Cross-View Time-Frequency Diffusion for Extreme-Aware Time-Series Generation

Lin Jiang; Rongchao Xu; Guang Wang

cs.LGOct 12, 2026

Cross-View Time-Frequency Diffusion for Extreme-Aware Time-Series Generation

Authors: Lin Jiang, Rongchao Xu, Guang Wang

Organizations: Department of Computer Science, Florida State University, Tallahassee, FL 32306, USA

Abstract

Generating realistic time-series requires faithfully reproducing rare but high-impact extreme events. Existing approaches often rely on specialized representations or extreme-focused training objectives, which may restrict the diversity of captured extremes or compromise overall distributional fidelity. We propose Cross-View Time-Frequency Diffusion (CrossTF), a framework that exploits discrepancies between time- and frequency-view denoisers for extreme-aware time-series generation. Our key empirical finding is extreme-sensitive cross-view asymmetry: moving along the direction connecting the two views' clean-sample estimates substantially changes extreme fidelity while having limited effects on overall generation quality. We further identify a late-stage cross-view window in which this discrepancy stabilizes and cross-view adjustments have a particularly strong effect on extreme fidelity. These findings motivate a staged optimization strategy in CrossTF: after training and freezing both denoisers, it only needs to learn step-specific fusion parameters within this window using an Extreme Value Theory-based objective under an energy-distance constraint. This formulation supports interpolation between and extrapolation beyond the view-specific estimates while limiting degradation in overall generation quality. Extensive experiments on seven real-world datasets against 11 baselines show that CrossTF improves extreme fidelity by 26.1% and overall performance by 7.4% relative to the strongest baselines. These results highlight cross-view discrepancy as an effective basis for low-dimensional optimization in extreme-aware time-series generation.

Figures & tables

	Relative Max–Min Range ( $\alpha_{i}\in[0,1]$ )			Ratio
Dataset	Loss	Overall	Extreme	Ext./Loss	Ext./Overall
Traffic	4.5%	8.4%	290.4%	65.22 $\times$	34.44 $\times$
Transportation	7.5%	51.1%	254.2%	34.11 $\times$	4.97 $\times$
Temperature	7.3%	12.6%	145.6%	19.91 $\times$	11.52 $\times$
Electricity	8.7%	78.4%	85.2%	9.82 $\times$	1.09 $\times$
Precipitation	33.3%	339.9%	160.3%	4.81 $\times$	0.47 $\times$

Table 1: Extreme-sensitive cross-view asymmetry across seven datasets.

Dataset	Extreme Fidelity				Overall Performance				W–L
Dataset	Best	Ours	Baseline	Improve	Best	Ours	Baseline	Improve	W–L
Traffic	ImagenTime	0.0343	0.0591	+42.0%	FourierDiff	0.0083	0.0138	+39.9%	110–0
Precip.	ImagenTime	0.0755	0.1086	+30.5%	ImagenTime	0.0050	0.0051	+2.0%	103–7
Build.	ImagenTime	0.0762	0.1012	+24.7%	ImagenTime	0.0040	0.0046	+13.0%	102–8
Temp.	ImagenTime	0.0884	0.1222	+27.7%	FIDE	0.0131	0.0165	+20.6%	101–9
Elect.	ImagenTime	0.0691	0.0734	+5.9%	ImagenTime	0.0220	0.0193	$-14.0\%$	102–8

Table 2: Summary of comparisons on seven datasets. Best denotes the strongest baseline. W–L counts Wins-Losses against 11 baselines across 10 metrics, yielding 110 pairwise comparisons per dataset. Lower is better.

Dataset	Type	Method	Extreme Fidelity				Overall Fidelity
Dataset	Type	Method	Mag-Rate	Chg-Rate	Mag-Excess	Chg-Excess	Wass.	Marg.	ACD
Traffic	GAN	TimeGAN	0.6852	0.6682	1.2587	0.7178	0.1240	0.0027	0.1393
	VAE	KoVAE	0.6755	0.9931	0.6919	1.0784	0.3751	0.0100	0.1384
	LLM	SDForger	0.1641	0.7892	0.2229	0.9543	0.2521	0.0053	0.0690
	Diffusion	DiffTime	0.2229	0.2625	0.2053	0.2194	0.1098	0.0020	0.0258
		Diffusion-TS	0.2756	0.6143	0.2531	0.3993	0.1817	0.0036	0.0388

Table 3: Generation performance on the Traffic dataset. All metrics are lower-is-better.

Appendix figures & tables26 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 8 — Figure 8: Representative extremes across different real-world time-series datasets.

	Loss		Overall		Extreme
Dataset	$\alpha$ Var.	Seed Var.	$\alpha$ Var.	Seed Var.	$\alpha$ Var.	Seed Var.
Traffic	4.5%	1.45%	8.4%	9.21%	290.4%	17.10%
Transportation	7.5%	1.70%	51.1%	12.50%	254.2%	10.81%
Temperature	7.3%	1.70%	12.6%	14.49%	145.6%	9.62%
Electricity	8.7%	0.28%	78.4%	3.76%	85.2%	4.50%
Precipitation	33.3%	1.01%	339.9%	4.63%	160.3%	14.73%

Appendix

Table 4: Comparison between

\alpha

-induced variation and seed variation across seven datasets.

Dataset	$T$	Delay	Emb.	Time Res.	$(n_{\mathrm{fft}},h)$	Frequency Res.
Traffic	144	3	48	$48\times 48$	$(95,3)$	$48\times 48$
Precip.	90	2	32	$32\times 32$	$(63,3)$	$32\times 32$
Build.	144	3	48	$48\times 48$	$(95,3)$	$48\times 48$
Temp.	144	3	48	$48\times 48$	$(95,3)$	$48\times 48$
Elect.	144	3	48	$48\times 48$	$(95,3)$	$48\times 48$
Transp.	144	3	48	$48\times 48$	$(95,3)$	$48\times 48$

Appendix

Table 5: View-specific representation configurations across datasets.

Panel of Figure 9 — Figure 9: Representative sequences from the seven datasets described above. Each panel presents two typical samples and one sample exhibiting pronounced extreme behavior.

Baseline	Category	Venue	Link
TimeGAN ( Yoon et al., 2019 )	GAN	NeurIPS’19	Implementation Used
KoVAE ( Naiman et al., 2024b )	VAE	ICLR’24	Official Implementation
SDForger ( Rousseau et al., 2025 )	LLM	NeurIPS’25	Official Implementation
DiffTime ( Coletta et al., 2023 )	Diffusion	NeurIPS’23	Implementation Used
Diffusion-TS ( Yuan and Qiao, 2024 )	Diffusion	ICLR’24	Official Implementation
FourierDiff ( Crabbé et al., 2024 )	Diffusion	ICML’24	Official Implementation

Appendix

Table 6: Overview of the baselines.

Dataset	Time-Only	Freq.-Only	CrossTF	Gain vs. Time	Gain vs. Freq.
Elect.	0.1531	0.1018	0.0691	+54.9%	+32.1%
Build.	0.1031	0.1280	0.0762	+26.0%	+40.4%
Precip.	0.0963	0.1899	0.0755	+21.7%	+60.3%
Temp.	0.0979	0.2217	0.0884	+9.7%	+60.1%
ECG	0.1534	0.1667	0.1421	+7.4%	+14.8%
Transp.	0.0512	0.1627	0.0477	+7.0%	+70.7%

Appendix

Table 7: Detailed cross-view ablation on extreme fidelity across seven datasets. Extreme fidelity is summarized by the geometric mean of the four extreme-fidelity metrics. “Gain” denotes the relative improvement of CrossTF over each single-view baseline, where positive values indicate improvement. Lower is better. Best and second-best fidelity values are shown in bold and underlined, respectively.

Dataset	Time-Only	Freq.-Only	CrossTF	Gain vs. Time	Gain vs. Freq.
Elect.	0.0142	0.0184	0.0139	+2.3%	+24.5%
Build.	0.0025	0.0037	0.0025	+0.3%	+32.7%
Precip.	0.0015	0.0031	0.0015	+0.0%	+53.3%
Temp.	0.0111	0.0133	0.0111	-0.6%	+16.3%
ECG	0.0179	0.0187	0.0180	-0.9%	+3.7%
Transp.	0.0139	0.0189	0.0135	+2.4%	+28.5%

Appendix

Table 8: Detailed cross-view ablation on overall fidelity across seven datasets. Overall fidelity is summarized by the geometric mean of the three overall-fidelity metrics. “Gain” denotes the relative improvement of CrossTF over each single-view baseline, where positive values indicate improvement. Lower is better. Best and second-best fidelity values are shown in bold and underlined, respectively.

Dataset	Method	Extreme Fidelity				Overall Fidelity
Dataset	Method	Mag-Rate	Mag-Excess	Chg-Rate	Chg-Excess	Wass.	Marg.	ACD
Elect.	Time-Only	0.1070	0.1991	0.1669	0.1546	0.0327	0.0107	0.0082
	Frequency-Only	0.0772	0.0564	0.0818	0.3009	0.0456	0.0194	0.0070
	CrossTF	0.0802	0.1329	0.0345	0.0619	0.0315	0.0127	0.0067
Build.	Time-Only	0.0518	0.0840	0.1632	0.1587	0.0294	0.0000	0.0177
	Frequency-Only	0.0746	0.0952	0.1624	0.2326	0.0388	0.0000	0.0370

Appendix

Table 9: Detailed cross-view ablation results on extreme and overall fidelity across seven datasets. All metrics are lower-is-better. Best results are shown in bold and second-best results are underlined.

Dataset	Cross-View Window						Gain vs. Single $\bm{\alpha}$
Dataset	$\bm{\alpha_{1}}$	$\bm{\alpha_{2}}$	$\bm{\alpha_{3}}$	$\bm{\alpha_{4}}$	$\bm{\alpha_{5}}$	$\bm{\alpha_{6}}$	Gain vs. Single $\bm{\alpha}$
Elect.	0.546	0.440	0.480	0.846	0.654	0.681	+45.4%
Build.	1.271	1.544	1.871	1.905	1.812	1.735	+20.3%
Precip.	0.954	1.006	1.101	0.979	0.701	0.404	+5.8%
Temp.	1.502	1.460	1.335	0.939	0.804	0.779	+8.0%
ECG	0.571	0.666	0.977	1.143	0.911	0.830	+0.7%

Appendix

Table 10: Learned step-wise fusion parameters

\alpha_{i}

within the cross-view window across seven datasets. The final six denoising steps (

i=6,\ldots,1

) form the cross-view window. Parameters within the interpolation range (

0\leq\alpha_{i}\leq 1

) and extrapolation range (

\alpha_{i}<0

\alpha_{i}>1

) are shown in blue and orange , respectively. The last column reports the relative gain in extreme fidelity over using a single shared

\alpha

across the window.

Figure 10: Cross-view complementarity versus same-view model diversity. Left: relative max–min range of extreme fidelity along cross-view and same-view directions, with annotations showing their ratio. Right: endpoint gap normalized by sampling standard error; the dashed line marks the $2$ -standard-error noise threshold. Cross-view directions exhibit substantially stronger and more stable extreme-sensitive variation.

Dataset	Sensitivity Range			Gap / Standard Error
Dataset	Cross-View	Same-View	Ratio	Cross-View	Same-View
Transp.	238.8%	9.1%	26.28 $\times$	19.73	0.72
Traffic	250.3%	11.6%	21.54 $\times$	5.60	0.87
Precip.	214.3%	11.9%	18.02 $\times$	8.85	0.51
Temp.	130.8%	11.7%	11.14 $\times$	8.39	0.78
Elect.	85.0%	11.8%	7.17 $\times$	6.86	1.59

Appendix

Table 11: Comparison of cross-view and same-view sensitivity across seven datasets. The range ratio is computed as the cross-view range divided by the same-view range, while Gap / Standard Error measures the observed gap relative to sampling variability. Values of Gap / Standard Error

\geq 2

are considered beyond sampling noise. For the median row, the range ratio is computed from the median cross-view and same-view ranges using the unrounded values.

Method	Training (min) $\downarrow$	Sampling 1K (s) $\downarrow$	Relative Sampling
TimeGAN	108.0	2.90	0.78 $\times$
KoVAE	6.2	0.03	0.01 $\times$
SDForger	19.7	151.10	40.84 $\times$
DiffTime	60.0	0.42	0.11 $\times$
Diffusion-TS	8.1	24.10	6.51 $\times$
FourierDiff	2.7	23.20	6.27 $\times$

Appendix

Table 12: Training and sampling efficiency comparison. Total training time is reported in minutes, and sampling time is measured for generating 1,000 samples. Relative sampling time is normalized by CrossTF, with CrossTF set to

1.00\times

; values above

1\times

indicate slower sampling than CrossTF.

Dataset	Type	Method	Extreme Fidelity				Overall Fidelity
Dataset	Type	Method	Mag-Rate	Chg-Rate	Mag-Excess	Chg-Excess	Wass.	Marg.	ACD
Precip.	GAN	TimeGAN	0.2923	0.4502	1.0694	1.0721	0.1259	2.18e-05	0.0136
	VAE	KoVAE	0.9404	0.9779	0.7589	0.7514	0.2005	2.23e-05	0.0063
	LLM	SDForger	0.9623	0.4326	0.9122	0.7071	0.6871	1.04e-04	0.0162
	Diffusion	DiffTime	0.2816	0.1978	0.2209	0.1667	0.0607	1.76e-05	0.0074
		Diffusion-TS	0.9686	0.8395	0.4960	0.4518	0.2537	4.83e-05	0.0063

Appendix

Table 13: Generation performance on the Precip. dataset. All metrics are lower-is-better.

Dataset	Type	Method	Extreme Fidelity				Overall Fidelity
Dataset	Type	Method	Mag-Rate	Chg-Rate	Mag-Excess	Chg-Excess	Wass.	Marg.	ACD
Build.	GAN	TimeGAN	0.3299	0.4519	0.1554	1.1183	0.1900	1.82e-04	0.2302
	VAE	KoVAE	0.3504	0.5416	0.2563	0.4590	0.4135	3.00e-04	0.1417
	LLM	SDForger	0.2244	0.5211	0.2174	0.4442	0.3577	2.23e-04	0.0910
	Diffusion	DiffTime	0.1902	0.2676	0.1616	0.2347	0.1552	6.52e-05	0.0478
		Diffusion-TS	0.2428	0.4228	0.2093	0.4149	0.2102	6.74e-05	0.0777

Appendix

Table 14: Generation performance on the Build. dataset. All metrics are lower-is-better.

Dataset	Type	Method	Extreme Fidelity				Overall Fidelity
Dataset	Type	Method	Mag-Rate	Chg-Rate	Mag-Excess	Chg-Excess	Wass.	Marg.	ACD
Temp.	GAN	TimeGAN	1.4295	15.7082	0.6670	5.7697	0.2666	0.0089	0.2837
	VAE	KoVAE	0.6441	1.0221	0.7101	1.5098	0.2467	0.0077	0.1475
	LLM	SDForger	0.1175	0.6380	0.1528	1.2320	0.2247	0.0058	0.0804
	Diffusion	DiffTime	0.1903	0.1545	0.1360	0.3976	0.3028	0.0065	0.0308
		Diffusion-TS	0.1410	0.3274	0.2299	0.4479	0.1726	0.0040	0.0253

Appendix

Table 15: Generation performance on the Temp. dataset. All metrics are lower-is-better.

Dataset	Type	Method	Extreme Fidelity				Overall Fidelity
Dataset	Type	Method	Mag-Rate	Chg-Rate	Mag-Excess	Chg-Excess	Wass.	Marg.	ACD
Elect.	GAN	TimeGAN	0.2936	1.0724	0.8155	1.3465	0.1261	0.0522	0.0694
	VAE	KoVAE	0.9229	1.1475	0.7631	0.9310	0.3385	0.0778	0.0422
	LLM	SDForger	0.4007	1.4693	0.7653	1.8697	0.2040	0.0575	0.0408
	Diffusion	DiffTime	0.2456	0.1872	0.1802	0.1525	0.1143	0.0256	0.0246
		Diffusion-TS	0.3145	0.6035	0.3155	0.4491	0.3212	0.0510	0.0286

Appendix

Table 16: Generation performance on the Elect. dataset. All metrics are lower-is-better.

Dataset	Type	Method	Extreme Fidelity				Overall Fidelity
Dataset	Type	Method	Mag-Rate	Chg-Rate	Mag-Excess	Chg-Excess	Wass.	Marg.	ACD
Transp.	GAN	TimeGAN	0.2161	0.8154	0.4333	0.7877	0.1951	0.5131	0.0298
	VAE	KoVAE	0.6015	0.8455	0.6152	0.7580	0.2056	0.5539	0.0635
	LLM	SDForger	0.1201	0.3637	0.4108	0.6160	0.1127	0.2715	0.0268
	Diffusion	DiffTime	0.2473	0.2002	0.2661	0.1386	0.1560	0.3159	0.0194
		Diffusion-TS	0.2835	0.5090	0.2599	0.3218	0.1393	0.1938	0.0391

Appendix

Table 17: Generation performance on the Transp. dataset. All metrics are lower-is-better.

Dataset	Type	Method	Extreme Fidelity				Overall Fidelity
Dataset	Type	Method	Mag-Rate	Chg-Rate	Mag-Excess	Chg-Excess	Wass.	Marg.	ACD
ECG	GAN	TimeGAN	0.8675	0.4654	0.9233	1.7869	0.0886	0.0581	0.0282
	VAE	KoVAE	2.7715	1.9206	3.7157	2.1064	0.3909	0.1586	0.1084
	LLM	SDForger	1.9948	1.8672	3.4791	2.1706	0.3934	0.1243	0.0546
	Diffusion	DiffTime	0.5198	0.6658	0.3663	0.7390	0.2807	0.0723	0.0298
		Diffusion-TS	0.4689	0.5354	0.2841	0.5571	0.1496	0.0440	0.0153

Appendix

Table 18: Generation performance on the ECG dataset. All metrics are lower-is-better.

Metric	Method	Traffic	Precip.	Build.	Temp.	Elect.	Transp.	ECG	#Best
Disc $\downarrow$	CrossTF (Ours)	0.0126 †	0.0212 †	0.0466	0.0088	0.0470 †	0.0189 †	0.0342 †	5
	ImagenTime	0.0396 †	0.0157 †	0.0086 †	0.0214	0.0295 †	0.0076 †	0.0067 †	6
	DiffTime	0.0968	0.1053 †	0.0784	0.1266	0.1000 †	0.1307	0.1867 †	3
	FIDE	0.3897	0.0354	0.2595	0.0016	0.0364 †	0.1913	0.2550	2
	FourierDiff	0.0209 †	0.4929	0.0082	0.0263	0.1091	0.1989	0.3025	1
	E4GEN	0.3240	0.3325	0.0992	0.1053	0.2038	0.1780 †	0.2658	1

Appendix

Table 19: Downstream task utility across seven real-world datasets. Bold denotes the best or tied-best result. A result is regarded as tied with the best method (

\dagger

) when their performance ranges across random seeds overlap. The last column reports the number of best or tied-best results.

Panel of Figure 11 — Figure 11: Distribution visualization on the Traffic dataset. Each panel triplet shows the PCA projection, t-SNE embedding, and kernel density estimate for one method against the real data.

Panel of Figure 12 — Figure 12: Distribution visualization on the Transportation dataset. Each panel triplet shows the PCA projection, t-SNE embedding, and kernel density estimate for one method against the real data.

Panel of Figure 13 — Figure 13: Distribution visualization on the Temperature dataset. Each panel triplet shows the PCA projection, t-SNE embedding, and kernel density estimate for one method against the real data.

Panel of Figure 14 — Figure 14: Distribution visualization on the Electricity dataset. Each panel triplet shows the PCA projection, t-SNE embedding, and kernel density estimate for one method against the real data.

Panel of Figure 15 — Figure 15: Distribution visualization on the Precipitation dataset. Each panel triplet shows the PCA projection, t-SNE embedding, and kernel density estimate for one method against the real data.

Panel of Figure 16 — Figure 16: Distribution visualization on the ECG dataset. Each panel triplet shows the PCA projection, t-SNE embedding, and kernel density estimate for one method against the real data.

Panel of Figure 17 — Figure 17: Distribution visualization on the Building dataset. Each panel triplet shows the PCA projection, t-SNE embedding, and kernel density estimate for one method against the real data.

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Jun 1, 2026J/K move · Enter open · S save

E4GEN: Event-level Explainable Extreme-Enhanced Time-series Generation

Lin Jiang, Dahai Yu, Ximiao Li, Guang Wang

Florida State University

Time Series Generation Generative Modeling Diffusion Models

Open paper AskPDF arXiv

Generating realistic time series is essential for scientific research and real-world applications. However, existing methods often emphasize overall distributional fidelity while failing to faithfully capture extreme events. To advance existing research, we propose E4GEN, an explainable diffusion framework for extreme event-aware time-series generation. E4GEN provides systematic insights into when, what, and how to control extreme-event generation through three key components. First, E-Activator learns the dataset-adaptive extreme-control signal activation step during the denoising process without interfering with regular temporal components, including trend and seasonality. Second, E-Predictor determines what control signal to enforce through Self-Driven Semantic Prediction, where each sample derives its own control signal by inferring latent extreme-event information during generation. It also includes a novel Data-Conditioned Training, Noise-Initiated Sampling mechanism to address the issue of unavailable training labels. Third, E-Control specifies how to control extreme-event generation through a trainable Extreme Control Network, which transforms the semantic control signal into layer-wise signals and injects it into the denoising process. We evaluate E4GEN on six datasets with 17 metrics, and extensive experiments show that E4GEN outperforms state-of-the-art models across multiple dimensions, including overall fidelity, extreme-event fidelity, and downstream utility.

Abstract

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E4GEN: Event-level Explainable Extreme-Enhanced Time-series Generation

ChronoFlow: Hierarchical Flow Matching for Irregular Time Series Generation

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