From Local Recovery to Unified Generation: Discovering Triple Set in Knowledge Graphs via Observation-Anchored Latent Diffusion

Jiaqi Wang; Yisen Gao; Huayang Shi; Junhao Hou; Wengen Li; Jihong Guan; Yichao Zhang; Shuigeng Zhou

cs.LGOct 29, 2026

From Local Recovery to Unified Generation: Discovering Triple Set in Knowledge Graphs via Observation-Anchored Latent Diffusion

Authors: Jiaqi Wang, Yisen Gao, Huayang Shi, Junhao Hou, Wengen Li, Jihong Guan, Yichao Zhang, Shuigeng Zhou,

Organizations: Tongji University · The Chinese University of Hong Kong · The Hong Kong University of Science and Technology · Fudan University

Abstract

Triple set prediction (TSP) is to recover missing relational triples in a knowledge graph by predicting the triple set instead of isolated links. Existing approaches predominantly rely on the subgraph-based completion paradigm, where the original graph is first partitioned into local subgraphs which are then independently completed. Such a paradigm suffers from fragmented structural reasoning, limited cross subgraph dependency modeling, and missing predictions across subgraphs. This paper proposes LatentDiff, a novel unified latent generative framework for TSP, which reformulates knowledge graph completion as latent space graph generation. LatentDiff first learns a compact latent representation using a relation-aware residual-quantized knowledge graph autoencoder, which encodes the whole graph into relation-aware latent embeddings, quantizes them with chunked residual codebooks, and reconstructs triples through a factorized decoder. On top of this latent space, we introduce an observation-anchored latent graph diffusion model, where the target latent graph representation is perturbed toward the observed latent. The reverse process recovers missing triples through progressive latent denoising. Experiments on three benchmark datasets show that LatentDiff outperforms the SOTA in terms of F_{tsp} by 5.4 percentage points on average. Code: https://anonymous.4open.science/r/LKGDiff-44A5.

Figures & tables

Figure 1. Comparison between subgraph-based completion paradigm and our unified latent generation paradigm.

Figure 2. Overview of LatentDiff. Stage I learns a relation-aware residual-quantized latent space for KG reconstruction. Stage II performs observation-anchored latent diffusion to recover the target KG from the observed KG.

Datasets	Entity	Relation	Train	Valid	Test
Wiki79k	7,983	85	57,033	6,337	15,843
Wiki143k	13,928	109	103,415	11,490	28,727
CFamily	2,378	12	16,549	1,839	4,598

Table 1. Statistics of datasets in experiments.

Datasets	Models	Number of Triples in			RS-POWA Metrics				CWA Metrics
		${\mathcal{T}}_{\mathrm{pred}}$	${\mathcal{T}}^{\mathrm{POWA}}_{\mathrm{pred}}$	${\mathcal{T}}^{\mathrm{POWA}+}_{\mathrm{pred}}$	$JPrecision$	$STRecall$	$F_{\rm TSP}$	$F_{1}^{\dagger}$	$JPrecision$	$F_{\rm TSP}$
Wiki79k	HAKE ( Zhang et al., 2020 )	125 $\pm$ 87	119 $\pm$ 83	30 $\pm$ 7	0.246 $\pm$ 14.8%	0.044 $\pm$ 0.4%	0.075 $\pm$ 0.3%	0.004	0.240	0.074
	PairRE ( Chao et al., 2020 )	29742 $\pm$ 105	10217 $\pm$ 51	2901 $\pm$ 7	0.191 $\pm$ 0.1%	0.428 $\pm$ 0.0%	0.264 $\pm$ 0.2%	0.187	0.097	0.158
	AstarNet ( Zhu et al., 2023 )	5689 $\pm$ 287	1750 $\pm$ 116	1328 $\pm$ 52	0.496 $\pm$ 0.8%	0.289 $\pm$ 0.5%	0.365 $\pm$ 0.2%	0.143	0.233	0.258
	ULTRA ( Galkin et al., 2024 )	9743 $\pm$ 0	2945 $\pm$ 0	1062 $\pm$ 0	0.235 $\pm$ 0.0%	0.258 $\pm$ 0.0%	0.246 $\pm$ 0.0%	0.104	0.109	0.153
	GPHT(HAKE) ( Zhang et al., 2024 )	209 $\pm$ 47	191 $\pm$ 47	44 $\pm$ 8	0.220 $\pm$ 8.0%	0.053 $\pm$ 0.4%	0.085 $\pm$ 1.1%	0.006	0.210	0.084

Table 2. The results on Wiki79k and Wiki143k, where

\mathcal{T}^{\rm POWA+}_{\rm pred}

is the number of correctly predicted test triples, and

\mathcal{T}^{\rm POWA}_{\rm pred}

is the triple set that can be judged under the RS-POWA assumption. The best results are in bold, and the second-best results are underlined.

F_{\rm TSP}

is the primary comparison metric.

\dagger

: Standard

F_{1}

under RS-POWA.

Models	Number of Triples in			CWA Metrics
	${\mathcal{T}}_{\mathrm{pred}}$	${\mathcal{T}}^{\mathrm{CWA}}_{\mathrm{pred}}$	${\mathcal{T}}^{\mathrm{CWA}+}_{\mathrm{pred}}$	$JPrecision$	$STRecall$	$F_{\rm TSP}$	$F_{1}^{\dagger}$
HAKE ( Zhang et al., 2020 )	3186 $\pm$ 543	3186 $\pm$ 543	1788 $\pm$ 321	0.561 $\pm$ 1.8%	0.624 $\pm$ 5.9%	0.591 $\pm$ 3.1%	0.459
PairRE ( Chao et al., 2020 )	5732 $\pm$ 2062	5732 $\pm$ 2062	1747 $\pm$ 694	0.305 $\pm$ 1.8%	0.616 $\pm$ 13.7%	0.408 $\pm$ 4.9%	0.338
RGCN ( Schlichtkrull et al., 2018 )	30608 $\pm$ 3443	30608 $\pm$ 3443	3026 $\pm$ 137	0.099 $\pm$ 6.0%	0.811 $\pm$ 0.5%	0.176 $\pm$ 5.2%	0.172
CompGCN ( Vashishth et al., 2019 )	38931 $\pm$ 3745	38931 $\pm$ 3745	2599 $\pm$ 47	0.067 $\pm$ 4.8%	0.752 $\pm$ 0.3%	0.123 $\pm$ 1.7%	0.119
AstarNet ( Zhu et al., 2023 )	2075 $\pm$ 360	2075 $\pm$ 360	911 $\pm$ 187	0.439 $\pm$ 1.7%	0.445 $\pm$ 4.6%	0.442 $\pm$ 3.3%	0.273

Table 3. The results on the CFamily dataset, where

{\mathcal{T}}^{\mathrm{CWA}+}_{\mathrm{pred}}

is the set of correctly predicted test triples. The best results are in bold, and the second-best results are underlined.

F_{\rm TSP}

is the primary comparison metric.

\dagger

: Standard

F_{1}

under CWA.

Variant	Wiki79k	Wiki143k	CFamily	Avg.
LatentDiff	0.585	0.521	0.691	0.599
LatentDiff-Subgraph	0.539	0.472	0.653	0.555
w/o Relational view Attention	0.576	0.495	0.674	0.582
w/o CRVQ (VQ-VAE)	0.030	0.075	0.455	0.187
w/o Quantization (Vanilla AE)	0.498	0.414	0.332	0.415
w/o Factorized Decoder	0.557	0.481	0.659	0.566

Table 4. Ablation study of LatentDiff on three datasets. We report

F_{\mathrm{TSP}}

for TSP evaluation.

Figure 3. Effect of codebook size in CFamily and Wiki79k.

Figure 4. Performance under different CRVQ configurations in CFamily.

Figure 5. Effect of diffusion steps in CFamily and Wiki79k.

Dataset	#Train	#Retained	#Uncovered	Uncovered Ratio	#Test	#Same-subgraph	#Partition-boundary	Boundary Ratio
CFamily	16,549	16,514	35	0.21%	4,598	4,551	47	1.02%
Wiki79k	57,033	53,937	3,096	5.43%	15,843	12,452	3,391	21.40%
Wiki143k	103,415	88,984	14,431	13.95%	28,727	16,781	11,946	41.58%

Table 5. Partition-induced fragmentation statistics on three datasets.

Target Triple	GPHT	DiffTSP	LatentDiff
( October , follows, September )	Missed	Missed	Recalled $(s=0.98)$
( 2006 Asian Games , follows, 2002 Asian Games )	Missed	Missed	Recalled $(s=0.97)$
( Châlons-en-Champagne , twinned with, Neuss )	Missed	Missed	Recalled $(s=0.95)$
( Épinal , located in, Vosges )	Missed	Missed	Recalled $(s=0.91)$
( Braga , shares border with, Guimarães )	Missed	Missed	Recalled $(s=0.89)$
( Bonn , country, Weimar Republic )	Missed	Missed	Recalled $(s=0.75)$

Table 6. Cases of cross-subgraph triples.

Dataset	Method	Recalled	${STRecall}_{\mathrm{bd}}$
Wiki79k	GPHT	$0/3{,}391$	0.000
	DiffTSP	$0/3{,}391$	0.000
	LatentDiff	$178/3{,}391$	0.229
Wiki143k	GPHT	$0/11{,}946$	0.000
	DiffTSP	$0/11{,}946$	0.000
	LatentDiff	$456/11{,}946$	0.195

Table 7. Diagnostic evaluation on partition-boundary test triples.

{STRecall}_{\mathrm{bd}}

is computed only over the partition-boundary subset.

Dataset	GPHT	DiffTSP	LatentDiff	Speedup
CFamily	46.25	8.13	1.64	4.9 $\times$
Wiki79k	151.94	83.77	12.79	6.5 $\times$
Wiki143k	583.69	101.07	35.93	2.8 $\times$

Table 8. Inference time (s) comparison and speedup. The speedup is computed against the fastest baseline DiffTSP.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Hyperparameter	CFamily	Wiki79k	Wiki143k
Stage-I Training
Encoder hidden dimension	64	64	32
Chunks of CRVQ $K$	4	4	4
Number of residual quantizers $L_{c}$	4	4	2
Latent dimension	16	16	16
Codebook size $C$	1024	1024	2048

Appendix

Table 9. Training hyperparameters on three datasets.

Variant	CFamily	Wiki79k	Wiki143k
LatentDiff	0.9703	0.6918	0.7145
w/o Relational view Attention	0.9057	0.6229	0.6927
w/o CRVQ (VQ-VAE)	0.4591	0.0575	0.1098
w/o Quantization (Vanilla AE)	0.9898	0.7187	0.7339
w/o Factorized Decoder	0.8895	0.5891	0.6219

Appendix

Table 10. Stage-I reconstruction ablation results. We report reconstruction

RF_{1}

on three datasets.

Figure 6. Sensitivity to the observed ratio $\rho_{\rm obs}$ . We vary the ratio of observed triples from 0.5 to 0.9 and report $F_{\mathrm{TSP}}$ on CFamily and Wiki79k.

Figure 7. Performance under different CRVQ configurations in Wiki79k.

Dataset	Prediction Time (s)		Peak Memory (MB)
	$S=50$	$S=100$	$S=50$	$S=100$
CFamily	0.72	1.64	2,136	2,136
Wiki79k	12.79	22.96	12,366	12,366
Wiki143k	35.93	45.76	19,872	19,872

Appendix

Table 11. Inference efficiency of LatentDiff under different diffusion steps.

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Open paper AskPDF arXiv

Triple set prediction (TSP) aims to discover missing facts from an incomplete knowledge graph without predefined queries. Existing approaches typically construct the predicted set through triple-level scoring, sometimes preceded by entity pair filtering that can exclude valid missing facts. We propose DiffTSP, a conditional discrete diffusion model that formulates missing fact discovery as conditional subgraph generation. In each subgraph, DiffTSP directly predicts the missing relational structure without a separate entity pair selection stage. The model learns to generate masked target relation states at different corruption levels, with the observed support subgraph retained as conditioning context. Our structure-aware denoising network integrates a Relational Context Encoder, which captures local relational patterns through relation-guided message passing, and a Relational Graph Diffusion Transformer, which models broader structural interactions through relational attention. During generation, partially generated relations can also serve as provisional context for subsequent predictions. Experiments on three public datasets demonstrate improved TSP performance over strong baselines. Additional analyses show lower conflict rates in the predicted triple sets relative to the evaluated baselines. Code: https://anonymous.4open.science/r/DiffTSP-0F92/.

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