BUSSARD: Normalizing Flows for Bijective Universal Scene-Specific Anomalous Relationship Detection

Melissa Schween; Mathis Kruse; Bodo Rosenhahn

cs.CVMar 17, 2026

BUSSARD: Normalizing Flows for Bijective Universal Scene-Specific Anomalous Relationship Detection

Authors: Melissa Schween, Mathis Kruse, Bodo Rosenhahn

Organizations: Institute for Information Processing, L3S - Leibniz University Hannover

Abstract

We propose Bijective Universal Scene-Specific Anomalous Relationship Detection (BUSSARD), a normalizing flow-based model for detecting anomalous relations in scene graphs, generated from images. Our work follows a multimodal approach, embedding object and relationship tokens from scene graphs with a language model to leverage semantic knowledge from the real world. A normalizing flow model is used to learn bijective transformations that map object-relation-object triplets from scene graphs to a simple base distribution (typically Gaussian), allowing anomaly detection through likelihood estimation. We evaluate our approach on the SARD dataset containing office and dining room scenes. Our method achieves around 10% better AUROC results compared to the current state-of-the-art model, while simultaneously being five times faster. Through ablation studies, we demonstrate superior robustness and universality, particularly regarding the use of synonyms, with our model maintaining stable performance while the baseline shows 17.5% deviation. This work demonstrates the strong potential of learning-based methods for relationship anomaly detection in scene graphs. Our code is available at https://github.com/mschween/BUSSARD .

Figures & tables

Figure 1: Example image from SARD dataset [ 32 ] . A non complete scene graph consists of: ‘plate-on-chair’, ‘plate-near-clock’, ‘cup-on-table’, ‘chair-near-table’. The anomaly to detect is ‘plate-on-chair’.

Figure 2: The components of BUSSARD . The images are parsed using a pretrained scene graph generator. Each triplet is then encoded using a pretrained word embedding model. The embeddings of the triplets are each concatenated and the dimension is reduced using an autoencoder. In the end, a normalizing flow is used to predict the likelihood of the triplets being anomalous.

Figure 3: The 40 most frequent triplets of the dining room scene. The labels belong to the highlighted bars, showing example triplets.

Scene	Model	AUROC ( $\uparrow$ )	AUC-Recall@k ( $\uparrow$ )
Dining Room	SARD-o	90.30	69.48
	SARD-c	90.50	91.50
	BUSSARD (ours)	97.85 $\pm$ 0.6	92.85 $\pm$ 1.52
Office	SARD-o	81.80	64.52
	SARD-c	82.50	82.70
	BUSSARD (ours)	95.29 $\pm$ 1.65	89.57 $\pm$ 3.46

Table 1: AUROC and AUC-Recall@k on the SARD dataset. SARD-o refers to the original baseline results with incomplete data (some ground truth anomalies missing from top 30 triplets). SARD-c refers to the baseline re-run with corrected data where all ground truth anomalous triplets are present. BUSSARD is evaluated on the corrected data. Both baselines are included for transparency. BUSSARD was executed with ten different seeds and the average and standard deviation are provided. The best performing model is highlighted .

Figure 4: Ablation results with AUROC (

\uparrow

) and AUC-Recall@k (

\uparrow

) of BUSSARD and SARD-c for different synonym rates for the dining room scene. The synonym rate represents the probability of substituting words using synonym mappings. For BUSSARD the dots represent the average results after running with ten different seeds, and the shaded area visualizes the corresponding standard deviation. SARD-c was run only once for each rate as the calculation is deterministic.

Train Set	Test Scene	AUROC ( $\uparrow$ )	AUC-Recall@k ( $\uparrow$ )
SARD	Dining Room	97.46 $\pm$ 0.59	91.60 $\pm$ 2.11
SARD	Office	96.73 $\pm$ 2.06	88.53 $\pm$ 7.31
MIT-67	Dining Room	92.45 $\pm$ 2.50	74.79 $\pm$ 7.93
MIT-67	Office	60.03 $\pm$ 4.45	20.70 $\pm$ 5.63

Table 2: AUROC and AUC-Recall@kk k comparing multi-scene training on MIT-67 and SARD, evaluated per scene on the SARD test set.

Figure 5: Ablation results with the AUROC (

\uparrow

) for different latent space dimensions of the autoencoder.

Experiment	$d_{z}$	AUROC ( $\uparrow$ )	AUC-Recall@k ( $\uparrow$ )
Feature Sum	128	91.22 $\pm$ 2.49	78.88 $\pm$ 4.59
Feature Mult	128	96.48 $\pm$ 0.83	90.02 $\pm$ 2.11
Node Only	512	95.20 $\pm$ 1.66	89.33 $\pm$ 3.32
No AE	900	85.44 $\pm$ 2.33	63.40 $\pm$ 4.78
BUSSARD (ours)	512	97.85 $\pm$ 0.6	92.85 $\pm$ 1.52

Table 3: Ablation study results for the dining room scene. All experiments were executed with ten different seeds and the average results are listed with their standard deviation.

d_{z}

is the input dimension to the normalizing flow.

Figure 6: The 40 most frequent triplets of the office scene . The labels belong to the highlighted bars, showing example triplets.

Figure 7: Ablation results with AUROC (

\uparrow

) and AUC-Recall@k (

\uparrow

) of BUSSARD and SARD-c for different synonym rates for the office scene . The synonym rate represents the probability of substituting words using synonym mappings. For BUSSARD the dots represent the average results after running with ten different seeds, and the shaded area visualizes the corresponding standard deviation. SARD-c was run only once for each rate as the calculation is deterministic.

Scene	Experiment	AUROC ( $\uparrow$ )	AUC-Recall@k ( $\uparrow$ )
Dining Room	RelTR	95.57 $\pm$ 0.88	87.29 $\pm$ 3.2
	$\sigma=0.01$	97.43 $\pm$ 0.57	93.08 $\pm$ 1.41
	$\sigma=0.05$	97.46 $\pm$ 0.47	93.44 $\pm$ 1.18
	$\sigma=0.10$	96.11 $\pm$ 1.22	90.37 $\pm$ 2.54
Office	RelTR	96.09 $\pm$ 1.16	89.47 $\pm$ 3.11
	$\sigma=0.01$	95.39 $\pm$ 1.54	89.77 $\pm$ 3.22

Table 4: Results for experiments for the scene graph generator robustness, with a different scene graph generator and gaussian noise with different

\sigma

. AUROC and AUC-Recall@k on the SARD dataset.

Scene	Embedding Model	AUROC ( $\uparrow$ )	AUC-Recall@k ( $\uparrow$ )
Dining Room	all-MiniLM-L6-v2 [ 63 ]	96.34 $\pm$ 0.69	90.98 $\pm$ 1.35
	all-mpnet-base-v2 [ 55 ]	97.25 $\pm$ 0.55	93.16 $\pm$ 1.22
	Qwen3-Embedding-8B [ 68 ]	97.99 $\pm$ 0.58	94.77 $\pm$ 1.48
	GloVe [ 7 ]	97.85 $\pm$ 0.6	92.85 $\pm$ 1.52
Office	all-MiniLM-L6-v2	95.43 $\pm$ 2.30	89.68 $\pm$ 4.81
	all-mpnet-base-v2	95.40 $\pm$ 2.74	89.69 $\pm$ 5.79

Table 5: Results for experiments with different word embedding models. All variations were executed with ten different seeds and the average and standard deviation is provided. The best performing model is highlighted .

Figure 8: Ablation results with the AUC-Recall@k (

\uparrow

) for different latent space dimensions of the autoencoder.

Experiment	$d_{z}$	AUROC ( $\uparrow$ )	AUC-Recall@k ( $\uparrow$ )
Feature Sum	128	94.18 $\pm$ 2.45	87.35 $\pm$ 5.23
Feature Mult	128	94.65 $\pm$ 3.18	88.24 $\pm$ 6.74
Node Only	512	90.89 $\pm$ 4.33	80.16 $\pm$ 9.26
No AE	900	85.74 $\pm$ 2.98	71.82 $\pm$ 5.18
BUSSARD (ours)	512	95.29 $\pm$ 1.65	89.57 $\pm$ 3.46

Table 6: Ablation study results for office scene. All experiments were executed with ten different seeds and the average results are listed with their standard deviation.

d_{z}

is the input dimension to the normalizing flow.

Panel of Figure 9 — Figure 9: Example images from dining room (left) and office (right). The top images (a) and (d) are normal, while the others contain anomalies.

Panel of Figure 10 — Figure 10: Example scene graphs from dining room images, constructed from the top 30 triplets. The last two scene graphs contain anomalies, which are highlighted red.

Panel of Figure 11 — Figure 11: Example scene graphs from office images, constructed from the top 30 triplets. The last two scene graphs contain anomalies, which are highlighted red.

Panel of Figure 12 — Figure 12: Example subsets of scene graphs with normalized anomaly scores. The red highlighted elements belong to the two triplets with the highest anomaly score and the ground truth is marked with an additional, yellow circle.

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Abstract

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