Selective Denoising Diffusion Model for Time Series Anomaly Detection

Kohei Obata; Zheng Chen; Yasuko Matsubara; Lingwei Zhu; Yasushi Sakurai

cs.LGFeb 27, 2026

Selective Denoising Diffusion Model for Time Series Anomaly Detection

Authors: Kohei Obata, Zheng Chen, Yasuko Matsubara, Lingwei Zhu, Yasushi Sakurai

Organizations: SANKEN, The University of Osaka, Osaka, Japan · Great Bay University, Dongguan, China

Abstract

Time series anomaly detection (TSAD) has been an important area of research for decades, with reconstruction-based methods, mostly based on generative models, gaining popularity and demonstrating success. Diffusion models have recently attracted attention due to their advanced generative capabilities. Existing diffusion-based methods for TSAD rely on a conditional strategy, which reconstructs input instances from white noise with the aid of the conditioner. However, this poses challenges in accurately reconstructing the normal parts, resulting in suboptimal detection performance. In response, we propose a novel diffusion-based method, named AnomalyFilter, which acts as a selective filter that only denoises anomaly parts in the instance while retaining normal parts. To build such a filter, we mask Gaussian noise during the training phase and conduct the denoising process without adding noise to the instances. The synergy of the two simple components greatly enhances the performance of naive diffusion models. Extensive experiments on five datasets demonstrate that AnomalyFilter achieves notably low reconstruction error on normal parts, providing empirical support for its effectiveness in anomaly detection. AnomalyFilter represents a pioneering approach that focuses on the noise design of diffusion models specifically tailored for TSAD.

Figures & tables

Figure 1: Reconstruction examples of encoder-decoder models (i.e., BeatGAN and Anomaly-Transformer), conditional diffusion models (i.e., IMDiffusion), and proposed AnomalyFilter.

Figure 2: An overview of AnomalyFilter framework. The model is trained to predict masked Gaussian noise, with the aim of learning to denoise the anomaly parts (i.e., nonmasked parts) and retaining the normal parts (i.e., masked parts). Noiseless inference operates without noise at the beginning and during the denoising steps. Thus, when given a normal instance, it outputs an instance with no change. When given an anomaly instance, only anomalous parts are removed. AnomalyFilter captures temporal and inter-variable dependencies by temporal and feature transformer layers and predicts noise added to the input.

	UCR				AIOps			Yahoo real			Yahoo bench			SMD
	V-R	V-P	RF	Acc.	V-R	V-P	RF	V-R	V-P	RF	V-R	V-P	RF	V-R	V-P	RF
IsolationForest	0.641	0.106	0.041	0.236	0.798	0.169	0.061	0.699	0.358	0.000	0.611	0.295	0.000	0.735	0.245	0.093
OCSVM	0.645	0.167	0.092	0.300	0.848	0.336	0.152	0.715	0.443	0.000	0.608	0.289	0.000	0.698	0.239	0.156
BeatGAN	$\mathbf{0.746}$	$\underline{0.205}$	$\underline{0.137}$	$\underline{0.351}$	$\underline{0.889}$	$\underline{0.487}$	$\mathbf{0.239}$	0.751	0.503	0.060	0.720	$\underline{0.373}$	0.004	0.819	0.356	0.232
LSTM-VAE	$\underline{0.739}$	0.141	0.113	0.217	0.864	0.359	0.185	$\underline{0.899}$	$\underline{0.612}$	0.076	0.709	0.329	0.003	0.711	0.223	0.190
USAD	0.674	0.156	0.129	0.272	$\underline{0.889}$	0.445	0.227	0.830	0.571	0.075	0.612	0.305	0.000	0.508	0.145	0.088

Table 1: Anomaly detection performance. V-R and V-P are VUS-ROC and VUS-PR ( Paparrizos et al. 2022 ) . RF is Range F-score ( Tatbul et al. 2018 ) . Best results are in bold , and second-best results are underlined (higher is better).

	UCR				AIOps			Yahoo real			Yahoo bench			SMD
	V-R	V-P	RF	Acc	V-R	V-P	RF	V-R	V-P	RF	V-R	V-P	RF	V-R	V-P	RF
DAE	$\mathbf{0.760}$	$\mathbf{0.252}$	$\underline{0.190}$	$\underline{0.386}$	0.900	0.501	$\mathbf{0.266}$	0.888	0.614	$\underline{0.083}$	0.694	0.310	0.003	0.866	0.435	0.238
DAE w/ M	0.685	0.149	0.125	0.266	0.890	0.495	0.243	0.894	0.606	0.080	0.688	0.286	0.001	$\underline{0.878}$	0.452	0.257
DAE w/ N	$\underline{0.758}$	0.234	0.173	0.382	0.884	0.448	$\underline{0.257}$	0.887	0.593	0.073	0.687	0.284	0.001	0.875	$\underline{0.456}$	0.255
DAE w/ M&N	0.693	0.172	0.144	0.291	$\underline{0.915}$	$\underline{0.519}$	0.242	$\mathbf{0.905}$	$\underline{0.624}$	0.081	0.696	$\underline{0.316}$	$\underline{0.004}$	0.876	0.439	0.265
DDPM	0.660	0.071	0.054	0.110	0.761	0.183	0.100	0.865	0.550	0.064	0.714	0.280	0.001	0.786	0.337	$\underline{0.267}$

Table 2: Ablation study with different components. M and N refer to Bernoulli mask and Noiseless inference, respectively.

	UCR			AIOps			Yahoo real			Yahoo bench			SMD
	$MSE_{a}$	$MSE_{n}$	$\frac{MSE_{a}}{MSE_{n}}$	$MSE_{a}$	$MSE_{n}$	$\frac{MSE_{a}}{MSE_{n}}$	$MSE_{a}$	$MSE_{n}$	$\frac{MSE_{a}}{MSE_{n}}$	$MSE_{a}$	$MSE_{n}$	$\frac{MSE_{a}}{MSE_{n}}$	$MSE_{a}$	$MSE_{n}$	$\frac{MSE_{a}}{MSE_{n}}$
BeatGAN	0.0153	0.0030	5.1	0.0251	0.0005	50.6	9.6410	0.3539	27.2	0.0660	0.0296	2.2	0.0257	0.0053	4.8
LSTM-VAE	0.0171	0.0030	5.7	0.0361	0.0014	25.5	10.6639	0.3497	30.5	$\underline{0.1656}$	0.1131	1.5	$\underline{0.0387}$	0.0130	3.0
USAD	0.0394	0.0152	2.6	$\underline{0.0715}$	0.0068	10.5	$\underline{12.6297}$	0.7915	16.0	0.1593	0.1265	1.3	0.0036	0.0015	2.3
Anomaly-Transformer	0.0039	$\mathbf{0.0004}$	$\underline{10.3}$	0.0091	$\underline{0.0002}$	50.7	9.6449	0.2966	32.5	0.0266	0.0133	2.0	0.0239	0.0042	5.6
TranAD	0.0447	0.0328	1.4	$\mathbf{0.0892}$	0.0187	4.8	$\mathbf{12.6501}$	0.8379	15.1	$\mathbf{0.2679}$	0.2464	1.1	0.0183	0.0032	5.8

Table 3: Reconstruction quality performance.

MSE_{a}

and

MSE_{n}

are the MSE values of anomalous and normal parts during the inference. Not necessary, but

MSE_{a}

should be higher, and

MSE_{n}

should be lower. The higher the ratio

\frac{MSE_{a}}{MSE_{n}}

is, the easier it is to detect anomalies.

Panel of Figure 3 — Figure 3: Effect of loss weights and noise strength.

Train (Average per subdataset)
	UCR	AIOps	Yahoo real	Yahoo bench	SMD
# of Subdatasets	250	29	37	181	28
# of Features	1	1	1	1	38
Domain	Various	Cloud KPIs	Web traffic	Synthetic	Server
Sequence Length	30522	103588	860	1008	25300
# of Anomalies	0.00	42.35	0.84	5.53	-

Table 4: Statistics of the datasets.

Architecture
Design Parameter	Value
Attention heads	8
# of residual blocks $N$	8
Latent dimension $C$	64
Diffusion model
Forward diffusion step $T$	50

Table 5: Key hyperparameters for AnomalyFilter.

	UCR				AIOps				Yahoo real				Yahoo bench				SMD
	R-R	R-P	A-R	F	R-R	R-P	A-R	F	R-R	R-P	A-R	F	R-R	R-P	A-R	F	R-R	R-P	A-R	F
IsolationForest	0.653	0.114	0.613	0.057	0.825	0.217	0.824	0.187	0.813	0.595	0.601	0.000	0.705	0.487	0.502	0.000	0.764	0.275	0.799	0.171
OCSVM	0.662	0.187	0.618	0.092	0.874	0.463	$\mathbf{0.866}$	0.220	0.841	0.722	0.633	0.000	0.710	0.516	0.523	0.000	0.727	0.274	0.801	0.254
BeatGAN	$\mathbf{0.752}$	$\underline{0.209}$	$\mathbf{0.729}$	$\underline{0.158}$	$\underline{0.912}$	$\underline{0.594}$	0.814	0.214	0.852	0.723	0.655	0.063	0.799	$\underline{0.577}$	0.624	0.005	0.829	0.383	0.857	0.325
LSTM-VAE	$\underline{0.745}$	0.140	$\underline{0.719}$	0.117	0.881	0.419	0.830	0.197	$\mathbf{0.934}$	$\underline{0.782}$	$\mathbf{0.846}$	0.092	0.781	0.520	0.617	0.003	0.732	0.239	0.798	0.266
USAD	0.684	0.157	0.651	0.138	0.908	0.541	$\underline{0.862}$	0.221	0.892	0.758	0.771	0.081	0.695	0.485	0.527	0.000	0.550	0.183	0.583	0.118

Table 6: R-R, R-P, A-R, and F are Range-AUC-ROC, Range-AUC-PR ( Paparrizos et al. 2022 ) , AUC-ROC, and F1.

	UCR				AIOps			Yahoo real			Yahoo bench			SMD
	V-R	V-P	RF	Acc.	V-R	V-P	RF	V-R	V-P	RF	V-R	V-P	RF	V-R	V-P	RF
IsolationForest	0.262	0.201	0.125	0.425	0.103	0.125	0.077	0.220	0.193	0.000	0.195	0.176	0.000	0.145	0.189	0.104
OCSVM	0.271	0.267	0.203	0.459	0.115	0.201	0.132	0.225	0.218	0.000	0.210	0.173	0.000	0.159	0.202	0.199
BeatGAN	0.232	0.280	0.206	0.478	0.116	0.222	0.129	0.217	0.224	0.114	0.186	0.229	0.019	0.144	0.226	0.189
LSTM-VAE	0.208	0.231	0.186	0.412	0.117	0.207	0.125	0.125	0.269	0.161	0.195	0.223	0.021	0.147	0.181	0.210
USAD	0.235	0.257	0.233	0.446	0.123	0.235	0.145	0.196	0.267	0.148	0.235	0.214	0.000	0.201	0.135	0.123

Table 7: Standard deviation of VUS-ROC, VUS-PR, and Range F-score.

Panel of Figure 4 — Figure 4: Critical difference diagram of VUS-PR.

Figure 5: Reconstruction examples across DDPM variants of $\#029$ ABP on UCR.

Panel of Figure 6 — Figure 6: Sensitivity analysis across four hyperparameters.

Panel of Figure 7 — Figure 7: Computational time for training and inference.

Panel of Figure 8 — Figure 8: Reconstruction examples across different methods of (a) AIOps, (b) Yahoo real, (c) Yahoo bench, and (d) SMD.

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FirstDiff: One-Step Diffusion-Based Anomaly Detection for Multivariate Time Series via Initial Noise Prediction

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Time-Series Anomaly Detection Anomaly Detection Unsupervised Anomaly Detection Diffusion Model Inference Acceleration

Open paper AskPDF arXiv

Diffusion models have recently shown strong potential for multivariate time-series anomaly detection by learning the distribution of normal data through iterative denoising. Existing diffusion-based approaches, however, typically perform anomaly detection after completing the reverse diffusion process, relying primarily on the final reconstructed signal and overlooking informative representations produced during denoising. This design incurs substantial computational cost and limits the use of intermediate diffusion information for anomaly detection. In this paper, we propose FirstDiff, a diffusion-based anomaly detection framework based on the observation that the predicted diffusion noise at the initial reverse-diffusion evaluation already contains sufficient information for accurate anomaly detection. FirstDiff models the statistical distribution of predicted diffusion noise under normal behavior using validation data, enabling anomaly inference from a single denoising-network evaluation rather than completing the reverse diffusion trajectory. To model complex temporal and inter-sensor dependencies, FirstDiff employs a Diffusion Transformer as the denoising backbone. Extensive experiments on five public benchmark datasets demonstrate that FirstDiff achieves state-of-the-art performance while reducing diffusion inference from the full reverse trajectory to a single denoising-network evaluation.

Abstract

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