Multivariate Time Series Anomaly Detection via Dual-Branch Reconstruction and Autoregressive Flow-based Residual Density Estimation

Jun Liu; Ying Chen; Ziqian Lu; Qinyue Tong; Jun Tang

cs.LGMar 29, 2026

Multivariate Time Series Anomaly Detection via Dual-Branch Reconstruction and Autoregressive Flow-based Residual Density Estimation

Authors: Jun Liu, Ying Chen, Ziqian Lu, Qinyue Tong, Jun Tang

Organizations: Zhejiang University, Hangzhou, China · Zhejiang Sci-Tech University, Hangzhou, China

Abstract

Multivariate Time Series Anomaly Detection (MTSAD) is critical for real-world monitoring scenarios such as industrial control and aerospace systems. Mainstream reconstruction-based anomaly detection methods suffer from two key limitations: first, overfitting to spurious correlations induced by an overemphasis on cross-variable modeling; second, the generation of misleading anomaly scores by simply summing up multivariable reconstruction errors, which makes it difficult to distinguish between hard-to-reconstruct samples and genuine anomalies. To address these issues, we propose DBR-AF, a novel framework that integrates a dual-branch reconstruction (DBR) encoder and an autoregressive flow (AF) module. The DBR encoder decouples cross-variable correlation learning and intra-variable statistical property modeling to mitigate spurious correlations, while the AF module employs multiple stacked reversible transformations to model the complex multivariate residual distribution and further leverages density estimation to accurately identify normal samples with large reconstruction errors. Extensive experiments on seven benchmark datasets demonstrate that DBR-AF achieves state-of-the-art performance, with ablation studies validating the indispensability of its core components.

Figures & tables

Fig. 1: The left subplot reveals the fatal flaws of existing reconstruction-based methods: cross-variable interference induces large amplitude errors and spurious non-stationary characteristics in reconstructed signals, and anomaly scores are dominated by variables with significant reconstruction errors, thereby giving rise to false positive detections. In contrast, the right subplot demonstrates the advantages of our proposed method: it effectively suppresses cross-variable interference to achieve high-fidelity reconstructions that align with the original multivariate time series and exhibits strong robustness to large-amplitude reconstruction errors during anomaly discrimination. Ground-truth anomaly segments are shaded in pink.

Fig. 2: Overall Framework Diagram of Our Method DBR-AF. Without loss of generality, each transformation in our autoregressive flow is represented as a Scale $\&$ Shift operation. The dashed box illustrates the distribution transformation in the autoregressive flow module. Specifically, the reconstructed residual is given by $\boldsymbol{x}^{\mathrm{residual}}=\{\boldsymbol{x}_{1}^{\mathrm{residual}},\cdots,\boldsymbol{x}_{T}^{\mathrm{residual}}\}$ , and each residual at time step $t$ is independent and identically distributed (i.i.d.), denoted as $\boldsymbol{z}_{0}$ . The residual $\boldsymbol{z}_{0}$ is transformed through $K$ layers of autoregressive flow to obtain the latent variable $\boldsymbol{z}_{K}$ , which is assumed to follow the prior distribution $p_{0}$ . Our autoregressive flow model computes the log-likelihood of the original residual $\boldsymbol{z}_{0}$ by combining the log-likelihood of $\boldsymbol{z}_{K}$ under the prior $p_{0}$ and the sum of log-Jacobian determinants accumulated during the invertible transformations.The negative log-likelihood is then used as the optimization objective. The 3D distribution visualization in the dashed box is for illustrative purposes only and does not represent the actual dimensionality of the distribution. In practice, the distribution dimension is typically equal to the number of variables in the temporal signal.

Dataset	Domain	Train	Valid	Test	Dimension	AR (%)
SMD	Server Machine	566724	141681	708420	38	4.2
MSL	Spacecraft	46653	11664	73729	55	10.5
SMAP	Spacecraft	108146	27037	427617	25	12.8
SWaT	Water Treatment	396000	99000	449919	51	12.1
PSM	Server Machine	105984	26497	87841	25	27.8
NIPS-TS-GECCO	Water Treatment	55408	13852	69261	9	1.1

TABLE I: Statistics of the seven benchmarks, including the domain of the dataset and the number of feature dimensions, as well as the total length of the training, valid, and test sets. AR denotes the abnormal proportion of the test set.

Dataset	SMD			MSL			SMAP			SWaT			PSM
Metric	P	R	F1	P	R	F1	P	R	F1	P	R	F1	P	R	F1
Isolation Forest	42.31	73.29	53.64	53.94	86.54	66.45	52.39	59.07	55.53	49.29	44.95	47.02	76.09	92.45	83.48
OC-SVM	44.34	76.72	56.19	59.78	86.87	70.82	53.85	59.07	56.34	45.39	49.22	47.23	62.75	80.89	70.67
LOF	56.34	39.86	46.68	47.72	85.25	61.18	58.93	56.33	57.60	72.15	65.43	68.62	57.89	90.49	70.61
DAGMM	67.30	49.89	57.30	89.60	63.93	74.62	86.45	56.73	68.51	89.92	57.84	70.40	93.49	70.03	80.08
MPPCACD	71.20	79.28	75.02	81.42	61.31	69.95	88.61	75.84	81.73	82.52	68.29	74.73	76.25	78.35	77.29

TABLE II: Performance comparison of different methods on five MTSAD benchmark datasets (P: Precision, R: Recall, F1: F1-score). A dash (

-

) denotes missing performance data for benchmark datasets not evaluated by these methods. Bold entries indicate optimal performance, and underlined entries indicate suboptimal performance.

Dataset	SMD		MSL		SMAP		SWaT		PSM		Avg
Metric	A-R	A-P	A-R	A-P	A-R	A-P	A-R	A-P	A-R	A-P	A-R	A-P
A.T.	47.28	3.70	48.72	10.64	49.67	12.50	29.40	8.82	48.56	29.42	44.73	13.02
MEMTO	73.24	10.35	49.99	10.48	59.59	16.29	45.41	11.45	49.75	26.96	55.60	15.11
DCdetector	48.77	4.19	50.06	10.61	48.87	12.48	49.74	11.60	49.83	27.64	49.45	13.30
TFMAE	35.76	3.68	51.93	11.06	54.96	14.56	50.22	12.13	48.21	27.28	48.22	13.74
D3R	64.20	12.24	65.26	16.99	41.35	10.62	56.65	13.30	50.03	26.31	55.50	15.89

TABLE III: Performance comparison of different methods on five MTSAD benchmark datasets (A-R: AUC-ROC, A-P: AUC-PR).

Dataset	NIPS-TS-Swan			NIPS-TS-GECCO
Metric	A-R	A-P	F1	A-R	A-P	F1
A.T.	43.49	28.62	73.09	33.46	1.48	19.20
MEMTO	51.12	49.06	73.91	60.96	4.21	69.60
DCdetector	48.50	31.71	73.56	50.53	1.72	28.35
TFMAE	48.35	32.18	73.43	49.29	1.07	42.87
D3R	53.40	40.97	67.57	80.32	12.39	58.66

TABLE IV: Performance comparison of different methods on the other two MTSAD benchmark datasets.

Component					Avg
channel-only	cosine	residual	detach	shuffle	A-R	A-P	F1
✗	✓	✓	✓	✓	73.03	36.50	96.65
✓	✓	✓	✓	✓	61.60 ( -11.43 )	28.82 ( -7.68 )	94.82 ( -1.83 )
✗	✗	✓	✓	✓	70.05 ( -2.98 )	35.14 ( -1.36 )	93.85 ( -2.80 )
✗	✓	✗	✓	✓	70.19 ( -2.84 )	34.34 ( -2.16 )	96.16 ( -0.49 )
✗	✓	✓	✗	✓	66.76 ( -6.27 )	32.61 ( -3.89 )	96.06 ( -0.59 )

TABLE V: ”Channel-only” denotes the configuration retaining only the channel-wise reconstruction branch; ”cosine” refers to the cosine similarity constraint; ”residual” indicates that the input reconstruction residual is adopted as the input of AF; ”detach” represents the disconnection of gradient propagation from AF to DBR; and ”shuffle” corresponds to random channel permutation.

Module		SMD			MSL			SMAP			SWaT			PSM			Avg
DBR	AF	A-R	A-P	F1	A-R	A-P	F1	A-R	A-P	F1	A-R	A-P	F1	A-R	A-P	F1	A-R	A-P	F1
✗	✗	77.19	17.27	88.16	62.46	15.60	88.84	39.74	10.11	71.72	81.89	72.71	87.66	75.41	53.85	97.83	67.34	33.92	86.84
✓	✗	80.54	18.66	88.89	51.87	13.21	92.14	61.98	16.89	96.16	81.94	72.21	89.43	60.45	34.40	97.36	67.36	31.07	92.80
✗	✓	80.87	19.39	94.78	61.82	15.39	93.26	53.13	12.59	86.10	82.05	72.69	97.25	78.70	57.84	98.95	71.31	35.58	94.07
✓	✓	81.59	19.58	94.80	59.67	15.40	95.59	61.83	16.60	96.31	82.29	72.36	97.66	79.81	58.57	98.88	73.03	36.50	96.65

TABLE VI: DBR denotes the dual branch reconstruction encoder, and AF the autoregressive flow model.

Panel of Figure 9 — Fig. 3: Variations of F1-score with $D_{\mathrm{AF}}$ .

Prior Distribution	Trainable	MSL	SMAP	PSM	SWaT	SMD
Diagonal Gaussian	✗	95.20	94.70	97.11	97.23	94.03
Diagonal Gaussian	✓	95.25	94.55	97.02	97.40	94.18
Gaussian Mixture ( $n_{\mathrm{c}}$ = 2)	✗	95.59	96.31	98.88	97.66	94.80
Gaussian Mixture ( $n_{\mathrm{c}}$ = 2)	✓	95.26	95.74	98.80	97.83	94.37
Gaussian Mixture ( $n_{\mathrm{c}}$ = 3)	✗	96.02	94.93	97.44	97.79	95.01
Gaussian Mixture ( $n_{\mathrm{c}}$ = 3)	✓	95.42	95.21	98.12	97.83	94.91

TABLE VII: Performance comparison of the AF module with different prior distributions in our method.

Method	MSL		SMAP		PSM		SWaT		SMD
Method	F1	A-R	F1	A-R	F1	A-R	F1	A-R	F1	A-R
AF	95.59	59.67	96.31	61.83	98.88	79.91	97.66	82.29	94.80	81.59
GMM	95.05	57.67	96.44	56.29	97.66	78.91	96.51	82.10	93.66	81.15

TABLE VIII: Performance comparison between GMM (direct replacement) and the AF module.

Flow Type	Iteration Time(s/it)	MSL		SMAP		PSM		SWaT		SMD
Flow Type	Iteration Time(s/it)	F1	A-R	F1	A-R	F1	A-R	F1	A-R	F1	A-R
MAF	0.080	95.59	59.67	96.31	61.83	98.88	79.91	97.66	82.29	94.80	81.59
NerualSpline	0.068	94.78	59.20	96.47	59.21	98.19	78.99	96.63	82.38	95.15	81.77
NICE	0.052	95.26	58.99	96.22	58.24	98.30	79.58	96.56	82.47	93.77	79.95
RealNVP	0.052	95.30	59.05	96.12	58.42	97.60	78.51	95.88	82.40	94.09	81.10

TABLE IX: Performance comparison of DBR-AF integrated with different normalizing flow architectures. Iteration Time denotes the average per-iteration time calculated across five datasets.

Panel of Figure 13 — Fig. 4: AUC-ROC and F1-score distributions by number of encoder Layers, averaged over five real-world benchmark datasets.

Panel of Figure 14 — Fig. 5: Variations of AUC-ROC and F1-score with Window Size.

Panel of Figure 15 — Fig. 6: Variations of AUC-ROC and F1-score with Encoder Dimension of Temporal Branch $D_{\mathrm{enc}}$ .

Table 16

Fig. 7: Visualization of more anomaly detection results. From top to bottom in each subplot: time series signal, reconstruction signal, anomaly score.

Dataset	Method	Acc	F1	Aff-P	Aff-R	R-AR	R-AP	V-ROC	V-PR
SMD	DBR-AF	99.53	94.80	69.12	92.99	87.33	28.51	86.41	27.54
SMD	CATCH	95.01	62.08	76.14	93.07	84.04	24.08	83.34	23.30
MSL	DBR-AF	99.00	95.59	57.01	96.68	70.23	19.92	70.53	19.72
MSL	CATCH	94.48	78.24	57.38	96.02	68.56	20.90	67.81	20.56
SMAP	DBR-AF	99.30	96.31	53.11	97.94	64.12	18.04	63.95	18.04
SMAP	CATCH	92.93	67.31	45.42	70.02	52.55	12.34	52.50	12.33

TABLE XII: A comprehensive evaluation of DBR-AF versus CATCH using additional metrics across five benchmark datasets.

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