAEM
CLASS
DFMGAN
RealNet
Dirfissioo
FAST
mioU
Acc
milo
Acc
mloU
Acc
iiloU T
Ave
mlel
Avc
mlot
Acc
Acc
bottle
79.49
79.51
81.99
70.26
76.30
86.86
90.90
vable
55.40
60:49
64.52
70.77
58.81
62.32
62.10
64.87
62.51
69.27
62.49
74.48
73.71
77.94
capoale
35.15
40.29
$1.39
62.32
34.12
38.04
41.29
45.83
46.76
51,91
37.75
44.72
63.22
71.12
carpet
66.34
77.59
72:57
81.28
70.11
77.56
71.33
83.69
68.84
79.15
64.67
73.59
73.84
83.53
grid
72
37.43
bazel nut
56.95
60.72
84.22
99.74
55.51
57.43
83.43
86.03
60.18
63.49
48
90.81
94.79
leather
$7.23
63.49
64.12
71.49
62.05
73.38
60.96
68.02
68.29
77.16
56.45
62.51
66.60
74.18
netal_nux
88.78
90.94
93.51
96. 10
$8.15
90.52
92.77
94, 94.93
91.28
94.09
85.00
91.10
94,65
96.88
43.28
47.11
46.99
49.76
41.52
43.54
$7.19
90.05
47.32
58.31
83.21
89.00
90.17
94.07
serew
31.35
59.03
35.94
42.37
Gle
85.33
91.60
89.21
93.74
85.67
90.28
88.87
91.96
33.53
87.30
$4.29
89.72
90.13
93.77
boothbrush
39.40
63.93
65.35
79.43
53.75
60:46
61.00
70.50
57.68
72.03
4% 68
64. 41
74.9%
88.63
mansistor
65.03
71.05
59.96
62.18
29.
30.67
73.
78.48
63.71
66.79
79:27
91.74
91,80
94,50
73.28
50.91
74.62
zipper
65.39
71.89
69.29
79.36
98
79.31
66
70.50
68.78
78.50
36
72.6 66
72,80
84.73
Average
55.87
63.81
66.86
M.75
56.23
61.41
67.71
74.07
62.89
71.70
62.85
72.06
76.72
8337
Table 2: Evaluation of pixel-level segmentation accuracy on extended BTAD data using real-time Segformer, BiseNet V2 and STDC.
Buckboue
Category
CurtPaste
DRAEM
GLASS
DEMGAN
RealNet
AnumalyDiffemm Diffusson
FASY
Acc
mlcl
Ace
A.c
sanuU 1
Acc
mloU
Acc
[
Aoc
Auc
01
66.94
78.30
57.86
50.10 14
68:01
70.57
67.02
78.03
67.17
$0.20
66.55
76.31
75.03
86.12
Segformer
02
66.04
83.64
69.52
$2.95
69.99
83.58
63.75
$4.92
70.64
$3.90
68.05
84.74
70.63
81.63
03
50.96
60.41
50.39
54.30
51.77
53.53
33.95
41.55
48.76
$7.50
54.85
80:20
79.40
85.64
01
57.15
69.88
16
63.48
44,09
50:57
49.49
59.20
45.45
$7.65
46.66
55.18
58.74
68.95
BieeNet V2
02
59.45
82.05
66 46
80:29
66.37
79.46
66.02
79.31
66.
81.67
65.57
84.00
68.02
82.40
03
31,84
40.62
15
38
37.15
21.48
29.55
33.11
42,27
74.41
77.87
92.49
DF
48.06
39.86
FT
85.56
35.51
6012
4468
51.71
123
-.9.2
-9.85
35.55
-4335
55327
STDC
59,80
77.57
81.9
38.00
25.01
16.55
41.71
Anomaly Segmentation Table. and 2 report pixel-level segmentation results on various datasets using Segformer trained with FAST-augmented data. We observe that FAST achieves an average mIoU of 72% and accuracy of 83.97% significantly outperforming the strongest prior method, DRAEM (74.5%% Acc), by 9.22 points, respectively. Improvements are particularly notable in challenging categories: in capsule, FAST increases mIoU from 51.39% (DRAEM) to 63.22% (111;83); on grid, from 47.75% to 52.45% (14.70); and on transistor, from 84.22% to 91.80% (17.58). Even in relatively easier categories such as bottle and rile, FAST still yields consistent improvements of 7.35 and 0.92 mloU points, respectively. These results demonstrate that the combination of mask-aware noise injection via FARM and coarse-to-fine accelerated sampling via AIES enables more realistic and structurally coherent anomaly synthesis, leading to superior segmentation performance, Similar trends are observed when replacing Segformer with other real-time backbones such as BiseNetV2 and STDC, shown in Supplementary Materials A.6, confirming the generalizability of FAST across different segmentation architectures.
Qualitative Comparison. Fig. 3 visually compares anomaly samples synthesized by differ- ent anomaly synthesis methods across several MVTec-AD categories. It can be observed that traditional unsupervised methods such as CutPaste and DRAEM generate anomalies by over- laying arbitrary textures or patches without any semantic guidance. For instance, the ca- ble category, anomalies produced by CutPaste appear as artificial, block-like overlays lack- ing meaningful texture or structure. Similarly, DRAEM and GLASS introduce unrealistic color distortions and incoherent patterns in the transistor category, which deviate significantly
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from typical industrial anomalies. DL-based approaches (DFMGAN, RealNet, and Anomaly- Diffusion) generate more visually plausible results, but still exhibit noticeable shortcomings. For instance, RealNet often intro- duces color shifts and boundary ar- tifacts, as seen in the tile and cable cases, where anomalies appear overly smooth or blurred. DFMGAN and AnomalyDiffusion are able to synthe- size more coherent shapes (e.g., spray- paint-like anomalies in hazel nut), yet they suffer from inaccurate bound- aries and structural mismatches, as is especially evident in the file (Anoma- lyDiffusion) and cable (DFMGAN) categories. In contrast, FAST consis- tently produces anomalies that closely resemble realistic anomalies while maintaining precise alignment with the annotated masks. In the metal nur and hazel nut cases, FAST is the only method that preserves fidelity and shape within the intended regions, demonstrating superior controllabil- ity and structural consistency. These results validate the effectiveness of the proposed FAST in segmentation- oriented anomaly synthesis. 4.3 Ablation Studies
curas
DRADM
CLASS
DINEGAN
FAST
RRRE
Figure 3: Visualization results of different anomaly synthesis methods on the MVTec dataset. Columns correspond to synthesis methods (from left to right: MVTee AD, CutPaste, DRAEM, GLASS, DFMGAN, RealNet, Anomaly Diffusion, FAST), and rows correspond to product categories (from top to bottom: hazel_nut, transistor, tile, metal_nut cable).
The Impact of AIAS. We compare proposed AIAS strategy with several widely-used training- free samplers, including DDPM [12] with 1000 steps, DDIM [27] with 50 steps and PLMS [17] with 50 steps. These methods represent sfat-offthhe-at discrete-time sampling approaches for diffusion- models. To ensure fairness, we exclude continuous timen solvers, as they rely on fundamentally different formulation based on ODEs or SDEs, which necessitates distinct training paradigm and architectural adjustments incompatible with our discrete-time framework. Quantitative results are reported in Fig. 5. While DDPM achieves competitive results on certain categories carpet tile), it requires 1000 iterative steps, making it over 20x slower than AIAS in practice. DDIM and PLMS, though more ef- ficient, exhibit inconsistent perfor- mance across categories and often underperform AIAS, particularly challenging textures such as capsule, grid, and transistor. In contrast, AIAS achieves the best results on the ma- jority of categories and consistently provides competitive or superior per- formance in both mloU and accu- racy, demonstrating its ability to gen- anomalies
Hazel, pat
Scew
erate segmentation-alignen with significantly fewer steps. It fur- ther indicates that by analytically ag- gregating multiple DDPM transitions into coarse-to-fine segments, AIAS reduces the discretization eтror in- herent in single-step samplers (e.g.. DDIM) or fixed multistep solvers (e.g., PLMS), allowing closer ap- proximation of the true posterior within just 50 steps. Fig. further illustrates the qualitative advantage. For example, in the hazel _ut class, the anomalies produced
Misec
DDPM
DDIM
PLMS
AIAS
Figure 4: SIAS results with other sampling strategies. Columns correspond to sampling strategies (from left to right: ground truth, DDPM (1000 steps). DDIM (50 steps), PLMS (50 steps), AIAS (50 steps), and rows correspond to categories (from top bottom: hazelnut, pill, screw). Fur- ther qualitative results (trained on MV'Tec and BTAD) are provided in the Supplementary Materials A.8.

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by DDPM, DDIM, and PLMS display noticeable color inconsistencies near the anomaly bound- ary, resulting from distributional mismatch with the background. In comparison, FAST-produced anomalies that are well blended into the context, with sharper and more realistic structural alignment.
Although this result may seem coun- terintuitive, since fewer sampling steps usually imply degraded visual quality. And we believe the difference primarily stems from the evaluation objective. Specifically, DDPM sam- pling remains the best performer in terms of pure visual fidelity metrics in our work, but AIAS is designed to optimize downstream segmentation performance rather than perceptual re- alism alone. As shown in Table 3, moderately increasing the sampling steps can slightly enhance image qual- ity. yet it also leads to a substantial rise in inference time. More impor- tantly, excessive steps tend to weaken the anomaly localization consistency and thus degrade segmentation per- formance. Therefore, AIAS achieves a more favorable trade-off between SIAS and visual fidelity. Table 3: Comparison of pixel-level anomaly segmentation using different steps on the MVTec dataset.
(1)
(61)
(e1)
(a2)
(12)
(1000 shops)
DDIM (50 steps)
PLMS (50 steps)
ATAS (50 stepe)
Figure 5: The effect of different sampling methods on SIAS in the MVTec dataset. Top row shows per-category segmen- tation performance using mloU; bottom row shows perfor- mance using Acc. Detailed per-category results of AIAS reported in Supplementary Material A.6.
Tailppey
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Figure 6: Segmentation-ooiennee industrial anomaly synthesis results different steps of AIAS. Columns correspond to increasing sampling steps T' (from left to right), and rows correspond to product categories (from top to bottom: capsule, bottle, carpet).
The Impact of AIAS under different steps. We further investigate the segmentation performance of AIAS under varying numbers of reverse steps, ranging from 2 to 1000, as reported in Table. 3. Remarkably, AIAS approximates the performance of full-step DDPM using only 10 steps, and reaches near-optimal results by 50 steps, demonstrating the effectiveness of our coarse-to-fin aggregation strategy. Performance improves rapidly as t increases from 2 to 50, since early segments capture the global layout and coarse structure of anomalies, which are most relevant for segmentation. This trend is also visually confirmed in Fig. 6. Beyond this point, performance gains gradually saturate, indicating that additional steps primarily refine high-frequency details with limited impact on segmentation accuracy. Notably, when é 1000, AISA degenerates to the original DDPM sampling

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process, where each segment [te, corresponds to single denoising step. The convergence of performance this point validates that our multi-step analytical updates provide faithful approximation of the full diffusion trajectory, preserving both global semantics and fine-grained anomaly cues while significantly reducing sampling cost. Furthermore, excessive denoising steps may introduce over-smoothing or amplify reconstruction inconsistencies, potentially weakening the structures. Overall, these results
alignment between synthesized anomalies and segmentation- highlight that AIAS not only accelerates sampling, but also introduces inductive structural bias beneficial for anomaly segmentation. In practice, the optimal balance between quality and efficiency is achieved within 10-50 steps.
The Impact of FARM. To evalu- ate the effectiveness of FARM, we conduct an ablation study by com- paring the model's s performance with (w/ FARM) and without (w/o FARM) FARM under identical AIAS settings. Results on the MVTec dataset are reported in Fig. 8. The inclusion of FARM leads to substantial im- provements in segmentation perfor- mance, with average mloU increas- ing from 65.33 to 76.42 and accu- racy increasing from 71 1.24 to 83.97. partieu-
Wood_color
Tile
Hazel_ Becee__ut__or crack
Cable missing,
Feaal 0/m)
NN Pawwee
Qualitative ablation results with and without FARM on MVtec dataset. Columns correspond to cate- gory-anomaly pairs (from left right: Wood Wood_color, Tile_oil oil, Hazel_nu crack, Cable_ Soble_missing. wire; and rows correspond to ablation strategy (from top to bottom: without FARM (w/o FARM) and with FARM (w/ FARM).
Figure 7:
The performance gains larly pronounced in challenging cat- egories characterized by fine-grained or complex structures, such as capsule (114.1 mloU), grid (114.7 mIoU), and transistor (129.5 mloU). Even in relatively easier categories like tile and hazel_nut, tently enhances accuracy and boundary localization, as shown Fig. 7. More detailed analysis of FARM can be found in Supplementary Material A.7.
nut, FARM consis-
máos
Effex FARM
100
PARSI
Figure 8: Qualitative ablation results with and without FARM on MVtec dataset. Columns correspond to product categories and rows correspond to mlou and Acc). Detailed per-category results for ablation study of FARM are reported in Supplementary Material A.7.
5 Conclusion
In this work, we proposed FAST, ceeementttiionooiinnte foreground- diffusion framework tailored for anomaly synthesis. To address the limitations of existing anomaly synthesis methods, specifically their limited controllability and lack of structural awareness, we introduced two key components: the Foreground-Awan Reconstruction Module (FARM), which adaptively injects anomaly-aware noise each sampling step, and the Anomaly- Informed Efficient Sampling (AIAS), a training- free strategy that accelerates sampling via coarse-to-fin aggregation. Built upon discrete- anomalies with
time latent diffusion backbone, FAST enables the synthesis of segmentation-aaignnn as few as 10 denoising steps. Extensive experiments on MVTec-AD and BTAD demonstrate that FAST outperforms existing baselines downstream segmentation. FAST represents promising step toward controllable and efficient segmentation-oriiette industrial anomaly synthesis.
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Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant No. 62206122) and the Tencent "Rhinoceros Birds" - Scientific Research Foundation for Young Teachers of Shenzhen University.
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NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: The abstract and introduction accurately reflect the contributions and scope of the paper. The paper introduces FAST, a foreground-awan aware diffusion framework with two core modules: Anomaly-Infone Informedd Accelerated Sampling (AIAS), which enables coarse- to-fine training-free sampling with up to 100x speed-up, and the Foreground-Aware Re- construction Module (FARM), which constructs anomaly-awan noise at each denoising step to enhance abnormal regions. These claims substantiated by theoretical derivations, algorithmic design, and comprehensive experiments showing consistent improvements on MVTec and BTAD datasets. The introduction does overclaim extend beyond the scope addressed in the experiments, and the focus remains tightly aligned with segmentation- oriented industrial anomaly synthesis.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made the paper and important assumptions and limitations. A No or
NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.
2. Limitations
Question: Does the paper discuss the limitations of the work performed by the authors? Answer: [Yes]
Justification: The paper includes a discussion of the limitations of the proposed approach in both the introduction and experimental sections. Specifically, it acknowledges that while the coarse-to finfiie accelerated sampling strategy in AIAS achieves substantial efficiency gains, it may introduce residual artifacts when the step is too small (t or 2). These parts are explicitly explained in the method and ablation sections. The discussion also reflects the balance hetween sampling speed and segmentation accuracy, thus providing a realistic scope for the claims.
Guidelines:
The answer NA means that the paper has no limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors encouraged to create separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g., independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect on the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution low or images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.
The authors should discuss the computational efficiency the proposed algorithms and how they scale with dataset size.
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If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and fairness.
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't 't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community, Reviewers will be specifically instructed
penalize honesty concerning limitations.
3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
Answer: [Yes]
The paper includes two key theoretical lemmas, both of which are formally stated with clearly defined assumptions and notations. The corresponding full proofs are provided in the supplementary materials, and their relevance to the proposed multi-step posterior approximation is explicitly discussed in Section. 4.3. These results establish the mathematical validity of the accelerated sampling trajectory used in AIAS, All theorem statements are cross-referenced and grounded in standard DDPM formulations, ensuring both correctness and completeness.
Justification:
Guidelines:
The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced in the statement of any theorems.
The proofs can either appear in the main paper or the supplemental material, but they appear in the supplemental material, the authors are encouraged to provide short proof sketch to provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should properly referenced.
4. Experimental result reproducibility
Question: Does the paper fully disclose all the information needed to reproduce the main ex- perimental results of the paper to the extent that it affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided or not)?
Answer: [Yes]
Justification: The paper fully discloses all implementation details necessary to reproduce its main experimental findings. including used datasets, model settings, evaluation metrics, and comparison baselines. The supplementary material provides further configuration details such as prompt templates, sampling step schedules, hyperparameters, and segmentation backbones. its algorithms offer full pseudocode of the core modules. This level of detail ensures that other researchers can independently replicate the results.
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Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution a novel architecture, describing the architecture fully might suffice, or if the contribution is specific model and empirical evaluation, it may be necessary to either make possible for others to replicate the model with the same dataset, provide access to the model. In general. releasing code and data is often
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one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how replicate the results, access to a hosted model (e.g., in the case of a large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
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Diverse segmentation models: For each synthesis method, train and evaluate three real-time segmentation backbones (SegFormer, BiSeNet V2, and STDC), yielding consistent performance gains across architectures.
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We demonstrate the robustness and statistical reliability of our findings through extensive evaluations that span multiple benchmarks, segmentation backbones, and anomaly-synthesis baselines. we report results across 18 categories 3 backbones 6 baselines-iee over 324 individual experimental settings, and observing uniform improvements, we effectively capture variability arising from different data domains, network initializations, and anomaly types. Although we did not include classical eπror bars, this large scale, cross domain evaluation serves as a comprehensive measure of statistical significance.
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21

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A Supplementary Materials
A.1 Proof of Lemma
Lemma [Linear-Gaussian closure] Let {oa] C Rd satisfy the recursion
Tk-1 = Cs T& + dx + Ek: Es),
Ek di F
(12)
where Cg RRdd dg Rd, and Σn Rddd deterministic. 1 S m S ki Th-m is again an Gaussian function of Txi
Then, for every integer with
Tk-m
II ==0
Ck-
Ik
+
Σ EII
Ck-)
du-i + &k
(m)
(13)
=:0(m
= mm)
where
m-
&k
(m)
NO0, _(())
[(m)
Σ
(II
[I
Ck-}
Ex-i Ck-))
(14)
j=1
Proof.
Base case (m 1).
Eq. 13 with is exactly the recursion Eq. 12.
Induction step.
Assume Eq. 13 and .14 hold for m = with 1 s k:
Tk-r = xf xx
dl + t
(r)
(r)
~ ~(0,
st Lat
*k
Apply Eq. 12 once more:
I [k-(r+1) CK- + de-r + ER--
-Ck-r(C) dle +e( + d t
(15)
Ck-rck (r) ark + Ck-rdh (1) de Ck-red (r)
+ eek-r
cfr+1)
el
(r+1) Since (1) and Ek-r are independent zero-mean mean Gaussians, their linear combination ek remains Gaussian with covariance >)(+1) Ck-, CT_ + Σk-r, exactly matching Eq. 14 for m r Hence the statement holds for all m by induction.
Remark 1. The empty product convention IT; Ck-j La is used in Eq. 13.
A.2 Proof of Lemma
Lemma 2 [Closed-form reverse from t, + tz] Fix indices 0 < te < <t, < T, and let the single- step coefficients (A,, B, of) be defined in Eq. 12. Then the aggregated reverse kernel over + le is affine-Gausiin:
Dt. I1 Fí, + Et. so + Elat
(16)
where
Bi, E =
Σ
A II Bj,
Et. ~ N 0, Σ
II j=i-1
Bj
o
is +1
is
j=i+1
imte+1
22

---

Proof. Apply Lemma with Cs Bk. d2 = A, Ex = L and m = = -, Equations Eq. 16
coincide with the general expressions Eq. 13 Eq. 14, so the result follows directly.
A.3 Loss function
The training objective of FAST consists of two components: the standard denoising loss and the reconstruction loss. The denoising loss encourages accurate noise prediction across all spatial regions, while the reconstruction loss ensures that FARM accurately reconstructs anomaly-only content, and allowes the inserted noise remain compatible with the global sampling dynamics, thereby preserving the stability of the overall generation process.
FAST X1- Exxoe,t ||E Es (Xi, (x,,,t))1 1)]l
(17)
+ A2 E Exg x..M
(1,( - x0 [
where e ~ ((0, is the reference noise for the denoising target, the x is the anomaly-only content with pure background, eo (x,, and Fg denote LDM and FARM, respectively. The scalar weights Å and x2 balance the contributions of the two losses
A.4 Pseudo-code of AIAS
Algorithm Anomaly-Infommn Accelerated Sampling
Input:
Mask M, clean background full+ clean background latent x prediction Xy from co boundary schedule B = {t1 < t2 < ... tx T} and t1 2 in our experiments
bg
Output: Syntheised image Xfull
Initialize noisy latent Xxx (0. for K do 1 < lg. te 4- 4-11
Coarse multi-step reverse from to + to
Define cofficients A₁ = I-6e
I6. B₁ = (- and o/ = 1-ā.-1
1-a, Be
Compute μ - (II B.)x,, + +Ei A IT
B,)
Sample noise E ~ NO0, (Eiro+1 (I B,) B3)00 0?)1))
X1, #
Forward diffuse background to te X by (1 (t,)1)
x N(Van,
bg
x + FXRM(X..)
X,, MO R (1- x
end for
Fine posterior refinement for 11 down to 0 do
Predict &n < (x,, X,-1 +- q(x,11 X,, Xo)
end for
Xfull f- .M 3 Decode(x0) (x)) +11 (1- MM ②
bg Xfull
A.5 Training Configuration
To synthesize abnormal data, we utilize the complete set of normal images, their corresponding masks, and associated textual descriptions for each type of anomaly within every category of products. Notably, the original GLASS framework comprises three branches,a normal-sample branch, feature- level anomaly synthesis branch guided by gradient ascent, and an image-level branch that overlays external textures. Therefore, its output unsuitable directly for pixel-level anomaly segmentation and other downstream sgementation models. Accordingly, we revised its synthesis process to align with our segmentation-basse evaluation protocol. We release the modified implementation together with the FAST to ensure fairness.
23

---

Model Settings. We set the total number of diffusion steps during training to T = 1000. For sampling, the range from step 2 1000 is uniformly divided into 50 steps, followed by a fine-grained adjustment phase over the initial steps (0, 2] to enhance reconstruction fidelity. The model is trained with a batch size of and a learning rate of 1.5e-4. The text embedding E consists of 8 tokens.
Prompt Construction. For the MVTec dataset, prompts are formed by appending the anomaly type the product category name. For BTAD, due anonymized category labels, we use a generic prompt: "damaged". Textual embeddings follow the protocol of AnomalyDiffusion. where each prompt is tokenized into 8 discrete units and embedded using pre-trained BERT encoder [5].
Hardware and Runtime, All models are trained on a setup of eight NVIDIA A100 GPUs (40GB each), with training proceeding for roughly 80k iterations.
A.6 Other quantitative experiments
We provide extended evaluation results to complement the findings reported in the main manuscript. We present detailed, category-wiss performance metrics on the MV'Tc and BTAD benchmarks, employing BiseNet V2 and STDC as the segmentation backbones. Moreover, we further analyze the influence of different sampling exccept our AIAS method downstream segmentation performance using Segformer.
All experiments are conducted under identical settings to those used in the main study. The results consistently demonstrate that our proposed FAST framework significantly outperforms existing anomaly synthesis techniques in enhancing segmentation accuracy across diverse categories.
Table 4: Evaluation of pixel-level segmentation accuracy on extended MVTTe data using real-time
BiseNet V2.
Calegory
CaiPasle
GLASS
DFMGAN
RealNel
FAST
Acc
minl
mlot
Acc
mloL
boute
71.77
78.37
75.13
79.17
57.81
60.75
61128
71.31
72.16
75.35
75:25
85.11
78.48
83.18
cable
46.00
57.08
53.88
60.96
16.63
16.65
57.09
63.25
51.22
62.32
60.55
74.96
70.91
75.77
eapsale
37.04
36.82
19.53
51.
28.40
35.97
26.77
32.87
48.56
54.22
varpel
58.98
72.22
68.42
77.21
64.77
73.93
62.13
67.98
8.98
9.01
58.18
64.69
68.94
77.20
grid
24.68
44.17
42,81
63.34
6.50
6.91
10.17
15.23
10.61
11,47
18.98
24.30
39,
51.77
bazel nut
47,93
53.57
74,83
81.35
71. 54
75.62
79.78
84.37
60.16
65.93
57.32 26
70:41
88.08
93.45
lenther
31,11
58.36
55,07
61.58
57.98
71.84
31.77
34.82
50.02
10
67.18
74.23
metal_nut
91.58
pill
55.62
67.04
45.23
48.99
23.88
24.15
$2.40
84.30
72.59
86.32
$0.87
87.02
85.12
89.60
screw
4,88
6.63
25.08
35.77
12.32
13.11
38.14
40.36
22.35
23.78
23.23
29.91
33.49
41.12
tile
76.25
85.75
86. 17
90.45
77.32
80.28
85.69
90.12
77.16
84.84
79.32
85.63
86.86
92.12
noothbrush
79.15
38
$1.97
73.04
N7.34
tramsistor
44.18
51.79
59. 88
96
44.93
53.04
76.52
82.13
61.68
68.59
76.34
89.94
91.10
93.81
wood
35.51
46.00
49.0 82
62.09
36.41
51.10
$1.84
63.70
47.29
61.35
$2.06
72.75
681 15
72 60
zipper
$1.61
63.09
66.88
75.75
61.90
70.07
60.61
71.11
66.09
77.54
57 86
62. 64
66.
78.16
Average
Table 5: Evaluation of pixel-level segmentation accuracy on extended MV'Tec data using real-time STDC.
Category
CutPaste
DRAKM
GLANS
DFMGAN
RealNet
Anomaly Diffission mlot.
FAST
mint
Acc
mint!
Acc
minU
Acc
minUT
Acc
mlot
Ace
Ace
minll
Acc
71.37
63.22
69.25
76.82
cable
42.88
54.74
501022
49.38
57.80
$7.74
62.86
35.97
38.81
74.23
capeale
21.73
30.72
36.51
41.68
22.91
27.18
25.60
27.96
31.08
34.25
22.00
26.06
49.35
55.29
50.79
66.68
66.28
76.70
63.18
77.85
58.58
71.83
57.48
68.51
56.16
68.47
64.52
75.00
grid
25.75
301.2
19.89
24.72
24.63
20. 82
255
bazel
75.75
83.66
68.57
85.83
leather
38.12
58.63
24.63
56.84
57.53
73.90
21:29
22.28
36.76
53.88
46.98
50.89
60.38
75.90
metal_nut
$1.13
86.63
91.12
94.08
83.97
89.37
90.58
92.73
86.85
91.45
85.81
90.06
93.01
95.32
50.00
60.28
55.47
61.05
44.18
48.11
80.41
82.55
63.96
65.96
75.23
81.35
82.15
86.48
2.00
69.86
18
84.75
91.31
79
88.6
89.72
70.29
77.70
76.96
26.29
noochbrush
41.19
$2.81
53.72
76.55
37.46
40.91
36.78
38.94
33.85
43.03
35.39
48.93
75.76
87.32
tramsistor
58.24
68.80
65.57
80.31
62.6
69.32
78. 38.38
87.23
62.57
72.45
96
83.28
93.01
96.05
zipper
59.24
61.03
68.53
59 07
69.39
71.52
52.03
67
Average
45.41
$3.90
57.51
66.19
$1.02
59.13
52.76
S6.81
49.27
$6.24
$2.76
63.30
65.80
72.85
A.7 More analysis of FARM
These improvements of FARM are not only empirically significant, but also consistent with intuitive understanding. Without FARM, the segmentation-oriente industrial anomaly synthesis relies solely
24

---

Table 6: Ablation study of FARM on the MVTec dataset using the real-time Segformer.
Category
mloU (w/ FARM)
Acc (w/o FARM)
mioU (w/ FARM)
Acc (w/ FARM)
bottle
80.65
83.46
86.86
90.90
cable
65.99
70.50
73.71
77.94
capsule
49.08
53.25
63.22
71.12
carpet
72.46
73.84
83.53
grid
37.79
42.61
52.45
70.70
hazelnut
69.20
72.55
90.81
94.79
leather
61.42
65.91
66.60
74.18
metal_nu
89.59
94.3
94.65
96.88
pill
46.73
48.44
90.17
94.07
screw
46.48
54.42
49.94
57.48
tile
88.91
93.28
90.13
93.77
toothbrush
66.29
81.40
74.98
88.63
transistor
62.35
67.46
91.80
94,50
wood
71.55
79.47
78.77
86.31
zipper
71.40
72.80
Average 65.33
71.24
76.72
83.97
Table Ablation Study of AIAS with other training- free sampling Methods MVTec-AD data via
Segformer.
Category
DDPM (1000 steps)
DDIM (50 steps)
PLMS (50
steps)
ATAS (50 steps)
mloU f
Acc f
mloU
Acc 1
mIoU f
Ace
mloU
Acc
bottle
81.65
84.83
82.87
86.03
81.49
84.44
86,86
90.90
cable
73.45
78.06
74.21
78.41
74.78
78.91
73.71
77.94
capsule
60.01
66.87
58.02
64.03
56.92
61.90
63.22
71.12
carpet
75.99
84.14
75.33
83.58
75.41
82.39
73.84
83.53
grid
50.91
63.19
50.85
67.91
50.43
61.42
$2.45
70.70
hazel_nut
89.81
93.31
89.69
93.03
89.42
92.96
90.81
94.79
leather
71.03
80.32
66.00
72.48
71.85
81.47
66.60
74.18
metal nut
94.63
97.18
94.50
96.47
93.93
96.69
94.65
96.88
pill
89.36
93.79
89.84
93.03
89.93
93.66
90.17
94.07
screw
49.35
59.18
48.89
57.26
48.78
55.62
49.94
57.48
tile
91.01
94.72
89.23
92.90
89.96
93.25
90.13
93.77
toothbrush
76.10
91.25
74.79
88.48
76.02
91.00
74.98
88.63
transistor
89.59
93.41
89.35
92.37
89.17
91.99
91.80
94.50
wood
80.03
85.30
79.29
84.03
79.61
84.65
78.77
86.31
zipper
72.45
82.35
71.01
83.00
72.06
81.02
72.80
84.73
Average
76.36
83.19
75.59
82.20
75.98
82.09
76.72
83.97
on frozen pre-trained weights and weak conditioning from learned textual embeddings. This limits the model's s ability capture the structural characteristies of industrial anomalies, often leading visually perturbed but semantically uninformative results. contrast, FARM explicitly reconstructs anomaly-only content from noisy latents and produce spatially localized, anomaly- awware noise into the sampling process. Additionally, by incorporating both spatial masking and timestep encoding, FARM guides the model focus on abnormal regions-information that would otherwise be uniformly treated in the absence of FARM. Together, these mechanisms improve the structural fidelity, localization precision, and segmentation relevance of synthesized anomalies.
A.8 Other qualitative experiments
We also provide additional qualitative results to supplement the main paper. Specifically, we present synthesized anomalies across multiple categories from MVTec and BTAD, along with comparisons against CutPaste, DRAEM, GLASS, RealNet, DFMGAN, and AnomalyDiffusion. Each figure includes both the generated images and their corresponding segmentation masks.
25

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Mviec A1>
CurPaste
DRAEM
GLASS
DEMGAN
RealNet
Anomaly Diffasion
PAST
Bottic
Cabble
Capsoic
500
Carpet
Gnd
(6)
(c) (d)
(e)
(h)
Figure 9: Visualization results of different anomaly synthesis methods on the MVTec dataset. Columns correspond synthesis methods (from left right: MVTec AD, CutPaste, DRAEM, GLASS, DFMGAN, RealNet, Anomaly Diffusion, FAST), and rows correspond to product categories bottle, cable, capsule, carpet, grid).
(from top bottom:
Mvttc AD
CutPaste
DRAEM
GLASS
DEMGAN
RealNet
Anomaly Dillusion
FAST
Hazel jitt
Lesther
Metal nut
PIL
Screw
(a)
(b)
(c)
(d) (e)
(e)
(
Figure 10: Visualization results of different anomaly synthesis methods on the MVTec dataset. Columns correspond to synthesis methods (from left right: MVTec AD, CutPaste, DRAEM, GLASS, DFMGAN, RealNet, Anomaly Diffusion, FAST), and rows correspond to product cate- gories (from top bottom: hazel_nute leather, metal_nut nut, pill, screw).
26

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Blad
GLASS
DEMGAN
Anomaly Diffision
O
@
Visualization results of different anomaly synthesis methods on the BTAD dataset. Columns correspond to synthesis methods (from left to right: MVTec AD, CutPaste, DRAEM,
Figure 11:
GLASS, DFMGAN, RealNet, Anomaly Diffusion, FAST), and rows correspond product categories.
27


Reviews:
[{"review_id": "ANdW6ahVWm", "reviewer": "Reviewer_XC3D", "summary": "This paper proposes FAST, a novel framework for unsupervised anomaly segmentation. Existing self-training methods often suffer from foreground-background imbalance and error accumulation in pseudo-labels. To address this, FAST introduces two key components:  \n1. Foreground Guidance Module: Uses CLIP-based saliency to focus learning on foreground objects, reducing background bias in normal-only training.  \n2. Two-Branch Self-Training: Combines a soft label branch (probabilistic supervision) and a hard label branch (high-confidence pseudo-labels filtered by saliency) to enhance training stability and segmentation accuracy.", "questions": "1. CLIP Reliability.  \nHave the authors tested the robustness of CLIP-based saliency guidance across different domains (e.g., grayscale, medical, or low-resolution images)?  \n2. Inference Latency.  \nCan the authors provide runtime analysis or memory benchmarks compared to one-branch baselines? Is the method suitable for real-time applications?", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 2, "strengths_and_weaknesses": "**Strenghts**\n1. Clear and Well-Motivated Problem Setup.  \nThe paper identifies a key challenge in anomaly segmentation—foreground suppression due to background-dominated normal samples—and addresses it directly.\n2. Foreground-Aware Design.  \nLeveraging CLIP-based saliency maps for guidance is a novel and practical way to enhance semantic focus.\n3. Solid Theoretical Justification.  \nThe framework is conceptually well-grounded, and the proposed design choices are supported with theoretical proofs.\n\n**Weakness**\n1. Marginal Performance Gains.  \nThe improvements over strong baselines are relatively small on standard benchmarks, limiting the perceived practical impact.\n2. CLIP Dependency.  \nThe method relies heavily on CLIP saliency, which may not generalize well to domains with domain shift or non-natural images.\n3. Saliency Map Heuristic.  \nThe use of CLIP-derived saliency as ground-truth guidance is not learned, and may introduce biases or fail in complex backgrounds.", "was_revised": true, "final_justification": "I appreciate the authors’ detailed and well-prepared rebuttal, which has clarified several of my earlier concerns. In particular, the additional experiments on medical datasets, the explanation of CLIP dependency, and the runtime analysis have addressed many of my questions and strengthened the paper. I also acknowledge that the theoretical grounding of the framework and the foreground-aware design are well-motivated and conceptually sound.\n\nHowever, some issues remain only partially resolved. While the rebuttal provides evidence of performance gains, the improvements over baselines are still perceived as marginal on standard benchmarks, and the dependency on saliency-based guidance continues to raise concerns regarding robustness in more diverse domains. Paper clarity could also be further improved to ensure accessibility to a broader audience.\n\nTaking these points into account, I believe the paper presents a technically solid contribution with a meaningful idea and practical potential, but with limitations in generalization and clarity that prevent me from being fully convinced of its broader impact. For these reasons, I will maintain my current score.", "rebuttal": "We sincerely thank you for your thoughtful comments, particularly for **\"solid theoretical grounding\"** and our proposed **\"foreground-aware design.\"** Below we address the key concerns.\n\n---\n\n**Q1: Limited performance gains.**\n\nWe respectfully note that FAST consistently outperforms all prior anomaly synthesis methods across multiple segmentation architectures and datasets (see Table 1, Table 2, and Supplementary A.6). In particular, FAST improves the average segmentation accuracy by +9.22, +9.46, and +6.67 points of segmentation models like SegFormer, BiSeNetV2, and STDC on MVtec-AD compared with the second strongest baselines.\n\nAdditionally, ablation studies demonstrate substantial gains over the baseline LDM in both quality and controllability of the synthesized anomalies. FAST achieves these improvements with as few as 10 sampling steps, offering over 100× speedup compared to standard DDPM (Table 3). We believe these improvements are non-trivial and practically meaningful for real-world industrial deployment.\n\n---\n\n**Q2: CLIP dependency and generalization.**\n\nWe appreciate your concern regarding CLIP-based saliency guidance. In our setup, instead of directly relying on CLIP embeddings, FARM learns to reconstruct anomaly-aware content in a data-driven manner and is fully decoupled from CLIP during inference, and FAST does not treat CLIP-based saliency as fixed ground truth.\n\nAs also demonstrated in the ablation study (Fig. 8), this strategy significantly improves anomaly localization without relying on saliency maps. Specifically, we follow AnomalyDiffusion by employing Bert/CLIP just for textual embeddings initialization, and embeddings are still optimized during training.\n\nTo further assess generalization under domain shift, we conduct additional experiments on a grayscale medical dataset (Montgomery X-ray). We extract 1,200 image–mask pairs (256×256) for training and 400 for testing, and augment the training data with 500 synthetic samples generated by FAST.\n\nThe results show encouraging improvements in downstream lesion segmentation, suggesting that FAST holds promise in domains with domain shift or limited visual structure, even when saliency may be less reliable.\n\n**Table: Segmentation results on the Montgomery County X-ray dataset using Segformer**  \n*Original data refers to training using only real samples, while Augmented data includes both real and FAST-synthesized samples.*\n\n| **Experiment**    | **mIoU (%)** | **Accuracy (%)** |\n|:------------------|:------------:|:----------------:|\n| Original data     |    87.79     |      90.26       |\n| Augmented data    |    89.41     |      91.82       |\n\n---\n\n**Q3: Inference latency.**\n\nThanks for this important question. As reported in Table 3 and Sec. 4.3, FAST achieves impressive performance with only 10–50 steps, compared to 1000 steps in DDPM.\n\nFurthermore, FAST does not require retraining for different step sizes, making it highly practical for real-time or resource-constrained scenarios. We also provide the time cost for varying the number of AIAS segments (batch size = 8), which illustrates that FAST achieves up to 100× speedup while maintaining high-quality generation, as shown in Table 2.\n\nIn terms of inference latency, FAST is also highly efficient. It operates with minimal additional trainable parameters and achieves competitive results. We report runtime benchmarks under a consistent setting (batch size = 1), comparing FAST with other diffusion-based anomaly synthesis methods, as shown in Table 3.\n\nThese results confirm the suitability of FAST for downstream real-time segmentation tasks.\n\n**Table: Time cost (in seconds) of pixel-level anomaly segmentation with different diffusion steps on the MVTec dataset (batch size = 8)**\n\n| **Step Count** |   2   |   5   |  10   |  30   |  50   |  100  |  200  |  500   | 1000  |\n|:--------------:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|:-----:|:------:|:-----:|\n| **Time (s)**   | 1.39  | 2.92  | 3.87  | 10.64 | 18.16 | 36.73 | 74.21 | 183.34 | 367.97 |\n\n**Table: Inference FLOPs and number of trainable parameters of different models**\n\n| **Model**            | **Inference FLOPs (TFLOPs)** | **Trainable Parameters (M)** |\n|:---------------------|:----------------------------:|:----------------------------:|\n| AnomalyDiffusion     |            0.61              |            356.0             |\n| RealNet              |            1.11              |            556.7             |\n| FAST                 |            0.51              |             3.40             |"}, {"review_id": "xgW5KuT7OY", "reviewer": "Reviewer_CbJy", "summary": "The paper presents a new method to synthesize anomalies in industrial settings. The paper proposes an anomaly-informed accelerated sampling module and a foreground-aware reconstruction module. The experiments are performed on MVTec and BTAD datasets, obtaining state-of-the-art results.", "questions": "-\tThe evaluation metrics used mean Intersection over Union and pixel-wise accuracy are not very common in anomaly detection. I understand that in terms of image-level AUROC and pixel-level AUROC, the performance is saturated, but most methods report these metrics (including DRAEM, GLASS etc).\n-\tThe method section is full of formulas, however the underlying intuition behind the method is not present. Therefore, the method is hard to follow.\n-\tSome data sets are not used such as VisA and MPDD datasets.\n-\tHow are the masks generated in the first place?", "limitations": "I could not find a limitation section, where the authors describe the limitation of their methods. I would have liked to find one paragraph describing the limitation along with the conclusion section.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n-\tThe quality of the synthesized anomalies is high.\n-\tThe quantitative results on both datasets are state-of-the-art.\n\nWeaknesses:\n\n-\tThe paper is not self-contained. A brief introduction of Segformer, BiseNetV2 and STDC should be added, at least in the supplementary file.\n-\tThe evaluation metrics used mean Intersection over Union and pixel-wise accuracy are not very common in anomaly detection. I understand that in terms of image-level AUROC and pixel-level AUROC, the performance is saturated, but most methods report these metrics (including DRAEM, GLASS etc).\n-\tThe method section is full of formulas, however the underlying intuition behind the method is not present. Therefore, the method is hard to follow.\n-\tSome data sets are not used such as VisA and MPDD datasets.\n-\tHow are the masks generated in the first place?\n\n\nOverall: The paper presents a novel high quality anomaly synthesis model, however, major details are missing (see weaknesses) and the method section is not clear, missing the underlying intuition behind the proposed method.", "was_revised": true, "final_justification": "The authors answered all my questions, including additional experiments showing that their method is also useful for industrial anomaly detection.", "rebuttal": "We sincerely thank you for the thoughtful and constructive feedback. We address the concerns below:\n\n* * *\n\n**Q1: Lack of description for segmentation backbones, method intuition and limitations.**\n\nThank you for the suggestion. We will add brief descriptions of SegFormer, BiSeNetV2, and STDC in the supplementary material for completeness. These three models are widely adopted in industrial scenarios due to their favorable trade-off between performance and inference speed. Specifically, SegFormer is a transformer-based model known for its lightweight design and robust accuracy; BiSeNetV2 employs a dual-branch structure for real-time segmentation; and STDC leverages short-term dense concatenation for fast and effective feature extraction. Evaluating performance across these architectures can further validate FAST's practical value in boosting segmentation performance under real-time constraints.\n\nFor the method intuition, we will revise Section 3 to better explain the underlying intuitions behind AIAS. Specifically, traditional diffusion models rely on dense, step-by-step denoising with predicted noise or clean image at each timestep. In contrast, AIAS accelerates this process by dividing the trajectory into a small number of coarse-to-fine segments. Within each segment, we fix the clean image estimate $\\hat{x}_0$ instead of predicting it at each step, and analytically aggregate multiple DDPM transitions into a single closed-form update. By progressing from coarse to fine segments, AIAS compensates for the accumulated error that may arise due to temporal sparsity, enabling fast yet semantically consistent synthesis.\n\nAs for limitations, FAST currently relies on binary anomaly masks as input, which may limit applicability in scenarios where such masks are difficult to obtain. Extending it to weakly- or self-supervised mask generation is an exciting direction.\n\n* * *\n\n**Q2: Uses other metrics instead of common ones in anomaly detection.**\n\nWe appreciate your concern. As stated in Sec.1 and Table 1, our work targets a fundamentally different task from anomaly detection. While anomaly detection focuses on image- or region-level classification, which are often evaluated using AUROC, our work, segmentation-oriented industrial anomaly synthesis (SIAS), is a novel and emerging task that focuses on generating fine-grained plausible anomalies to enhance downstream pixel-level segmentation performance.\n\nTherefore, our evaluation strictly follows segmentation-centric benchmarks. AUROC is unsuitable for evaluating spatial alignment and structural fidelity, and the most appropriate metrics are mIoU and Acc, which are standard choices in segmentation tasks. However, we agree that evaluating generation quality is also reasonable, no matter in anomay detection- or anomaly segmentation-based anomaly synthesis. We additionally provide generation quality assessments such as Inception Score (IS) and Improved Conditional LPIPS (IC-LPIPS) as follows.\n\n**Table: Comparison of IS and IC-LPIPS for anomaly synthesis across various methods**\n| Category    | CutPaste (IS / IC-LPIPS) | DRAEM | GLASS |DFMGAN | RealNet| AnomalyDiffusion |FAST|\n|:-----------:|:------------------------:|:--------------:|:--------------:|:--------------:|:--------------:|:----------------:|:---------------:|\n| bottle      |     1.38 / 0.19          |  1.65 / 0.26   |  1.52 / 0.22   |  1.95 / 0.44   |  1.75 / 0.20   |   1.47 / 0.25    | 1.78 / 0.27 |\n| cable       |     1.75 / 0.40          |  1.73 / 0.38   |  1.79 / 0.43   |  1.64 / 0.47   |  1.65 / 0.42   |   1.85 / 0.44    | 2.04 / 0.51 |\n| capsule     |     1.29 / 0.20          |  1.92 / 0.25   |  1.17 / 0.22   |  1.39 / 0.27   |  1.91 / 0.27   |   1.47 / 0.28    | 1.67 / 0.29 |\n| carpet      |     0.85 / 0.26          |  1.38 / 0.36   |  1.16 / 0.30   |  1.26 / 0.32   |  1.08 / 0.32   |   1.02 / 0.33    | 1.47 / 0.37 |\n| grid        |     2.15 / 0.42          |  2.14 / 0.44   |  2.10 / 0.45   |  1.63 / 0.48   |  2.51 / 0.38   |   2.70 / 0.50    | 2.59 / 0.52 |\n| hazel_nut   |     1.07 / 0.32          |  2.00 / 0.43   |  2.13 / 0.33   |  2.01 / 0.45   |  2.46 / 0.42   |   2.10 / 0.36    | 2.48 / 0.42 |\n| leather     |     1.10 / 0.31          |  1.38 / 0.46   |  1.12 / 0.41   |  1.39 / 0.49   |  1.48 / 0.44   |   1.59 / 0.47    | 1.65 / 0.48 |\n| metal_nut   |     1.88 / 0.40          |  2.09 / 0.36   |  1.90 / 0.38   |  2.03 / 0.38   |  2.07 / 0.44   |   2.19 / 0.42    | 2.34 / 0.48 |\n| pill        |     1.87 / 0.28          |  1.35 / 0.38   |  1.97 / 0.29   |  1.87 / 0.36   |  1.52 / 0.34   |   1.45 / 0.32    | 1.91 / 0.38 |\n| screw       |     0.95 / 0.42          |  1.06 / 0.40   |  1.17 / 0.42   |  1.23 / 0.31   |  1.20 / 0.46   |   1.26 / 0.49    | 1.22 / 0.51 |\n| tile        |     1.29 / 0.47          |  1.38 / 0.51   |  1.98 / 0.49   |  1.69 / 0.50   |  1.38 / 0.49   |   1.91 / 0.54    | 2.25 / 0.56 |\n| toothbrush  |     1.39 / 0.25          |  1.37 / 0.27   |  1.36 / 0.33   |  1.32 / 0.27   |  1.40 / 0.32   |   1.42 / 0.29    | 1.43 / 0.35 |\n| transistor  |     1.66 / 0.37          |  1.78 / 0.41   |  1.77 / 0.36   |  1.48 / 0.39   |  1.48 / 0.39   |   1.66 / 0.40    | 1.84 / 0.46 |\n| wood        |     1.61 / 0.34          |  1.48 / 0.42   |  1.20 / 0.44   |  1.75 / 0.48   |  1.44 / 0.38   |   1.83 / 0.39    | 2.34 / 0.46 |\n| zipper      |     1.44 / 0.25          |  1.39 / 0.32   |  1.28 / 0.26   |  1.47 / 0.26   |  1.55 / 0.22   |   1.60 / 0.28    | 1.72 / 0.34 |\n| **Average** | **1.45 / 0.33**  | **1.61 / 0.38** | **1.57 / 0.36** | **1.61 / 0.39** | **1.56 / 0.37** | **1.70 / 0.38**  | **1.91 / 0.43** |\n\n\n* * *\n\n**Q3: Mask generation**\n\nWe apologize for not clarifying this. Our mask generation strategy follows the setup of AnomalyDiffusion, and employs two approaches:\n\n1.  Augmenting real anomaly masks via transformations (e.g., rotation, flipping).\n2.  Generating novel masks using a Latent Diffusion Model (LDM) trained on a small set of real anomaly masks.\n\nAll generated masks are visually screened to ensure structural plausibility and diversity. We will provide further implementation details to the supplementary material and refer readers to the AnomalyDiffusion paper for reproducibility.\n\n* * *\n\n**Q4: Missing studies on other datasets**\n\nWe thank you for this observation. In response, we have conducted additional experiments on VisA dataset and included the results below. These results reinforce our claim that FAST is a downstream-backbone-agnostic and dataset-agnostic framework for segmentation-oriented industrial anomaly synthesis.\n\n**Table: Pixel-level segmentation results (mIoU / Accuracy) on VisA using SegFormer trained on synthetic anomalies**\n\n| Category | CutPaste | DRAEM | GLASS | RealNet | DFMGAN | AnomalyDiff. | FAST |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| candle | 27.67 / 38.21 | 6.63 / 37.84 | 32.47 / 41.46 | 30.47 / 38.09 | 32.47 / 44.65 | 30.37 / 39.04 | 39.91 / 46.66 |\n| capsules | 60.31 / 74.74 | 69.05 / 80.52 | 65.05 / 68.11 | 65.38 / 74.81 | 59.29 / 64.24 | 65.90 / 72.41 | 70.08 / 78.32 |\n| cashew | 86.79 / 88.52 | 87.33 / 89.40 | 86.23 / 88.16 | 85.30 / 87.92 | 86.55 / 88.66 | 86.50 / 88.32 | 88.92 / 90.98 |\n| chewinggum | 68.52 / 78.29 | 69.37 / 81.15 | 70.96 / 76.67 | 68.50 / 80.91 | 67.41 / 76.32 | 67.03 / 79.36 | 71.15 / 80.21 |\n| fryum | 47.17 / 49.01 | 49.15 / 65.11 | 38.65 / 39.97 | 50.80 / 51.98 | 54.08 / 55.13 | 60.07 / 65.22 | 63.65 / 66.13 |\n| macaroni1 | 32.60 / 42.13 | 32.70 / 39.20 | 29.70 / 36.65 | 20.02 / 25.35 | 23.91 / 31.06 | 27.96 / 37.06 | 37.19 / 45.18 |\n| macaroni2 | 22.68 / 25.46 | 22.98 / 28.21 | 24.90 / 28.66 | 17.45 / 22.42 | 13.20 / 14.66 | 20.31 / 24.50 | 30.78 / 38.68 |\n| pcb1 | 13.22 / 13.47 | 13.89 / 14.10 | 12.14 / 12.42 | 5.59 / 5.65 | 7.22 / 7.31 | 23.76 / 24.41 | 27.18 / 26.94 |\n| pcb2 | 18.14 / 20.04 | 23.61 / 26.60 | 20.37 / 22.85 | 19.64 / 21.61 | 18.32 / 19.80 | 23.04 / 32.59 | 26.40 / 36.37|\n| pcb3 | 35.40 / 37.61 | 39.21 / 43.14 | 33.22 / 36.02 | 32.70 / 36.43 | 56.87 / 66.84 | 38.19 / 45.93 | 46.75 / 51.46 |\n| pcb4 | 55.88 / 64.59 | 57.54 / 68.18 | 55.07 / 66.44 | 54.94 / 68.06 | 57.81 / 68.17 | 57.50 / 68.93 | 60.62 / 72.91 |\n| pipe_fryum | 84.54 / 88.64 | 84.10 / 86.04 | 86.75 / 88.65 | 82.59 / 86.47 | 86.78 / 89.09 | 84.08 / 88.23 | 88.72 / 91.14 |\n| **Average** | **46.08 / 51.73** | **45.67 / 53.72** | **46.29 / 50.50** | **44.91 / 48.90** | **47.12 / 52.54** | **47.79 / 56.24** | **54.28 / 60.41** |"}, {"review_id": "utGxKnMpyP", "reviewer": "Reviewer_QVrM", "summary": "1. Existing methods uniformly process the entire region of defect images and are unable to generate specific defect structures for downstream segmentation. This paper proposes a defect-aware generation method based on diffusion models, namely FAST.\n2. The method consists of two modules. The first module, AIAS, is a training-free sampling algorithm for industrial defect generation. This module reduces the number of sampling steps and accelerates the generation speed through a coarse-to-fine aggregation approach. The second module, FARM, adaptively adjusts the noise in the masked region after each sampling step to preserve the defect features in the denoising process.\n3. Experiments demonstrate that the proposed method outperforms existing anomaly generation methods in terms of metrics on downstream segmentation tasks across multiple datasets.", "questions": "1. When conducting experiments, the strategy of generating 500 images for each category of objects seems to lack a basis. Is the number of generated images insufficient?\n2. The paper requires an input mask during inference. Therefore, we would like to know how the input mask is obtained during the experiments.\n3. This paper proposes an accelerated sampling algorithm. Thus, we are curious about how long it takes to train a defect generation model and how long the inference process takes.\n4. At what value of t does the experiment start to perform the fine-grained standard DDPM?", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\n1. This paper proposes an accelerated sampling algorithm AIAS. Experiments demonstrate that compared with the DDIM and PLMS sampling methods, AIAS can improve the metrics of anomaly segmentation.\n2. This paper proposes FARM, which reconstructs the foreground defect and adds noise during the sampling process, enabling the model to generate realistic local foreground defects. The effectiveness of the FARM module is verified through ablation experiments.\n\nWeaknesses\n1. The paper did not compare with the few-shot defect generation method AnoGen [1]. We worry that such experiments may not be sufficient.\n2. Only mIoU and Acc are used as evaluation metrics. We are afraid that such a setting may not be perfect. We think that it is necessary to test the Inception Score (IS) of the generated images and the Intra-cluster pairwise LPIPS distance (IC - LPIPS) [2].\n\n[1]\tGui, Guan, et al. \"Few-shot anomaly-driven generation for anomaly classification and segmentation.\" European Conference on Computer Vision. Cham: Springer Nature Switzerland, 2024.\n\n[2]\tOjha U, Li Y, Lu J, et al. Few-shot image generation via cross-domain correspondence[C]//Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2021: 10743-10752.", "was_revised": true, "final_justification": "The Author has addressed all my concerns, so I’ve raised my score to “Borderline Accept.”", "rebuttal": "We sincerely thank you for your positive comments about our innovations. Below are our responses to your specific questions.\n\n---\n\n**Q1: Comparison to AnoGen.**\n\nWe thank you for highlighting AnoGen, which is an important and well-recognized contribution to few-shot anomaly synthesis. We will cite AnoGen in the final version and now we provide a direct comparison between FAST and AnoGen. Our preliminary results show that AnoGen achieves impressive performance in most classes, and FAST also demonstrates excellent segmentation performance (e.g., higher mIoU and Acc in some classes), highlighting its effectiveness in segmentation-oriented anomaly synthesis.\n\n**Table: Comparison of mIoU and pixel-wise Accuracy (%) across 15 MVTec categories**\n\n| Method | bottle       | cable        | capsule      | carpet       | grid         | hazel_nut    | leather       | metal_nut     |\n|--------|--------------|--------------|--------------|--------------|--------------|--------------|---------------|---------------|\n| AnoGen | 74.93 / 81.21| 59.24 / 69.12| 46.68 / 62.52| 69.72 / 75.80| 41.60 / 66.50| 72.30 / 81.34| 57.71 / 73.48 | 90.07 / 92.72 |\n| FAST   | 86.86 / 90.90 | 73.71 / 77.94 | 63.22 / 71.12 | 73.84 / 83.53 | 52.45 / 70.70 | 90.81 / 94.79 | 66.60 / 74.18 | 94.65 / 96.88 |\n\n| Method | pill         | screw        | tile         | toothbrush    | transistor    | wood         | zipper        | Average       |\n|--------|--------------|--------------|--------------|---------------|---------------|--------------|---------------|----------------|\n| AnoGen | 80.51 / 86.75| 43.61 / 59.96| 86.24 / 91.27| 58.05 / 72.71 | 72.30 / 82.65 | 68.28 / 78.92| 66.60 / 74.29 | 65.48 / 75.42  |\n| FAST   | 90.17 / 94.07 | 49.94 / 57.48 | 90.13 / 93.77 | 74.98 / 88.63 | 91.80 / 94.50 | 78.77 / 86.31 | 72.80 / 84.73 | 76.72 / 83.97 |\n\n\n---\n\n**Q2: Evaluation Metrics: IS and IC-LPIPS.**\n\nWe appreciate your suggestion to evaluate IS and IC-LPIPS, and we report the results in the following table. FAST achieves competitive scores, indicating that our method generates visually realistic and diverse samples, even though it is not explicitly optimized for generic image generation. However, segmentation-oriented industrial anomaly synthesis (SIAS) is a novel direction and different from conventional image generation or anomaly detection. Our objective is not to maximize perceptual quality, but to synthesize structurally coherent and spatially aligned anomalies that benefit downstream segmentation. We agree that IS and IC-LPIPS can still offer helpful auxiliary insights, but pixel-level metrics such as mIoU and Acc on real unseen anomalies are more indicative of a method’s value in SIAS.\n\n**Table: Comparison of IS and IC-LPIPS for anomaly synthesis across various methods**\n| Category     |  CutPaste    |   DRAEM     |   GLASS     |  DFMGAN     | RealNet     | AnomalyDiffusion |   FAST       |\n|:-------------:|:------------:|:-----------:|:-----------:|:-----------:|:-----------:|:----------------:|:------------:|\n| bottle        | 1.38 / 0.19  | 1.65 / 0.26 | 1.52 / 0.22 | 1.95 / 0.44 | 1.75 / 0.20 | 1.47 / 0.25      | 1.78 / 0.27  |\n| cable         | 1.75 / 0.40  | 1.73 / 0.38 | 1.79 / 0.43 | 1.64 / 0.47 | 1.65 / 0.42 | 1.85 / 0.44      | 2.04 / 0.51  |\n| capsule       | 1.29 / 0.20  | 1.92 / 0.25 | 1.17 / 0.22 | 1.39 / 0.27 | 1.91 / 0.27 | 1.47 / 0.28      | 1.67 / 0.29  |\n| carpet        | 0.85 / 0.26  | 1.38 / 0.36 | 1.16 / 0.30 | 1.26 / 0.32 | 1.08 / 0.32 | 1.02 / 0.33      | 1.47 / 0.37  |\n| grid          | 2.15 / 0.42  | 2.14 / 0.44 | 2.10 / 0.45 | 1.63 / 0.48 | 2.51 / 0.38 | 2.70 / 0.50      | 2.59 / 0.52  |\n| hazel_nut     | 1.07 / 0.32  | 2.00 / 0.43 | 2.13 / 0.33 | 2.01 / 0.45 | 2.46 / 0.42 | 2.10 / 0.36      | 2.48 / 0.42  |\n| leather       | 1.10 / 0.31  | 1.38 / 0.46 | 1.12 / 0.41 | 1.39 / 0.49 | 1.48 / 0.44 | 1.59 / 0.47      | 1.65 / 0.48  |\n| metal_nut     | 1.88 / 0.40  | 2.09 / 0.36 | 1.90 / 0.38 | 2.03 / 0.38 | 2.07 / 0.44 | 2.19 / 0.42      | 2.34 / 0.48  |\n| pill          | 1.87 / 0.28  | 1.35 / 0.38 | 1.97 / 0.29 | 1.87 / 0.36 | 1.52 / 0.34 | 1.45 / 0.32      | 1.91 / 0.38  |\n| screw         | 0.95 / 0.42  | 1.06 / 0.40 | 1.17 / 0.42 | 1.23 / 0.31 | 1.20 / 0.46 | 1.26 / 0.49      | 1.22 / 0.51  |\n| tile          | 1.29 / 0.47  | 1.38 / 0.51 | 1.98 / 0.49 | 1.69 / 0.50 | 1.38 / 0.49 | 1.91 / 0.54      | 2.25 / 0.56  |\n| toothbrush    | 1.39 / 0.25  | 1.37 / 0.27 | 1.36 / 0.33 | 1.32 / 0.27 | 1.40 / 0.32 | 1.42 / 0.29      | 1.43 / 0.35  |\n| transistor    | 1.66 / 0.37  | 1.78 / 0.41 | 1.77 / 0.36 | 1.48 / 0.39 | 1.48 / 0.39 | 1.66 / 0.40      | 1.84 / 0.46  |\n| wood          | 1.61 / 0.34  | 1.48 / 0.42 | 1.20 / 0.44 | 1.75 / 0.48 | 1.44 / 0.38 | 1.83 / 0.39      | 2.34 / 0.46  |\n| zipper        | 1.44 / 0.25  | 1.39 / 0.32 | 1.28 / 0.26 | 1.47 / 0.26 | 1.55 / 0.22 | 1.60 / 0.28      | 1.72 / 0.34  |\n| **Average** | **1.45 / 0.33**  | **1.61 / 0.38** | **1.57 / 0.36** | **1.61 / 0.39** | **1.56 / 0.37** | **1.70 / 0.38**  | **1.91 / 0.43** |\n\n---\n\n**Q3: On the 500-images-per-class setting.**\n\nWe sincerely apologize for not clearly describing our data composition. The downstream segmentation models are trained on a combination of 1/3 real anomaly data and synthetic samples, while the remaining 2/3 real anomaly data are used for validation. Importantly, we generate 500 samples for each anomaly type within each class, rather than just 500 per class. Thus, the actual number of synthesized samples is much larger than 500 per class when multiple anomaly types exist. This design ensures sufficient structural diversity while maintaining training efficiency. We also conducted internal ablations showing that 500 per anomaly type strikes a good trade-off between segmentation performance and computational cost. We will clarify this design and rationale in the revised paper.\n\n---\n\n**Q4: Mask generation clarification.**\n\nWe apologize for not making this clearer in the paper. Our mask synthesis strategy adopts the protocol of AnomalyDiffusion, which consists of two complementary components:\n\n1. Geometric augmentation of real anomaly masks through operations such as rotation and flipping.\n2. Synthesis of new masks using a Latent Diffusion Model (LDM) trained on these real examples.\n\nAll synthesized masks are manually screened to ensure visual realism, diversity, and consistency with industrial abnormal structures. We refer readers to AnomalyDiffusion for further reference.\n\n---\n\n**Q5: Training and inference time & value of `t` for fine-grained sampling.**\n\nAs reported in Supplementary A.5, FAST is trained for approximately 80k iterations on a single A100 GPU. However, thanks to our training-free AIAS module, inference is significantly accelerated. To illustrate this, we provide the inference time under different numbers of AIAS segments (with batch size set to 8, the image size is 256 × 256), shown in the following table:\n\n**Table: Inference time for different sampling step settings (MVTec, batch size = 8)**\n\n| Step Count | 2    | 5    | 10   | 30    | 50    | 100   | 200   | 500     | 1000    |\n|------------|------|------|------|-------|-------|-------|--------|---------|---------|\n| Time (s)   | 1.39 | 2.92 | 3.87 | 10.64 | 18.16 | 36.73 | 74.21 | 183.34  | 367.97  |\n\nAs noted in our supplementary material, coarse sampling is applied until t = 2, after which we perform standard posterior updates to refine fine-scale textures. This choice of t is empirically determined through extensive analysis, balancing segmentation performance and inference efficiency. Under this setting, FAST maintains high segmentation quality while significantly reducing computational cost."}, {"review_id": "XYJnGCTu0b", "reviewer": "Reviewer_Wznz", "summary": "This paper proposes FAST, a diffusion-based framework for generating industrial anomaly synthesis data for segmentation tasks. The framework consists of two main components: first, AIAS, a training-free sampling strategy that reduces the denoising steps from the DDPM standard of 1000 to 10, and second, FARM, a module that reconstructs anomaly-specific content from noisy inputs and injects anomaly-aware noise at each sampling step to preserve anomaly signals throughout the overall denoising process. The authors evaluate their method by generating 500 synthetic samples per category on two datasets and training multiple segmentation models with the synthetic data, achieving performance improvements.", "questions": "read weakness please", "limitations": "The core approximation of AIAS relies on assumptions that may not hold in practice, particularly with complex noise schedules or highly variable x^_0 predictions. The theoretical analysis of approximation error bounds and convergence properties is limited, and the error accumulation patterns according to segment length are not sufficiently characterized. And it is questionable whether reducing sampling steps to 10 is truly a priority in synthetic data generation. In industrial deployment, final segmentation performance may be more important than generation speed, and the potential quality degradation at extremely few steps has not been sufficiently analyzed.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strength\n1. AIAS provide well-formulated theorems that justify the multi-step backward approximation. The supplementary material clearly explains the proof and derivation process for this procedure.\n2. There is computational efficiency by reducing sampling steps to around 10 during the generation phase.\n3. Systematic comparison and justification through various ablation studies.\n4. FARM's foreground-aware processing tends to address the uniform spatial processing limitation of existing diffusion models.\n\nWeaknesses\n1. It is questionable whether the characteristic feature of this paper - reducing sampling steps to around 10 - is truly a significant advantage for synthetic data generation. In industrial anomaly detection, fast inference is important only during the anomaly segmentation stage, but for synthetic data generation, wouldn't quality be more important? Wouldn't it be better to keep only the foreground-aware processing and use multiple steps for sampling?\n2. While the fixed x̂_0 assumption is somewhat acknowledged, isn't it the case that x̂_0 actually changes quite significantly over 10 steps? This raises concerns since Lemma 2 relies on this assumption.\n3. In the experimental phase, it was mentioned that 500 synthetic samples were generated, with 1/3 used for training and the rest for evaluation, but a clearer explanation seems necessary regarding the methods used, including masks.\n4. In core multi-step aggregation formula x_te = Πx_ts + Σx̂_o + ε_te of AIAS, there is insufficient theoretical analysis of how approximation errors accumulate with respect to segment length (t_s - t_e). Information about how errors are amplified in the actual diffusion process seem necessary.", "was_revised": true, "final_justification": "I appreciate the authors' clear rebuttal. While you have addressed some of my concerns well, some concerns have only been partially resolved, so I have maintained my score in order to maintain a positive evaluation of the paper.", "rebuttal": "We sincerely thank you for your detailed comments and positive feedback, such as *\"clear theoretical justification\" and \"complete studies.\"* Below are our responses to your questions.\n\n**Q1: Practical benefit of fast sampling in anomaly synthesis.**\n\nWe thank you for this insightful comment. While synthesis quality is important, we argue that fast sampling is highly beneficial in segmentation-oriented industrial anomaly synthesis (SIAS).\n\n1. In real-world manufacturing, anomaly types evolve quickly, and segmentation models must be updated frequently. FAST enables engineers to generate hundreds of segmentation-aligned anomalies per class in minutes rather than hours or days after training, making rapid retraining feasible.  \n2. Our proposed AIAS achieves up to 100× speedup by reducing sampling steps from 1000 to 10, while still maintaining competitive segmentation performance (see Table 3 in the paper).  \n3. We observe that longer sampling may enhance visual realism but introduce overfitting to generative details at the cost of anomaly segmentation consistency. Therefore, in our context, slightly trading off fine-grained fidelity for significant speed gains is not only acceptable but necessary for practical deployment.\n\n---\n\n**Q2: Detailed experimental setup.**\n\nWe appreciate your suggestion and provide further explanation.\n\nIn the data synthesis phase, we follow AnomalyDiffusion’s mask generation strategy by employing two complementary methods:\n(1) augmenting real anomaly masks via geometric and morphological transformations, and\n(2) training a Latent Diffusion Model to learn the distribution of real masks and generate novel ones.\nAll generated masks are screened to ensure plausibility before being used to synthesize anomaly–mask pairs. Detailed information can be found in the AnomalyDiffusion paper. For each anomaly type within every object class, we generate 500 anomaly–mask pairs to ensure sufficient diversity for segmentation training.\n\nIn the downstream segmentation task, we employ SegFormer, BiseNetV2 and STDC as backbone models, as they are widely adopted in industrial scenarios due to their balance of accuracy and efficiency. Besides, we uniformly split the real anomalies from MVTec and BTAD into 2/3 for validation and 1/3 for training. The training set of segmentation models combines this 1/3 subset with the synthetic samples. This design ensures that the segmentation model is evaluated solely on unseen data while benefiting from synthetic samples during training. Additional implementation details, including model settings and training parameters, are available in Supplementary Materials A.5.\n\n---\n\n**Q3: The validity of the fixed $\\hat{x}_0$ assumption in Lemma 2.**\n\nWe appreciate your concern and provide the following reasons for the fixed $\\hat{x}_0$ assumption.\n\n1. **Training Objective Consistency:**  \nThe denoising diffusion model's training objective directly encourages consistency in predicting $\\hat{x}_0$ across different timesteps, particularly at lower $t$. This ensures that even when reused in a large segment, a fixed $\\hat{x}_0$ is still relatively accurate.\n\n2. **AIAS Theoretical support:**  \nIn AIAS, the reverse process is divided into limited segments. Within each segment, the trajectory is approximated by a fixed  $\\hat{x}_0$ to maintaini the denoising distribution.  At the start of each segment, the network re-calibrates  $\\hat{x}_0$ based on $x_t$  from the previous segment, effectively preventing error accumulation across segments. Previous work such as diffusion-based anomaly detection methods, also demonstrates that diffusion models are robust to small perturbations in $\\hat{x}_0$, especially when guided by strong cues like masks or backgrounds. Thus, even if $\\hat{x}_0$ from the previous segment is slightly biased, the trajectory remains aligned with the data manifold.\n\n3. **Denoising Distribution Dependence:**  \nThe denoising distribution is Gaussian, with its mean given by the posterior mean:\n\n&emsp;&emsp; $\\mu_{t-1 \\mid t} = A_t x_0 + B_t x_t$\n\n&emsp;&emsp; where the coefficient $A_t$ is defined as  \n\n&emsp;&emsp; $A_t = \\frac{\\sqrt{\\bar{\\alpha}_{t-1}} \\, \\beta_t}{1 - \\bar{\\alpha}_t}$.\n\n&emsp;&emsp; and the coefficient $B_t$ is defined as  \n\n&emsp;&emsp; $B_t = \\frac{\\sqrt{\\alpha_t}(1 - \\bar{\\alpha}_{t-1})}{1 - \\bar{\\alpha}_t}$.\n\n&emsp;&emsp; As $t$ decreases, $\\hat{x}_0$ becomes more reliable, with $A_t$ increasing and $B_t$ decreasing. Therefore, AIAS increasingly relies on the re-calibrated $\\hat{x}_0$, which helps mitigate the propagation of error from $x_t$. This also motivates the design of AIAS as a coarse-to-fine aggregation process.\n\n4. **Experimental Results:**  \nOur experiments show that increasing $K$ actually provides noticeable improvements within a certain range. However, with $K=10$, the results are already acceptable.\n\n---\n**Q4: Theoretical analysis of error accumulation.**\n\nThank you for your suggestion. The sampling approximation error in AIAS originates from two sources:  \n(1) *local segment-wise error*, introduced by keeping $\\hat{x}_0$ fixed within each segment, and  \n(2) *global cumulative error*, resulting from propagation across segments.\n\nIdeally $\\hat{x}_0^{(t)}$ should be adaptively estimated **at each time step t**. \n\nHowever, AIAS holds $\\hat{x}^k_0$ fixed within the  $k_{th}$ segment, leading to a local approximation error at the endpoint $t_e$.\n$$\n\\delta_{t_e} = \\Delta_{t \\rightarrow t_e} := \\Sigma (\\hat{x}_0 - \\hat{x}_0^{(t)})\n\\tag{1}\n$$\n\nAssuming the full reverse process is divided into $K$ segments with partition points:\n$$\nT = t_0 > t_1 > t_2 > \\cdots > t_K = 0,\n$$\nEach segment $(t_k \\rightarrow t_{k+1})$ contributes a local error and the global cumulative error can be described recursively. Specifically, the offset at time $t_1$ is computed as:  \n$\\delta_{t_1} = \\Sigma_0 (\\hat{x}_0^{(0)} - \\hat{x}_0^{(t_0)})$.\n\nThen, the state at $t_2$ follows:  \n$x_{t_2} = \\Pi_1 x_{t_1} + \\Sigma_1 \\hat{x}_0^{(1)}$,\n\nwhich leads to the offset propagation:  \n$\\delta_{t_2} = \\Pi_1 \\delta_{t_1} + \\Sigma_1 (\\hat{x}_0^{(1)} - \\hat{x}_0^{(t_1)})$.\n\nBy recursion, the total error at the final timestep $t_K$ can be expressed as:\n$$\n\\Delta_{\\text{total}} = \\delta_{t_K} = \\sum_{k=0}^{K-1} \\left( \\prod_{l = k+1}^{K-1} \\Pi_l \\right) \\cdot \\Sigma_k \\left( \\hat{x}_0^{(k)} - \\hat{x}_0^{(t_k)} \\right).\n\\tag{2}\n$$\n\nWe further assume that the prediction error of $\\hat{x}_0$ is uniformly bounded at each segment:\n- $\\|\\hat{x}_0^{(k)} - \\hat{x}_0^{(t_k)}\\| \\leq \\epsilon_0$\n- $\\|\\Sigma_k\\| \\leq C_\\Sigma$\n- $\\|\\Pi_k\\| \\leq \\alpha < 1$\n\nHere, $\\alpha$ represents the maximum norm of the inter-segment state propagation matrices $\\Pi_k$, and $C_\\Sigma$ denotes the influence of $\\hat{x}_0$ on the subsequent state within a segment. Notably, **both are deterministic and computable under known noise schedules, as shown in Lemma 1**.\n\nTherefore, the total error admits the following conservative upper bound:\n$$\n\\|\\Delta_{\\text{total}}\\| \\leq \\sum_{k=0}^{K-1} \\alpha^{K-1-k} \\cdot C_\\Sigma \\epsilon_0  \n= C_\\Sigma \\epsilon_0 \\sum_{m=0}^{K-1} \\alpha^m  \n= C_\\Sigma \\epsilon_0 \\cdot \\frac{1 - \\alpha^K}{1 - \\alpha}.\n\\tag{3}\n$$\n\n**This bound is highly conservative in practice**, $\\epsilon_0$ tends to decrease as $K$ increases, since shorter segments reduce approximation error and the overall procedure becomes closer to standard DDPM sampling. Moreover, the assumption that all errors accumulate in the same direction is pessimistic. Due to the inherent robustness of denoising diffusion models, the error introduced in one segment is typically corrected in the next, as $\\hat{x}_0$ is re-estimated from the updated $x_t$. This re-calibration helps mitigate the propagation of prior inaccuracies.\n\n\nThese observations further explain why AIAS remains effective even when using only $K = 10$ segments. The combined effect of theoretical error control, diffusion model robustness, and segment-wise re-estimation of $\\hat{x}_0$ ensures that the synthetic samples retain acceptable fidelity."}]

Author rebuttal:

Meta-review: This paper presents FAST, an innovative framework for unsupervised anomaly segmentation. Current self-training approaches frequently grapple with issues such as foreground-background imbalance and the accumulation of errors in pseudo-labels. To tackle these challenges, FAST incorporates two core components:
Foreground Guidance Module: Leverages CLIP-based saliency to direct learning toward foreground objects, thereby mitigating background bias in training that relies solely on normal samples.
Two-Branch Self-Training: Integrates a soft label branch (providing probabilistic supervision) and a hard label branch (utilizing high-confidence pseudo-labels filtered through saliency) to boost both training stability and segmentation accuracy.

All reviewers feel positive about this work. The authors have addressed all the issues.

The AC recommends the acceptance of this work.
Decision: Accept (poster)