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AR-Pro: Counterfactual Explanations for Anomaly Repair with Formal Properties
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Proposes AR-Pro, which formalizes four domain-independent counterfactual-explanation properties for linearly decomposable anomaly detectors and uses property-guided masked diffusion to repair anomalous inputs as explanations.
Problem
Anomaly detectors are black boxes that localize anomalies but do not explain what a non-anomalous version of the input should look like; counterfactual repairs need quality criteria.
Approach
Observes that many anomaly detectors are linearly decomposable (score = sum of feature-wise scores plus regularizer), uses this to define four formal properties (overall improvement, similarity, localized improvement, non-degradation) as loss functions, and guides a diffusion model with these losses plus masked in-filling of the non-anomalous region.
Key results
- On MVTec-AD and VisA with FastFlow, guided repair improves the four formal metrics by a median of +8.35% to +97% over unguided DDPM baseline (e.g., M_d +97.46% on VisA).
- On time series, guided repair improves formal metrics by 60.03% overall (Llama-2 +67.17%, GPT-2 +53.90%).
- Guided repairs reach a median TNR of 100% on VisA and MVTec-AD and an average guided TNR of 95.33% on SWaT/HAI/WADI versus 2.67% baseline average on time series.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add property guidance to diffusion | DDPM + FastFlow · VisA | M_s (overall anomaly score): +26.54% | Helped |
| Add property guidance to diffusion | DDPM + FastFlow · VisA | M_d (non-anomalous-region distance): +97.46% | Helped |
| Add property guidance to diffusion | DDPM + FastFlow · MVTec-AD | M_s (overall anomaly score): +8.35% | Helped |
| Add property guidance to diffusion | DDPM + FastFlow · MVTec-AD | M_d (non-anomalous-region distance): +97.34% | Helped |
| Add property guidance to diffusion | Diffusion-TS + Llama2/GPT-2 · SWaT, WADI, HAI | M_d (non-anomalous-region distance): +20.77% (Llama2); -34.37% (GPT-2) | Mixed |
| Add property guidance to diffusion | Diffusion-TS + Llama2/GPT-2 · SWaT, WADI, HAI | M_ω (anomalous-region score change): +110.32% (Llama2); +177.79% (GPT-2) | Helped |
| Add property guidance to diffusion | DDPM + FastFlow · VisA and MVTec-AD | TNR: 100% | Helped |
| Add property guidance to diffusion | Diffusion-TS + time-series detectors · SWaT, HAI, WADI | TNR: 95.33% vs. 2.67% | Helped |
| Add property guidance to diffusion | DDPM and Diffusion-TS · Vision and time-series | median runtime (seconds): 126.50 -> 236.37 (vision); 10.86 -> 12.49 (time-series) | Hurt |
| Vary the property-loss weights λ1, λ2, λ3, and λ4 (ablation) | AR-Pro · Time-series | formal property metrics | No clear effect |
| Vary the overall guidance scale λφ (ablation) | AR-Pro · Time-series and image data | formal property metrics | No clear effect |
Surprising findings
- Varying the lambda weights of the four property losses has no consistent effect on the metrics, suggesting little tuning is needed.
- On GPT-2 time series, the similarity metric M_d worsens (-34.37%) under guidance, showing the similarity property is not uniformly improved.
Limitations
- Guided generation is slower at inference, roughly doubling vision runtime.
- Formal properties are not guaranteed to be satisfied; the diffusion iterations only tend toward them.
- Requires a linearly decomposable anomaly detector and depends on detector and generative model quality.
Experimental setup
Datasets: MVTec-AD VisA SWaT WADI HAI
Benchmarks: MVTec-AD VisA SWaT WADI HAI
Metrics: M_s (overall score) M_d (similarity distance) M_omega (anomalous-region score change) M_omega-bar (non-anomalous-region score change) true negative rate
Baselines: non-guided diffusion repair (DDPM / Diffusion-TS baseline)
Builds on: DDPM guided diffusion Diffusion-TS FastFlow EfficientAD
Closest papers by meaning
- Supervision Recovery for Time Series Anomaly Detection via Counterfactual Pairing (NeurIPS 2026 · similarity 0.88)
- An Evidence-Based Post-Hoc Adjustment Framework for Anomaly Detection Under Data Contamination (NeurIPS 2025 · similarity 0.85)
- LogicAD: Explainable Anomaly Detection via VLM-based Text Feature Extraction (AAAI 2025 · similarity 0.85)
- Generating Counterfactual Explanations Under Temporal Constraints (AAAI 2025 · similarity 0.85)
- Towards Training-free Anomaly Detection with Vision and Language Foundation Models (CVPR 2025 · similarity 0.85)
- Unseen Visual Anomaly Generation (CVPR 2025 · similarity 0.85)
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