Denoising the Future: Context-Aware Spectral Diffusion for Temporal Knowledge Graph Extrapolation

Yanglei Gan; Peng He; Run Lin; Peiyuan Jiang; Yifan Wang; Qiao Liu

cs.CLAug 21, 2026

Denoising the Future: Context-Aware Spectral Diffusion for Temporal Knowledge Graph Extrapolation

Authors: Yanglei Gan, Peng He, Run Lin, Peiyuan Jiang, Yifan Wang, Qiao Liu

Organizations: Southwest Minzu University, Chengdu, China · University of Electronic Science and Technology of China, Chengdu, China · Weixin Group, Tencent, Gunagzhou, China · Zhejiang University, Hangzhou, China

Abstract

Temporal Knowledge Graph (TKG) extrapolation seeks to infer future facts from time-varying relational histories. Recent diffusion-based approaches improve uncertainty modeling through generative denoising, but their aggregated conditioning on subject histories may insufficiently distinguish query-specific evidence from non-salient historical facts, thereby diluting target-discriminative signals. To bridge this gap, we propose FreqDiff, a Frequency-aware Diffusion framework for TKG extrapolation. Specifically, FreqDiff formulates future object prediction as query-slot denoising and develops a dual-stream denoiser that integrates temporal dependency modeling with context-aware spectral calibration. The spectral branch synthesizes history-conditioned filters from learnable bases to adaptively re-calibrate denoising representations, while a frequency-domain regularizer is proposed to align the denoised target with the gold object in spectral space. Experiments on four public TKG benchmarks demonstrate that FreqDiff achieves state-of-the-art performance.

Figures & tables

Figure 1: Illustration of subject-oriented context in TKG. Red -linked facts denote query-oriented evidence, while other subject-related facts may act as contextual noise.

Figure 2: Overview of FreqDiff. Given a subject-oriented history, FreqDiff injects Gaussian noise into the target object representation and reconstructs it through reverse diffusion. The denoiser combines temporal modeling with context-aware spectral calibration, where history-conditioned filters re-calibrate frequency components and fuse them with time-domain representations for future object prediction.

Models	ICEWS14				ICEWS18				ICEWS05-15				GDELT
Models	MRR	Hit@1	Hit@3	Hit@10	MRR	Hit@1	Hit@3	Hit@10	MRR	Hit@1	Hit@3	Hit@10	MRR	Hit@1	Hit@3	Hit@10
DisMult ( 2015 )	15.44	10.91	17.24	23.92	11.51	7.03	12.87	20.86	17.95	13.12	20.71	29.32	8.68	5.58	9.96	17.13
ConvE ( 2018 )	35.09	25.23	39.38	54.68	24.51	16.23	29.25	44.51	33.81	24.78	39.00	54.95	16.55	11.02	18.88	31.60
RotatE ( 2019 )	21.31	10.26	24.35	44.75	12.78	4.01	14.89	31.91	24.71	13.22	29.04	48.16	13.45	6.95	14.09	25.99
TTransE ( 2018 )	13.72	2.98	17.70	35.74	8.31	1.92	8.56	21.89	15.57	4.80	19.24	38.29	5.50	0.47	4.94	15.25
TA-DisMult ( 2018 )	25.80	16.94	29.74	42.99	16.75	8.61	18.41	33.59	24.31	14.58	27.92	44.21	12.00	5.76	12.94	23.54

Table 1: Performance comparison (%) on four benchmarks with MRR and Hits@1/3/10. Best and second-best results are shown in bold and underlined , respectively.

\spadesuit

indicates results re-implemented using official code.

Settings	ICEWS14			ICEWS18
Settings	MRR	Hit@1	Hit@10	MRR	Hit@1	Hit@10
FreqDiff	50.85	39.82	71.48	36.85	26.85	61.47
w/o. $Freq$	48.68	38.94	70.64	35.81	26.04	58.79
w/o. $Time$	42.14	32.37	65.39	18.21	11.76	35.52
w/o. $\mathcal{L}_{\text{fft}}$	49.30	38.84	69.82	36.10	26.13	59.47
w. $\ell_{2}$ Distance	50.21	39.13	70.77	35.14	25.53	59.22

Table 2: Ablation study results ICEWS14 and ICEWS18 datasets in terms of MRR and Hit@1/10.

Panel of Figure 3 — Figure 3: Visualization of learned spectral energy distributions on ICEWS14. The y-axis represents frequency indices, and the x-axis represents latent channels. Red indicates higher spectral energy.

Panel of Figure 4 — Figure 4: Performance under different ratios of sequence corruption on ICEWS18 and GDELT.

Dataset	Metric	DiffuTKG		NADEx		CENET
Dataset	Metric	Base	+ $\mathcal{L}_{\mathrm{fft}}$	Base	+ $\mathcal{L}_{\mathrm{fft}}$	Base	+ $\mathcal{L}_{\mathrm{fft}}$
ICEWS14	MRR	47.58	48.67 +2.29%	48.12	49.03 +1.89%	39.02	43.39 +11.20%
ICEWS14	H@1	36.38	37.73 +3.71%	37.89	38.97 +2.85%	29.62	32.08 +8.31%
ICEWS18	MRR	35.65	36.24 +1.65%	35.37	36.04 +1.89%	27.85	29.96 +7.58%
ICEWS18	H@1	25.19	26.36 +4.64%	25.48	26.13 +2.55%	18.15	20.85 +14.88%
GDELT	MRR	21.35	22.90 +7.26%	21.78	23.18 +6.43%	20.23	21.90 +8.26%

Table 3: Effectiveness of the frequency regularizer. Red superscripts indicate the improvement rates.

Models	ICEWS14		ICEWS18
Models	MRR	Hit@1	MRR	Hit@1
RE-GCN	23.26	13.91	15.08	7.09
CEN	22.06	13.28	15.41	8.20
RETIA	24.17	14.67	16.62	9.08
HisMatch	27.49	19.04	17.51	11.13
DiffuTKG	25.22	15.23	16.48	8.84

Table 4: Performance of predicting unseen events in terms of MRR and Hit@1 on ICEWS14 and ICEWS18.

Panel of Figure 5 — Figure 5: Hyper-parameter sensitivity analysis on ICEWS14 (left) and ICEWS18 (right) datasets.

Model	ICEWS14		ICEWS18
Model	Inf. Time	Params.	Inf. Time	Params.
RE-GCN	28.96s	26.52Mb	393.67s	42.68Mb
TiRGN	32.88s	43.35Mb	159.90s	59.59Mb
NADEx	10.91s	16.30Mb	96.95s	32.42Mb
FreqDiff	7.28s	17.00Mb	81.24s	32.83Mb

Table 5: Computational efficiency test on ICEWS14/18.

Model	ICEWS14				ICEWS05-15				ICEWS18				GDELT
Model	MRR	H@1	H@3	H@10	MRR	H@1	H@3	H@10	MRR	H@1	H@3	H@10	MRR	H@1	H@3	H@10
LLM-DA ( 2024 )	47.10	36.90	52.60	67.10	52.10	41.60	58.60	72.80	35.70	25.50	40.30	57.00	–	–	–	–
MESH ( 2025 )	44.36	–	49.81	64.21	48.66	–	54.26	68.57	33.96	–	38.37	54.12	–	–	–	–
ANRE ( 2025 )	47.40	36.90	51.10	65.70	50.90	39.10	58.00	69.60	35.50	26.00	39.20	56.70	24.30	16.60	26.60	37.50
TV-LLM ( 2025 )	44.50	36.60	50.20	64.20	50.80	41.30	56.60	72.20	33.20	22.90	37.90	54.10	–	–	–	–
CRI ( 2026 )	49.80	38.10	55.10	70.20	53.10	40.70	59.30	75.10	38.80	27.40	42.10	57.80	–	–	–	–

Table 6: Performance comparison (%) with LLM-based forecasters. The best results are highlighted in bold .

Model	YAGO				WIKI
Model	MRR	H@1	H@3	H@10	MRR	H@1	H@3	H@10
TITer	87.47	80.09	89.96	90.27	73.91	71.70	75.41	76.93
TiRGN	87.95	84.34	91.37	92.92	81.65	77.77	85.12	87.08
DiffuTKG	88.29	84.36	91.79	93.55	82.21	78.96	85.69	88.03
NADEx	88.31	85.14	92.18	93.72	82.83	79.02	85.83	88.34
w/o Freq	86.65	84.78	89.24	89.90	82.55	81.43	84.89	86.38

Table 7: Performance comparison on YAGO and WIKI.

Appendix figures & tables6 assets

Supplementary material from the paper’s appendix.

Appendix

Datasets	$\|E\|$	$\|R\|$	Train	Valid	Test	Unseen Ratio
ICEWS14	6,869	230	74,845	8,514	7,371	58.43%
ICEWS18	23,033	256	373,018	45,995	49,545	55.69%
ICEWS05-15	10,094	251	368,868	46,302	46,159	39.82%
GDELT	7,691	240	1,734,399	238,765	305,241	43.72%

Appendix

Table 8: The statistics of the datasets.

|E|

and

|R|

denote the number of unique entities and event types, respectively.

Hyperparameter	ICEWS14	ICEWS18	GDELT	ICEWS05-15
Hidden dimension	200	200	200	200
Dropout	0.2	0.2	0.2	0.2
Embedding dropout	0.2	0.2	0.2	0.2
Maximum history length	128	128	128	128
Maximum input length	64	64	64	64
Number of epochs	100	100	100	100

Appendix

Table 9: Implementation details for each benchmark.

Panel of Figure 6 — Figure 6: Visualization of learned spectral energy distributions on ICEWS14. The y-axis represents frequency indices, and the x-axis represents latent channels. Red indicates higher spectral energy.

Panel of Figure 7 — Figure 7: Hyper-parameter Sensitivity analysis on ICEWS14 (left) and ICEWS18 (right) datasets.

	FreqDiff	FreqDiff w/o. $Freq$	DiffuTKG
Case #1 Date : 2014-12-18 Query : (Democratic Party (Nigeria), Criticize or denounce , ?) Gold : Muhammadu Buhari	1. Muhammadu Buhari (0.79056861) 2. Citizen (Nigeria) (0.06997431) 3. Congress (Nigeria) (0.04214321) 4. Government (Nigeria) (0.03278727) 5. Head of Government (Nigeria) (0.00737355)	1. Citizen (Nigeria) (0.712012) 2. Muhammadu Buhari (0.145593) 3. Government (Nigeria) (0.028617) 4. Congress (Nigeria) (0.024223) 5. Boko Haram (0.011203)	1. Citizen (Nigeria) (0.231514) 2. Government (Nigeria) (0.184501) 3. Muhammadu Buhari (0.076782) 4. Chibuike Rotimi Amaechi (0.029169) 5. Ministry (Nigeria) (0.029161)
Case #2 Date : 2014-12-25 Query : (Ethiopia, Sign formal agreement , ?) Gold : Sudan	1. Sudan (0.77821444) 2. China (0.14515885) 3. Portugal (0.00858667) 4. Angola (0.00622532) 5. France (0.00528247)	1. Portugal (0.471355) 2. Sudan (0.240765) 3. China (0.106766) 4. United Arab Emirates (0.070986) 5. Angola (0.012471)	1. Portugal (0.118397) 2. China (0.081131) 3. Iran (0.068646) 4. South Africa (0.065919) 5. Ethiopia (0.055098)

Appendix

Table 10: Case study of future entity prediction on ICEWS14. Given a query fact with the target entity masked, the table reports the top-5 predicted entities and their confidence scores produced by FreqDiff, FreqDiff w/o.

Freq

, and DiffuTKG. The red entries denote the ground-truth entities.

Panel of Figure 8 — Figure 8: Input event histories associated with the correct candidate and the misleading high-ranked candidate in Case #1.

Temporal KGs

Temporal knowledge graphs represent time-stamped facts and events to support reasoning about how relationships change and what may happen next.

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HiTS-CL: A Continual Learning Framework for Long-Horizon Temporal Knowledge Graph Extrapolation

Yansong Liu, Rui Liu, Yuan Zuo, Hongwei Zhao+5

Beihang University Beijing, China · Beijing University of Posts and Telecommunications Beijing, China · Hubei Engineering University Xiaogan, Hubei, China

Temporal Link Prediction Replay-Based Continual Learning Online Continual Learning Temporal KGs

Open paper AskPDF arXiv

Extrapolative temporal knowledge graph reasoning (TKGR) predicts future facts from historical snapshots. Most existing methods train once on an early prefix of the timeline and then use a frozen model for all future timestamps. We argue that this fixed-prefix protocol is misaligned with extrapolation. It learns from a static prefix, whereas the target stream is non-stationary: new entities and facts emerge, temporal dependencies shift across regimes, and recurring historical signals must be refreshed online. As a result, models trained only on early snapshots become outdated and degrade over long horizons. We address this mismatch by formulating extrapolative TKGR as continual learning over streaming snapshots. Under this view, effective extrapolation must jointly handle current dynamics, stable knowledge, and recurring historical evidence. Based on these requirements, we propose History-enhanced Two-Step Continual Learning (HiTS-CL), a backbone-agnostic continual learning framework for extrapolative TKGR. HiTS-CL tracks current dynamics via continual fine-tuning, preserves stable knowledge via multi-teacher adaptive distillation, and retains recurring historical evidence via a selective memory of recent and frequent facts. We integrate HiTS-CL into five representative TKGR backbones and evaluate it on four benchmark datasets. HiTS-CL consistently improves extrapolation accuracy, reduces long-horizon degradation, and outperforms strong continual-learning baselines, including a recent method for temporal knowledge graphs. Source code and data are available at https://github.com/liuyansong98/HiTS-CL.

Abstract

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