VariaFlow: Uncertainty-Aware Flow Matching for Unsupervised Anomaly Detection

Arnela Hadzic; Martin Urschler; Cosmin I. Bercea

cs.CVOct 30, 2026

VariaFlow: Uncertainty-Aware Flow Matching for Unsupervised Anomaly Detection

Authors: Arnela Hadzic, Martin Urschler, Cosmin I. Bercea

Organizations: Institute for Medical Informatics, Statistics and Documentation, Medical University of Graz, Graz, Austria · Institute of Visual Computing, Graz University of Technology, Graz, Austria · Technical University of Munich, School of Medicine and Health, TUM University Hospital, Klinikum rechts der Isar, Department of Diagnostic and Interventional Radiology, Munich, Germany

Abstract

Reconstruction-based anomaly detection no longer fails at reconstruction. Generative models produce high-quality pseudo-healthy reconstructions, and the remaining difficulty is the step of scoring residuals. The residual between a scan and its reconstruction has two indistinguishable sources, genuine pathology and the anatomical variation that separates one healthy brain from another. Scoring against a single reconstruction treats both as anomalous, inflating false positives where healthy anatomy varies most while small or subtle lesions are lost in the surrounding reconstruction error. We identify the missing quantity as the predictive variance, how much a healthy reconstruction can vary at each location. We introduce VariaFlow, which estimates this variance from an ensemble of mask-guided restorations under an unconditional flow matching prior, each started from a different noise initialization, and which normalizes the residual by the resulting standard deviation. Few-step flow matching keeps the ensemble computationally affordable, and restoring at two spatial scales captures lesions of different size. Across three brain MRI datasets spanning stroke and tumor, VariaFlow is trained once on healthy anatomy and generalizes across all three, attaining the highest AUROC (0.94, 0.80, 0.78) on each and the highest AUPRC on both cross-domain datasets, exceeding the strongest baseline by 37% and 50%. Under domain shift, the same baseline drops by up to 52% in AUPRC, whereas VariaFlow stays more stable and achieves the best small-lesion Dice on all three datasets.

Figures & tables

Figure 1: Given an input image, VariaFlow generates an ensemble of pseudo-healthy reconstructions ( $\hat{x}^{(1)},\hat{x}^{(2)},\dots,\hat{x}^{(N)}$ ). In anomalous regions, the model consistently generates healthy tissue, yielding a high residual ( $R$ ) and low predictive variance ( $\sigma^{2}$ ). Conversely, in variable healthy regions (e.g., ventricle boundaries), anatomical variability causes reconstructions to diverge, creating high predictive variance. Penalizing the residual with the variance suppresses false positives, isolating the pathology in the anomaly score map ( $S$ ).

Dataset	Small	Medium	Large
ATLAS	189	152	59
UCSF-PDGM	30	126	257
BraTS	26	78	217
Total	245	356	533

Table 1: Number of images per lesion size category and dataset.

ATLAS
				$\lceil$ Dice $\rceil$ (%) $\uparrow$
Method	AUROC $\uparrow$	AUPRC $\uparrow$	[email protected] (%) $\uparrow$	Average	Small	Medium	Large	Sens (%) $\uparrow$	Prec (%) $\uparrow$
AutoDDPM [ 12 ]	0.7116	0.0878	7.30	13.86	3.25	15.29	25.87	27.02	9.32
THOR [ 11 ]	0.7139	0.1389	8.59	21.72	6.71	26.68	27.96	24.66	19.40
IterMask² [ 24 ]	0.8582	0.4965	48.40	50.07	7.79	44.52	59.86	45.00	56.43
REFLECT [ 8 ]	0.9378	0.5812	61.14	55.86	9.42	46.86	66.78	56.62	55.13

Table 2: Quantitative results on the ATLAS, UCSF-PDGM, and BraTS datasets. VariaFlow is compared to several state-of-the-art diffusion- and flow-based baselines. Bold and underline indicate the best and the second-best score per metric, respectively.

Figure 2: Qualitative anomaly detection results on ATLAS, UCSF-PDGM, and BraTS. Rows 1-2 show the input images and ground truth masks. Rows 3-6 visualize the anomaly maps generated by the baseline methods, and Row 7 shows the maps generated by VariaFlow , demonstrating both superior detection and false positive suppression.

Panel of Figure 3 — Figure 3: Comparison of window sizes ( $s_{l}=32,s_{g}=64$ ) and fusion strategies, with geometric mean consistently yielding the highest AUPRC.

Scoring	AUROC $\uparrow$	AUPRC $\uparrow$	$\lceil$ Dice $\rceil$ (%) $\uparrow$
Mean residual	0.8463	0.3935	43.11
Median residual	0.8571	0.4008	43.91
Proposed $(S)$	0.9417	0.5262	54.86

Table 3: Comparison of different scoring formulations. Median residual alone as proposed in Eq. 3 . Mean residual is a variant that uses the mean reconstruction instead in Eq. 1 . Based on median residual, our proposed

(S)

additionally penalizes variance.

Panel of Figure 4 — Figure 4: Impact of the ensemble size $N$ on detection performance. Metrics stabilize at $N=5$ .

Figure 5: Examples of diverse anatomical and structural deviations. Left: The model detects an enlarged ventricle, dominating the lesion attached to it. Right: The model misses a lesion resembling cortical folding while detecting a prominent imaging artifact.

Method	Backbone Architecture	Steps	Time (s)	VRAM (GB)	Params (M)
THOR [ 11 ]	DDPM U-Net	350	3.58	0.52	$\sim 19$
REFLECT [ 8 ]	LDM U-Net + VAE	5	0.12	1.67	$\sim 246$
VariaFlow (single patch)	Restora-Flow U-Net [ 19 ]	8	0.32	0.40	$\sim 62$
VariaFlow (global scale, $N=1$ )			0.64	0.82
VariaFlow (local scale, $N=1$ )			2.92	3.34
VariaFlow (dual-scale, $N=1$ )			3.56	3.34

Table 4: Computational and architectural comparison between methods.

Medical Image Anomaly Detection

Medical image anomaly detection finds and localizes unusual anatomy or pathology in scans, often when labeled disease examples are scarce.

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We propose Flow Mismatching, an unsupervised anomaly detection method that deliberately avoids reconstruction-based paradigms. Instead, we treat flow matching as geometric dynamics and leverage a key insight: anomalies occur at places where the learned normal flow disagrees with the geometric path toward a test image. Given a flow matching model trained only on normal images, we probe its learned velocity field along affine paths from Gaussian noise to a target image. Along each path, we compare the model-predicted velocity, which follows normal generative dynamics, with the geometric velocity toward the target, which includes any anomalous content. Anomalies induce strong local disagreement between these velocities. Aggregating the mismatch over different time steps and multiple paths yields pixel-wise heatmaps and image-level scores without test-time optimization, feature memories, or additional calibration. Our analysis shows that the population mismatch decomposes into an irreducible denoising term and a Fisher-divergence term between the test-path and normal-path score functions, which identifies the score-gap component that drives anomaly separation and explains the effectiveness of robust path aggregation. Extensive experiments on MVTec-AD and VisA demonstrate superior performance compared with SOTA reconstruction-based and recent flow matching-based approaches.

Abstract

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