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MULDE: Multiscale Log-Density Estimation via Denoising Score Matching for Video Anomaly Detection
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Models the density of normal video features with a multiscale neural log-density estimator trained by denoising score matching (with a regularizer), fused across noise scales by a GMM for video anomaly detection.
Problem
One-class video anomaly detection without anomalous training data, where the challenge is to principled model the distribution of normal video features and choose a noise scale for denoising score matching.
Approach
Train a neural network to approximate the negative log-density (not its gradient) of noisy normal features via a modified multiscale denoising score matching loss with a regularizer that aligns log-density across noise levels, then fuse multi-scale anomaly scores with a Gaussian mixture model.
Key results
- Object-centric: MULDE reaches 94.3% micro AUC-ROC on Avenue and 86.7% on ShanghaiTech, outperforming all listed baselines in micro score.
- Frame-centric: MULDE improves micro AUC-ROC on UCFCrime to 78.5% (up 3.8 points over prior SOTA) and to 81.3% on ShanghaiTech and 72.8% on UBnormal.
- Regularization (beta=0.1) improves frame-centric micro AUC on ShanghaiTech from 78.4% to 81.3%; MULDE runs under 1 ms per feature beyond feature extraction.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the log-density regularization term (β=0.1) (ablation) | MULDE · ShanghaiTech (frame-centric) | AUC-ROC micro (%): 78.4 -> 81.3 | Helped |
| Add the log-density regularization term (β=0.1) (ablation) | MULDE · UCFCrime (frame-centric) | AUC-ROC micro (%): 75.9 -> 78.5 | Helped |
| Add the log-density regularization term (β=0.1) (ablation) | MULDE · UBnormal (frame-centric) | AUC-ROC micro (%): 71.3 -> 72.8 | Helped |
| Use β=1.0 instead of β=0.1 for regularization (ablation) | MULDE · ShanghaiTech (frame-centric) | AUC-ROC micro (%): 81.3 -> 81.4 | Helped |
| Use β=1.0 instead of β=0.1 for regularization (ablation) | MULDE · UCFCrime (frame-centric) | AUC-ROC micro (%): 78.5 -> 77.2 | Hurt |
| Use β=1.0 instead of β=0.1 for regularization (ablation) | MULDE · UBnormal (frame-centric) | AUC-ROC micro (%): 72.8 -> 72.5 | Hurt |
| Use a Gaussian mixture model to combine noise-scale scores (ablation) | MULDE · ShanghaiTech (frame-centric) | AUC-ROC micro (%) | Helped |
| Use 2 hidden layers with 4096 units rather than 1 hidden layer with 4096 units (ablation) | MULDE · ShanghaiTech (frame-centric) | AUC-ROC micro (%): 78.4 -> 81.3 | Helped |
| Use 2 hidden layers with 4096 units rather than 3 hidden layers with 4096 units (ablation) | MULDE · ShanghaiTech (frame-centric) | AUC-ROC micro (%): 79.5 -> 81.3 | Helped |
| Use 2 hidden layers with 4096 units rather than 4 hidden layers with 4096 units (ablation) | MULDE · ShanghaiTech (frame-centric) | AUC-ROC micro (%): 80.0 -> 81.3 | Helped |
| Replace the log-density anomaly indicator with the log-density-gradient norm | MULDE · Ped2, Avenue, and ShanghaiTech (object-centric) | AUC-ROC micro (%) | Hurt |
| Use neural density modeling instead of the AccI-VAD density-modeling approach | MULDE · Ped2, Avenue, and ShanghaiTech (object-centric) | AUC-ROC micro (%) | Helped |
Surprising findings
- The log-gradient norm of a multiscale score model (MSMA) is outperformed by the log-density itself, since gradient norms are low at density minima as well as modes.
Limitations
- Requires anomalous and normal features to be distinguishable; no theoretical guarantee depending on feature extractor.
- The upper limit of the noise range must be chosen manually; no automatic selection.
- Regularizer breaks the unbiased log-gradient estimate and beta is optimal differently per dataset.
Experimental setup
Datasets: Ped2 Avenue ShanghaiTech UBnormal UCFCrime
Benchmarks: Ped2 Avenue ShanghaiTech UBnormal UCFCrime
Metrics: AUC-ROC micro AUC-ROC macro
Baselines: CAE-SVM VEC SSMTL HF2 BA-AED Jigsaw-Puzzle AccI-VAD SSMTL++ MSMA STG-NF CT-D2GAN CAC
Builds on: denoising score matching multi-scale denoising score matching (NCSN) MSMA AccI-VAD
Closest papers by meaning
- Holmes-VAU: Towards Long-term Video Anomaly Understanding at Any Granularity (CVPR 2025 · similarity 0.88)
- VADTree: Explainable Training-Free Video Anomaly Detection via Hierarchical Granularity-Aware Tree (NeurIPS 2025 · similarity 0.88)
- Video Anomaly Detection with Motion and Appearance Guided Patch Diffusion Model (AAAI 2025 · similarity 0.88)
- Noise-Resistant Video Anomaly Detection via RGB Error-Guided Multiscale Predictive Coding and Dynamic Memory (CVPR 2025 · similarity 0.87)
- Track Any Anomalous Object:A Granular Video Anomaly Detection Pipeline (CVPR 2025 · similarity 0.87)
- Multi-Scale Video Anomaly Detection by Multi-Grained Spatio-Temporal Representation Learning (CVPR 2024 · similarity 0.86)
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