REF-CFA: Anomaly-Related Residual Fields for Cross-domain Anomaly Detection

REF-CFA is a novel framework for label-free anomaly detection under domain shift. It addresses the challenge where conventional residuals are dominated by stochastic noise. By explicitly modeling the Residual-Evolution Field (REF), this method isolates the persistent, anomaly-aligned signal from the non-anomalous dynamics. A Cross-domain Field Alignment (CFA) module then aligns these field representations across domains, enabling a detector trained on a labeled Source Domain to be robustly reused on an unlabeled Target Domain.

✨ Key Components

• Residual-Evolution Field (REF):
  • Constructs a spatio-temporal vector field from diffusion residuals using three primitives:
    • Gradient Residual ($R_t$): Captures amplitude discrepancies.
    • Directional Offset ($M_t$): Measures deviations orthogonal to the normal manifold flow.
    • Path-Integrated Drift ($Q_t$): Accumulates persistent drift over the reverse trajectory.
  • Field Transformer: A lightweight sequence model that aggregates these primitives to produce Adaptive Statistics (Energy $E$, Non-Stationarity $NS$, Directional Variability $DV$).
• Cross-domain Field Alignment (CFA):
  • Enables domain reuse via Temporal Alignment, Second-order Feature Alignment, and Directional Subspace Alignment.
• Supervised Field Detector:
  • A discriminative head ($f_\psi$) trained on the Source Domain using the extracted REF features.

🛠️ Installation

It is recommended to use Anaconda to create a virtual environment:

conda create -n refcfa python=3.8
conda activate refcfa

# Install PyTorch (Adjust CUDA version as needed)
pip install torch torchvision --index-url https://download.pytorch.org/whl/cu118

# Install dependencies
pip install numpy opencv-python pyyaml matplotlib scipy scikit-learn tqdm omegaconf

📂 Data Preparation

Please ensure your data directory structure matches the following layouts and update the root path in your config files.

1. MVTec AD

Standard MVTec structure:

/data/mvtec/
├── bottle
│   ├── train
│   │   └── good
│   └── test
│       ├── good
│       ├── broken_large
│       └── ...

2. VisA (Visual Anomaly)

Structure required for VisA:

/data/visa/
├── candle
│   ├── Data
│   │   ├── Images
│   │   │   ├── Normal
│   │   │   └── Anomaly
│   │   └── Masks
│   │       └── Anomaly

3. DAGM 2007

DAGM structure with _def suffix for defective samples:

/data/dagm/
├── Class1
│   ├── 0001.png
│   └── ... (Normal samples)
├── Class1_def
│   ├── 0001.png
│   └── 0001_mask.png (Defective samples and masks)

🚀 Getting Started

1. Stage S1 & T1: Score Network Training

Train the diffusion score networks ($S_{\theta_S}, S_{\theta_T}$) for both Source and Target domains.

# Train Source Score Network (e.g., MVTec Bottle)
python tools/train_net.py --config-file configs/experiments/mvtec/source_bottle.yaml

# Train Target Score Network (e.g., MVTec Cable)
# Note: Target training is unsupervised (on unlabeled mixture)
python tools/train_net.py --config-file configs/experiments/mvtec/target_cable.yaml

2. Stage S2: Source REF & Detector Training

Construct the Residual-Evolution Field (REF) on the source domain and train the Supervised Field Detector ($g_\phi, f_\psi$).

# Train the Field Transformer and Detector on Source
python tools/analyze_net.py \
  --config configs/experiments/mvtec/source_bottle.yaml \
  --checkpoint output/MVTec_Source_Bottle_Train/checkpoint_epoch_2000.pth \
  --train_localization

• This step learns to isolate anomaly-aligned components ($R, M, Q$) and optimizes the supervised loss $\mathcal{L}_S$.

3. Stage T2: Target CFA & Inference

Apply Cross-domain Field Alignment (CFA) to align the target REF to the source space, then reuse the detector for inference.

# Run Inference on Target Domain using Source Detector + CFA
python tools/analyze_net.py \
  --config configs/experiments/mvtec/target_cable.yaml \
  --checkpoint output/MVTec_Source_Bottle_Train/checkpoint_epoch_2000.pth \
  --run_supervised_localization

• This applies Temporal, Second-order, and Directional alignment before prediction.

4. Visualization & Analysis

REF Visualization (Residual Dynamics)

Visualize the evolution of the residual primitives ($R_t, M_t, Q_t$) and the stationarity break in anomalous regions.

python tools/analyze_net.py \
  --config configs/experiments/visa/target_pcb2.yaml \
  --checkpoint output/VisA_Source_Candle_Train/checkpoint_epoch_2000.pth \
  --analyze_residuals

• Results saved in output/vis_ref_dynamics/.

Field Transformer Analysis

Evaluate the Adaptive Statistics ($E, NS, DV$) generated by the Field Transformer.

python tools/analyze_net.py \
  --config configs/experiments/mvtec/target_cable.yaml \
  --checkpoint output/MVTec_Source_Bottle_Train/checkpoint_epoch_2000.pth \
  --analyze_transformer

⚙️ Configuration

Configurations are located in configs/ and use an inheritance mechanism.

• base/runtime.yaml: Global training parameters.
• base/models.yaml: Model architecture (UNet, Diffusion Steps).
• experiments/<dataset>/<config>.yaml: Experiment-specific configurations.

📊 Output Structure

Component	Description	Output Path
Score Network	$S_\theta$ weights	output/<ExpName>/checkpoint_epoch_X.pth
REF Detector	Field Transformer & Head weights	output/.../supervised_segmenter.pth
Inference	Anomaly Maps $A(u)$	output/vis_supervised/
Analysis	REF Dynamics ($R, M, Q$ plots)	output/vis_ref_dynamics/

📝 Citation

If you use this code, please cite our paper:

@article{refcfa2026,
  title={Anomaly-Related Residual Fields for Cross-domain Anomaly Detection},
  author={Anonymous},
  journal={CVPR Submission},
  year={2026}
}