CDGP: Contrastive Dual Gaussian Processes for Weakly Supervised Anomaly Segmentation

Seungjun Chu; Seokhee Han; Mateusz Nowak; Peter Chin

cs.CVAug 19, 2026

CDGP: Contrastive Dual Gaussian Processes for Weakly Supervised Anomaly Segmentation

Authors: Seungjun Chu, Seokhee Han, Mateusz Nowak, Peter Chin

Organizations: Korea University · Dartmouth College

Abstract

Industrial visual inspection must both decide whether a product is defective and localize the defect, yet pixel-level masks are costly to collect at scale. Most anomaly-segmentation methods learn only from defect-free images and score deviations from normality. A true defect and an unusual-but-normal region, however, can both deviate substantially and receive similarly high scores. We propose Contrastive Dual Gaussian Processes (CDGP), a weakly supervised framework that models normal and anomaly inducing-variable predictive distributions over dense tokens. Its posterior-dominance statistic standardizes their predictive-mean difference by the joint predictive uncertainty, providing both spatial evidence and image-level confidence. This evidence complements hierarchical normal-reconstruction residuals for fine localization. All calibration uses training data only, without human pixel annotations or test-time fitting. Across MVTec AD~~2, KSDD2, and VisA, CDGP ranks first among the evaluated methods on all MVTec AD~~2 localization metrics and is first-place or competitive on KSDD2 and VisA. Factorized and matched linear-head controls delimit the contribution and scope of the linear-kernel Gaussian process (GP) formulation.

Figures & tables

Panel of Figure 1 — Figure 1: Conceptual motivation for CDGP. One-sided normality scoring can assign equally low normal evidence to an unusual-but-normal region and a true anomaly. CDGP instead models normal and anomaly predictive distributions and scores their posterior dominance at each token.

Figure 2: Overview of CDGP. (a) Multi-scale tokens initialize the normal and anomaly GP inducing sets through diverse normal sampling and hard-candidate mining. (b) Their joint predictive mean and variance define posterior-dominance evidence. (c) A frozen teacher and normal-only reverse student provide hierarchical residual evidence. (d) Training-only calibration fuses the two signals into the final anomaly map.

Method	MVTec AD 2			KSDD2		VisA
Method	AUROC-P	[email protected]	[email protected]	AUROC-P	[email protected]	AUROC-P	[email protected]
Normal-only supervision
PaDiM Defard et al. [2021]	$85.0_{\pm 1.2}$	$49.5_{\pm 1.1}$	$18.2_{\pm 1.3}$	$93.4_{\pm 0.2}$	$87.1_{\pm 1.2}$	$97.2_{\pm 0.2}$	$83.3_{\pm 1.4}$
PatchCore Roth et al. [2022]	$91.2_{\pm 1.2}$	$63.0_{\pm 1.3}$	$36.1_{\pm 2.3}$	$91.6_{\pm 0.0}$	$85.2_{\pm 0.1}$	$97.6_{\pm 0.0}$	$85.5_{\pm 0.1}$
RD4AD Deng and Li [2022]	$86.7_{\pm 0.9}$	$59.2_{\pm 0.6}$	$29.6_{\pm 1.6}$	$95.0_{\pm 0.1}$	$90.0_{\pm 0.1}$	$99.0$ ±0.0	$93.0_{\pm 0.1}$
DRAEM Zavrtanik et al. [2021]	$57.3_{\pm 4.0}$	$23.9_{\pm 5.4}$	$7.1_{\pm 0.9}$	$51.5_{\pm 7.4}$	$26.7_{\pm 6.2}$	$53.8_{\pm 4.8}$	$31.1_{\pm 5.0}$

Table 1: Comparison with representative industrial anomaly segmentation baselines on MVTec AD 2, KSDD2, and VisA. Mean

\pm

std (

\times 100

) over three seeds. MVTec AD 2 uses our matched weak-supervision 80/20 split, not the official normal-only leaderboard protocol. Best is bold and second best is underlined.

Variant	AUROC-P	[email protected]	[email protected]
GP-free residual pipeline	$85.4_{\pm 2.0}$	$53.3_{\pm 0.8}$	$27.7_{\pm 3.6}$
Spatial GP only ( $+G_{\rm GP}$ )	$95.2_{\pm 1.3}$	$79.0_{\pm 1.3}$	$45.5_{\pm 1.9}$
Image GP only ( $+\widehat{p}_{A}$ )	$96.4_{\pm 0.6}$	$82.7_{\pm 0.3}$	$46.1_{\pm 1.8}$
Full CDGP (both GP paths)	$\mathbf{96.8}_{\pm 0.7}$	$\mathbf{84.4}_{\pm 0.7}$	$\mathbf{48.7}_{\pm 1.8}$

Table 2: Factorized GP contribution on MVTec AD 2 (mean

\pm

std,

\times 100

). The middle rows each add exactly one GP path to the first row; the first row contains neither

G_{\rm GP}

nor

\widehat{p}_{A}

Figure 3: Input, ground truth, normal/anomaly predictive evidence, and final CDGP map.

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Variant	AUROC-P	[email protected]	[email protected]
Direct linear head	$96.6_{\pm 0.7}$	$83.8_{\pm 0.4}$	$48.0_{\pm 1.9}$
CDGP mean margin $s_{\mu}$	$96.7_{\pm 0.7}$	$84.1_{\pm 0.7}$	$48.4_{\pm 2.0}$
CDGP posterior dominance $G_{\rm GP}$	$96.8_{\pm 0.7}$	$84.4_{\pm 0.7}$	$48.7_{\pm 1.8}$

Appendix

Table S2 : Matched scoring and parameterization controls on MVTec AD 2 (mean

\pm

std,

\times 100

). The two CDGP rows use the same trained models and differ only in inference scoring.

Variant	AUROC-P	[email protected]	[email protected]
Heteroscedastic linear	$96.6_{\pm 0.7}$	$83.5_{\pm 0.5}$	$47.7_{\pm 2.3}$
CDGP	$96.8_{\pm 0.7}$	$84.4_{\pm 0.7}$	$48.7_{\pm 1.8}$

Appendix

Table S3 : Strong functional-form control. The direct model learns two free linear means and two diagonal-plus-low-rank positive-semidefinite quadratic variances.

Factor	Setting	AUROC-P	[email protected]	[email protected]
Hard-pool fraction	10%	$96.8_{\pm 0.7}$	$84.5_{\pm 0.6}$	$48.8_{\pm 1.6}$
	20% (default)	$96.8_{\pm 0.7}$	$84.4_{\pm 0.7}$	$48.7_{\pm 1.8}$
	40%	$96.8_{\pm 0.7}$	$84.4_{\pm 0.6}$	$48.7_{\pm 1.8}$
Inducing budgets $(M_{N},M_{A})$	$(16,8)$	$96.6_{\pm 0.8}$	$83.9_{\pm 0.6}$	$48.3_{\pm 2.2}$
	$(32,16)$ (default)	$96.8_{\pm 0.7}$	$84.4_{\pm 0.7}$	$48.7_{\pm 1.8}$
	$(64,32)$	$96.7_{\pm 0.5}$	$84.3_{\pm 0.3}$	$47.5_{\pm 2.2}$

Appendix

Table S4 : One-factor sensitivity of the CDGP pipeline on MVTec AD 2. Hard-pool fraction changes only the farthest-token candidate percentile; inducing-budget rows change only

(M_{N},M_{A})

Setting	AUROC-P	[email protected]	[email protected]
Linear (default)	$96.8_{\pm 0.7}$	$84.4_{\pm 0.7}$	$48.7_{\pm 1.8}$
Spherical RBF, $\sigma=.25$	$94.7_{\pm 2.2}$	$76.6_{\pm 7.3}$	$42.8_{\pm 2.3}$
Spherical RBF, $\sigma=.5$	$96.7_{\pm 0.7}$	$84.1_{\pm 0.5}$	$48.3_{\pm 1.9}$
Spherical RBF, $\sigma=1$	$96.7_{\pm 0.8}$	$84.4_{\pm 0.5}$	$48.5_{\pm 2.1}$

Appendix

Table S5 : Kernel control for the CDGP pipeline on MVTec AD 2. RBF rows use

k(\mathbf{z},\mathbf{z}^{\prime})=\exp[-(1-\mathbf{z}^{\top}\mathbf{z}^{\prime})/\sigma^{2}]

on normalized tokens.

GP weight $w$	AUROC-P	[email protected]	[email protected]
$0$	$96.42_{\pm 0.62}$	$82.72_{\pm 0.31}$	$46.07_{\pm 1.76}$
$0.01$	$96.65_{\pm 0.66}$	$83.64_{\pm 0.41}$	$47.93_{\pm 1.87}$
$0.025$ (default)	$96.78_{\pm 0.70}$	$84.36_{\pm 0.74}$	$48.69_{\pm 1.80}$
$0.05$	$96.22_{\pm 0.64}$	$83.82_{\pm 1.53}$	$45.28_{\pm 1.10}$

Appendix

Table S6 : Inference-weight sensitivity on MVTec AD 2. (a) varies the GP–residual weight. The

w=0

row reports the image-only endpoint; positive-

w

rows use separately fitted training-only normal tails. Every row retains

\widehat{p}_{A}

, so

w=0

is not the GP-free pipeline. (b) varies the broadcast image coefficient at fixed

w=.025

Dataset	Category	AUROC-I	AUROC-P	[email protected]	[email protected]
MVTec AD 2	can	$100.0_{\pm 0.0}$	$97.5_{\pm 0.3}$	$89.1_{\pm 0.5}$	$42.1_{\pm 3.4}$
	fabric	$100.0_{\pm 0.0}$	$95.1_{\pm 0.3}$	$77.9_{\pm 3.5}$	$25.3_{\pm 3.6}$
	fruit_jelly	$100.0_{\pm 0.0}$	$98.5_{\pm 0.4}$	$94.2_{\pm 1.5}$	$67.3_{\pm 9.8}$
	rice	$100.0_{\pm 0.0}$	$96.0_{\pm 0.9}$	$87.2_{\pm 2.5}$	$53.8_{\pm 5.5}$
	sheet_metal	$100.0_{\pm 0.0}$	$92.5_{\pm 3.9}$	$48.1_{\pm 6.0}$	$10.5_{\pm 1.3}$
	vial	$100.0_{\pm 0.0}$	$98.4_{\pm 0.1}$	$97.3_{\pm 0.3}$	$83.6_{\pm 1.8}$

Appendix

Table S7 : CDGP results by dataset category. Entries are mean

\pm

std over three complete runs (

\times 100

). Dataset means are computed within each seed before the three-seed summary, matching the main-paper aggregation. [email protected] is reported for the primary MVTec AD 2 benchmark.

Panel of Table 12 — Table S8 : MVTec AD 2 qualitative decomposition, one defective example per category.

Panel of Table 13 — Table S9 : KSDD2 qualitative decomposition.

Panel of Table 14 — Table S10 : VisA qualitative decomposition, one defective example per category.

Figure S1 : Spatial-only and final-CDGP localization versus defective-image budget on MVTec AD 2. Left: [email protected]; right: low-FPR [email protected]. Error bars are standard deviations over three seeds.

		[email protected]		[email protected]
Defect images/category	AUROC-I	Spatial	Final	Spatial	Final
1	$69.6_{\pm 4.3}$	$53.4_{\pm 0.7}$	$55.3_{\pm 0.3}$	$27.8_{\pm 3.5}$	$29.8_{\pm 3.2}$
2	$76.6_{\pm 5.8}$	$53.9_{\pm 0.7}$	$58.1_{\pm 1.5}$	$28.3_{\pm 3.2}$	$29.7_{\pm 3.1}$
4	$85.2_{\pm 3.4}$	$54.3_{\pm 1.6}$	$60.2_{\pm 1.4}$	$27.9_{\pm 4.1}$	$29.9_{\pm 5.3}$
8	$93.2_{\pm 2.5}$	$63.3_{\pm 4.9}$	$69.3_{\pm 4.0}$	$35.9_{\pm 3.0}$	$35.8_{\pm 2.7}$
16	$95.6_{\pm 0.2}$	$68.0_{\pm 3.3}$	$74.9_{\pm 2.3}$	$40.8_{\pm 1.3}$	$42.5_{\pm 2.2}$

Appendix

Table S11 : Defective-image budget sensitivity on MVTec AD 2. AUROC-I evaluates image anomaly probability; Spatial retains the calibrated spatial map but omits broadcast image evidence; Final is complete CDGP.

Model	Params. (M)	Latency (ms)	Peak VRAM (MiB)
CDGP	63.8	$7.07\!\pm\!0.32$	357.4

Appendix

Table S12 : Inference complexity at

256\!\times\!256

. Latency is measured with batch size one on an RTX 6000 Ada after 10 warm-up iterations and over 50 timed iterations.

Component	Final setting
Input and encoder	RGB bilinear resize to $256\!\times\!256$ (MVTec AD 2/VisA) or $256\!\times\!704$ (KSDD2); ImageNet mean/std normalization; ImageNet-1K V2 WideResNet-50-2 weights; layer1–3; $D=256$ ; training-only color jitter $(.12,.12,.05,.02)$ .
Dual GP	Linear kernel; $M_{N}=32$ , $M_{A}=16$ ; hard pool $20\%$ ; jitter $10^{-3}$ ; variance floor $10^{-6}$ ; batch 16; 400 steps; AdamW, base LR $10^{-4}$ , inducing-value LR $10^{-3}$ , weight decay $10^{-4}$ except zero on inducing values; cosine decay to $0.05$ of the initial LR; margin $\gamma=.5$ ; $(\mathcal{L}_{\rm MIL},\mathcal{L}_{\rm CMP},\mathcal{L}_{\rm ABN})$ weights $(1,1,4)$ .
Residual student	Normal fit images only; batch 5 (MVTec AD 2/VisA) or 3 (KSDD2); 360 steps; AdamW LR $3\!\times\!10^{-4}$ , weight decay $10^{-4}$ , cosine decay to $10^{-6}$ ; three scales; hard fraction $q=.10$ , $(\lambda_{h},\lambda_{s})=(.65,.10)$ .
Normal corruption	Gaussian noise std $.035$ ; $3\!\times\!3$ local averaging with probability $.70$ ; zero rectangle with probability $.75$ , with each side sampled between approximately $1/16$ and $1/5$ of the corresponding image dimension.
Calibration/inference	Training fit/calibration split $80/20$ ; $w=.025$ ; identity spatial operator (no Gaussian smoothing or max blend); at most $10^{6}$ normal calibration pixels sampled deterministically; tail floor $e^{-16}$ ; LSE $r=8$ ; logistic $C=1$ , balanced classes, nonnegative slope; $\lambda_{I}=1/3$ .
Evaluation	Seeds $\{0,1,2\}$ ; final model at step 400; category mean within seed, then mean $\pm$ std over seeds.

Appendix

Table S13 : Complete final CDGP configuration. Settings are shared across all categories and datasets unless a dataset-specific batch/input size is stated.

Dataset	Partition and weak-label construction	Test overlap
MVTec AD 2	For each category and seed, pool the publicly labeled images, stratify by the binary normal/defective label, and assign $80\%/20\%$ to train/test. Split the resulting training partition again $80\%/20\%$ for fit/calibration using a fixed stratified partition for each seed. Remove mask paths before either training stage.	0 images
KSDD2	Official train/test split; reduce each training mask once to a binary image label; split official training images $80\%/20\%$ for fit/calibration.	0 images
VisA	Official 2cls_highshot train/test CSV; use its normal/anomaly training labels and split official training images $80\%/20\%$ for fit/calibration.	0 images

Appendix

Table S14 : Partition provenance. Absolute resolved paths are hashed in released seed/category manifests; all 24 MVTec AD 2 calibration–test audits report zero overlap. Pixel masks remain inaccessible until final metric computation.

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Industrial anomaly detection and localization are limited by scarce real anomalies and pixel-level annotations, a bottleneck that synthetic image-mask pairs can alleviate. However, existing few-shot mask-guided generation may over-follow mask geometry, produce weak anomalies, or use condition masks incompatible with the current object instance. We propose OSAGEN, which combines object-aware mask priors with multistage decoupled diffusion. Its three-stage adaptation sequentially learns normal appearance, defect appearance under coarse conditions, and fine-grained mask calibration, improving defect realization and local control. QBG injects object structure from a matched normal image into mask diffusion to produce object-aware priors, while ISC restricts anomaly propagation and preserves normal content during sampling. A lightweight materialization step recovers pixel-level labels aligned with the realized defects. On MVTec AD and VisA, OSAGEN achieves AP-P/F1-P scores of 88.1/82.2 and 68.5/66.1, respectively, under a unified downstream localization protocol. The code will be released upon acceptance.

Abstract

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