Conditional Diffusion Guided Knowledge Transfer for Multi-Domain Knowledge Graph Completion

# Conditional Diffusion Guided Knowledge Transfer for Multi-Domain Knowledge Graph Completion
Source: [https://arxiv.org/html/2607.03154](https://arxiv.org/html/2607.03154)
\(2026\)

###### Abstract\.

Multi\-domain knowledge graph completion \(MKGC\) aims to improve missing triple prediction in a target KG by transferring knowledge from other support KGs\. Existing methods typically enforce consistency constraints on equivalent entities across KGs to transfer knowledge, which risks suppressing domain\-specific contextual information of entities\. This design can also compromise entity representation information from all KG domains, impeding performance improvements, especially in low\-resource data scenarios\. To address this, we pioneer a generation\-based paradigm for MKGC and propose DMKGC, a conditional diffusion\-guided knowledge transfer framework\. Our key insight is to treat each KG as a partial view of the entity entire information, and generate informative domain\-general entity embeddings through diffusion models conditioned on support KGs\. Particularly, we first initialize domain\-agnostic entity embeddings as prior entity embeddings, and then encode them within individual KGs\. Afterward, we fuse equivalent entities from support KGs as the conditional diffusion generation guidance\. We leverage the prior entity embeddings as the proxy generation objective, which ensures this conditional generation to be unbiased towards any conditioned KGs\. Simultaneously, we also train the generated embeddings to be predictive across KGs, thus preserving domain\-specific information\. Extensive experiments on 14 KGs in 3 benchmarks demonstrate a 4\.3% average MRR improvement in tail entity prediction over state\-of\-the\-art methods, with sustained gains in low\-resource data settings\.

Knowledge Graph Completion, Multi\-Domain Learning, Diffusion Models, Representation Learning, Knowledge Transfer

††journalyear:2026††copyright:cc††conference:Proceedings of the ACM Web Conference 2026; April 13–17, 2026; Dubai, United Arab Emirates††booktitle:Proceedings of the ACM Web Conference 2026 \(WWW ’26\), April 13–17, 2026, Dubai, United Arab Emirates††doi:10\.1145/3774904\.3792252††isbn:979\-8\-4007\-2307\-0/2026/04††ccs:Computing methodologies Knowledge representation and reasoning††ccs:Computing methodologies Semantic networks## 1\.Introduction

Knowledge graphs \(KGs\), which structure knowledge as \(head, relation, tail\) triples, serve as a critical backbone for numerous web applications\(Liuet al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib242); Zhanget al\.,[2025](https://arxiv.org/html/2607.03154#bib.bib240); Lianget al\.,[2025](https://arxiv.org/html/2607.03154#bib.bib241)\)\. However, their practical utility is often hampered by inherent incompleteness, prompting the task of KG completion \(KGC\)\(Panet al\.,[2024](https://arxiv.org/html/2607.03154#bib.bib186); Wanget al\.,[2017](https://arxiv.org/html/2607.03154#bib.bib190)\)\. In general, KGC aims to infer missing elements within triples, typically predicting a missing tail entity given a head entity and a relation\. This task can be challenging in scenarios with scarce data, where the limited observed triples severely hinder predictive performance\(Luoet al\.,[2024](https://arxiv.org/html/2607.03154#bib.bib244); Shenget al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib243)\)\.

In recent years, numerous KGs have been constructed in different domains, which provide complementary knowledge and are promising for improving KGC\. To this end, this paper focuses onmulti\-domain KG completion \(MKGC\)111Here, we use the termdomainto generally denote a KG constructed from various sources, such as different languages or platforms\(Chenet al\.,[2017](https://arxiv.org/html/2607.03154#bib.bib136); Sunet al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib216); Zhanget al\.,[2024b](https://arxiv.org/html/2607.03154#bib.bib250); Yanget al\.,[2025a](https://arxiv.org/html/2607.03154#bib.bib217)\)\., a practical task that aims to predict missing triples in atarget KGby using other relatedsupport KGs\. As shown in Figure[1](https://arxiv.org/html/2607.03154#S1.F1), the task is to predict \(Microsoft,Founder, ?\) in the target KG \(EL\), but the contextual triples ofBillGatesare sparse for prediction\. With the related triples in the support KG\-1 \(EN\), the queried triple can be correctly inferred\. Here, the entities that appear simultaneously among multiple KGs \(e\.g\.BillGates\) are calledequivalent entities, which are previously aligned and connect across these KGs\(Huanget al\.,[2022](https://arxiv.org/html/2607.03154#bib.bib174); Tanget al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib175)\)\.

![Refer to caption](https://arxiv.org/html/2607.03154v1/x1.png)Figure 1\.A toy example of the MKGC task, which predicts missing triples in the target KG with support KGs\.Although the MKGC task is practical, it remains underexplored\. A core challenge lies in designing effective knowledge transfer modules to transfer valuable knowledge from support KGs to a target KG\. Most existing studies\(Chenet al\.,[2020c](https://arxiv.org/html/2607.03154#bib.bib222); Zhuet al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib133); Singhet al\.,[2021](https://arxiv.org/html/2607.03154#bib.bib141); Huanget al\.,[2022](https://arxiv.org/html/2607.03154#bib.bib174); Tanget al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib175); He and Yang,[2024](https://arxiv.org/html/2607.03154#bib.bib212)\)follow aconsistency\-basedparadigm for solutions\. They learn entity embeddings within individual KGs, and then enforce consistency constraints\(Chenet al\.,[2017](https://arxiv.org/html/2607.03154#bib.bib136); Huanget al\.,[2022](https://arxiv.org/html/2607.03154#bib.bib174); He and Yang,[2024](https://arxiv.org/html/2607.03154#bib.bib212)\)between equivalent entities to ensure semantic alignment of KGs \(shown in Figure[2](https://arxiv.org/html/2607.03154#S1.F2)\(a\)\)\. Despite their success, they mostly focus on the consistent information between KGs, neglecting entities’ diverse contextual information\. This enforcement can potentially overshadow unique domain\-specific information in each KG, which can overly regularize entity embeddings and limit predictability, especially in low\-resource scenarios \(shown in Section[4\.3](https://arxiv.org/html/2607.03154#S4.SS3)\)\.

To overcome this limitation, we propose ageneration\-basedknowledge transfer paradigm \(Figure[2](https://arxiv.org/html/2607.03154#S1.F2)\(b\)\)\. The core idea is to learn to generatedomain\-general entity embeddingsthat effectively preserve rich domain\-specific information while remaining unbiased across domains\. To achieve this, we employ diffusion models \(DMs\)\(Hoet al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib233)\), which generate such embeddings conditioned on the entity information from the support KGs\. Here, each KG can be seen as a partial observational view of the entire underlying entity\. This can be analogous to text\-conditioned image generation, where different texts can guide the generation of the same entire visual concept\(Ho and Salimans,[2022](https://arxiv.org/html/2607.03154#bib.bib246); Podellet al\.,[2024](https://arxiv.org/html/2607.03154#bib.bib235)\)\. In contrast to existing consistency\-based methods\(Chenet al\.,[2017](https://arxiv.org/html/2607.03154#bib.bib136); Huanget al\.,[2022](https://arxiv.org/html/2607.03154#bib.bib174); He and Yang,[2024](https://arxiv.org/html/2607.03154#bib.bib212); Tanget al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib175)\), our method generates a unified general\-purpose embedding for each entity across domains, thereby avoiding overly rigid consistency constraints and yielding a more informative representation\.

However, a pivotal challenge still remains: there are no real domain\-general entity embeddings available to supervise the generation process\. To address this, we instead propose using domain\-agnosticprior entity embeddingsas a proxy generation objective during training\. Since these priors are independent of any specific KG domains, they serve as an unbiased reference to guide the generation, ensuring that the resulting embeddings do not favor any particular conditioned KG\. Furthermore, to retain domain\-specific information, we explicitly encourage the generated embeddings to be predictively effective within each KG, thereby preserving the domain\-specific information presented in individual KGs\.

Following the above idea, we propose DMKGC, a conditionalDiffusion guided knowledge transfer framework forMKGC\. Specifically, given a target KG and multiple support KGs, we first share the initial entity embeddings as the prior entity embeddings, which are then independently encoded within the contextual structure of each individual KG\. Subsequently, we introduce a conditional diffusion model to generate domain\-general entity embeddings, conditioned on the encoded representations from the support KGs\. These prior entity embeddings \(prior to KG encoding\) are reused to ensure unbiased generation, and the generated embeddings are also trained to remain KGC task\-predictive in the target KG\. To realize the diffusion process, we design an attentive conditional denoiser that adaptively fuses the support KGs according to the target KG\. In addition, we further devise a single\-domain conditional regularization to enhance the generation stability, which treats each KG as an independent conditional guidance to generate a consistent objective\. Our major contributions can be summarized as follows:

- •We pioneerly formulate MKGC in a generation\-based manner, producing more informative domain\-general representations\.
- •We propose a novel DMKGC222Our code is available at[https://github\.com/JiaweiSheng/DMKGC](https://github.com/JiaweiSheng/DMKGC)\.framework with DMs\. It leverages support KGs as a condition, and simultaneously achieves task\-predictive and domain\-general information with constraints\.
- •Extensive experiments with 14 KGs in 3 benchmarks indicate significant 4\.3% averaged MRR improvements and show sustained improvements in low\-resource data scenarios\.

![Refer to caption](https://arxiv.org/html/2607.03154v1/x2.png)Figure 2\.Paradigm of consistency\-based and our generation\-based knowledge transfer\. Here,𝒮,𝒯\\mathcal\{S\},\\mathcal\{T\}are the support and target KG,𝒬\\mathcal\{Q\}is the query to predict new triples\.
## 2\.Preliminaries

In this section, we introduce the MKGC problem setup and the background of diffusion models\.

### 2\.1\.Problem Formulation

Formally, let𝒟=\{𝒢i\}i=1N\\mathcal\{D\}=\\\{\\mathcal\{G\}\_\{i\}\\\}\_\{i=1\}^\{N\}be a set of KGs, where each KG𝒢i=\(ℰi,ℛi,ℱi\)\\mathcal\{G\}\_\{i\}=\(\\mathcal\{E\}\_\{i\},\\mathcal\{R\}\_\{i\},\\mathcal\{F\}\_\{i\}\)involves entitiesℰi\\mathcal\{E\}\_\{i\}, relationsℛi\\mathcal\{R\}\_\{i\}and factual triplesℱi\\mathcal\{F\}\_\{i\}\. For any two KGs𝒢i\\mathcal\{G\}\_\{i\}and𝒢j\\mathcal\{G\}\_\{j\}, a small set of equivalent entity pairs is given:𝒜i​j=\{\(ei,ej\)∣ei≡ej,ei∈ℰi,ej∈ℰj\}\\mathcal\{A\}\_\{ij\}=\\\{\(e\_\{i\},e\_\{j\}\)\\mid e\_\{i\}\\equiv e\_\{j\},e\_\{i\}\\in\\mathcal\{E\}\_\{i\},\\ e\_\{j\}\\in\\mathcal\{E\}\_\{j\}\\\}\. Additionally, all KGs adhere to a unified relation schemaℛ\\mathcal\{R\}, meaning eachℛi⊆ℛ\\mathcal\{R\}\_\{i\}\\subseteq\\mathcal\{R\}\. The task is to predict query triples𝒬=\{\(h,r,?\)\}\\mathcal\{Q\}\\\!=\\\!\\\{\(h,r,?\)\\\}for a target KG𝒯=𝒢t,𝒢t∈𝒟\\mathcal\{T\}=\\mathcal\{G\}\_\{t\},\\mathcal\{G\}\_\{t\}\\in\\mathcal\{D\}, leveraging existing triples from both the target KG𝒯\\mathcal\{T\}and all other support KGs𝒮=\{𝒢s\|𝒢s∈𝒟,s≠t\}\\mathcal\{S\}=\\\{\\mathcal\{G\}\_\{s\}\|\\mathcal\{G\}\_\{s\}\\in\\mathcal\{D\},s\\neq t\\\}\.

### 2\.2\.Diffusion Model

In this paper, we leverage diffusion models \(DMs\)\(Hoet al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib233); Sohl\-Dicksteinet al\.,[2015](https://arxiv.org/html/2607.03154#bib.bib234)\)to transfer knowledge, which contains a forward and a reverse process\.

![Refer to caption](https://arxiv.org/html/2607.03154v1/x3.png)Figure 3\.The overview of our proposed framework, DMKGC\. It contains \(a\)multi\-domain entity encoderto extract KG features, \(b\)conditional diffusion transferto generate entity embeddings, and \(c\)joint training and inferenceto achieve the task\.#### 2\.2\.1\.Forward Process

Given an input data sample𝒙0∼q​\(x0\)\\bm\{x\}\_\{0\}\\sim q\(x\_\{0\}\), the forward process constructs a series of latent variables𝒙1:T\\bm\{x\}\_\{1:T\}through a Markov chain by gradually adding Gaussian noise acrossTTsteps\. Specifically, the transition at each time stepkkis defined by:

\(1\)q​\(xk\|𝒙k−1\)=𝒩​\(𝒙k;1−βk​𝒙k−1,βk​𝑰\),\\displaystyle q\(x\_\{k\}\|\\bm\{x\}\_\{k\-1\}\)=\\mathcal\{N\}\(\\bm\{x\}\_\{k\};\\sqrt\{1\-\\beta\_\{k\}\}\\bm\{x\}\_\{k\-1\},\\beta\_\{k\}\\bm\{I\}\),wherek∈\{1,2,…,T\}k\\in\\\{1,2,\.\.\.,T\\\},𝒩\\mathcal\{N\}denotes a Gaussian distribution, and factorβk∈\(0,1\)\\beta\_\{k\}\\in\(0,1\)controls the scale of noise added at stepkk\. The factors ensure that, whenT→∞T\\rightarrow\\infty, the variable𝒙k\\bm\{x\}\_\{k\}converges to a standard Gaussian, allowing sampling from a Gaussian noise to generate real samples in the reverse process\.

#### 2\.2\.2\.Reverse Process

DMs learn to iteratively reconstruct data by reversing the forward process trajectory\. Formally, starting from an initial state𝒙T∼𝒩​\(0,1\)\\bm\{x\}\_\{T\}\\sim\\mathcal\{N\}\(0,1\), DMs parameterize a Markov chain that transitions from𝒙k\\bm\{x\}\_\{k\}to𝒙k−1\\bm\{x\}\_\{k\-1\}via:

\(2\)pθ​\(𝒙k−1\|𝒙k\)=𝒩​\(𝒙k−1;𝝁θ​\(𝒙k,k\),Σθ​\(𝒙k,k\)\),\\displaystyle p\_\{\\theta\}\(\\bm\{x\}\_\{k\-1\}\|\\bm\{x\}\_\{k\}\)=\\mathcal\{N\}\(\\bm\{x\}\_\{k\-1\};\\bm\{\\mu\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},k\),\\Sigma\_\{\\theta\}\(\\bm\{x\}\_\{k\},k\)\),wherek∈\{T,T−1,…,1\}k\\in\\\{T,T\-1,\.\.\.,1\\\}denotes the reversed time step,𝝁θ​\(𝒙k,k\)\\bm\{\\mu\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},k\)and𝚺θ​\(𝒙k,k\)\\bm\{\\Sigma\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},k\)are the mean and covariance of the Gaussian distribution generated by a neural networkθ\\theta\. For simplicity and training stability,Σθ​\(𝒙k,k\)\\Sigma\_\{\\theta\}\(\\bm\{x\}\_\{k\},k\)is usually set to constantsσ2​\(k\)​𝑰\\sigma^\{2\}\(k\)\\bm\{I\}varying over time steps\(Hoet al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib233)\)\. In this way, the reverse process can be seen as a step\-by\-step denoising process capturing minor changes\.

#### 2\.2\.3\.Training

The objective function is optimized by maximizing the Evidence Lower Bound \(ELBO\) of the likelihood of the observed data𝒙0\\bm\{x\}\_\{0\}to enable data generation\(Hoet al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib233)\), which is:

\(3\)log⁡p​\(𝒙0\)\\displaystyle\\log p\(\\bm\{x\}\_\{0\}\)=log​∫p​\(𝒙0:T\)​d𝒙1:T=log⁡𝔼𝒒​\(𝒙1:T\|𝒙0\)​\[p​\(𝒙0:T\)q​\(𝒙1:T\|𝒙0\)\]\\displaystyle=\\log\\int p\(\\bm\{x\}\_\{0:T\}\)\\mathrm\{d\}\\bm\{x\}\_\{1:T\}=\\log\\mathbb\{E\}\_\{\\bm\{q\}\(\\bm\{x\}\_\{1:T\}\|\\bm\{x\}\_\{0\}\)\}\[\\frac\{p\(\\bm\{x\}\_\{0:T\}\)\}\{q\(\\bm\{x\}\_\{1:T\}\|\\bm\{x\}\_\{0\}\)\}\]≥𝔼𝒒​\(𝒙1\|𝒙0\)​\[log⁡pθ​\(𝒙0\|𝒙1\)\]⏟reconstruction term​ℒ0−DKL​\(q​\(𝒙T\|𝒙0\)∥p​\(𝒙T\)\)⏟prior matching term​ℒT\\displaystyle\\geq\\underbrace\{\\mathbb\{E\}\_\{\\bm\{q\}\(\\bm\{x\}\_\{1\}\|\\bm\{x\}\_\{0\}\)\}\[\\log p\_\{\\theta\}\(\\bm\{x\}\_\{0\}\|\\bm\{x\}\_\{1\}\)\]\}\_\{\\text\{reconstruction term\}\\ \\mathcal\{L\}\_\{0\}\}\-\\underbrace\{D\_\{\\mathrm\{KL\}\}\(q\(\\bm\{x\}\_\{T\}\|\\bm\{x\}\_\{0\}\)\\\|p\(\\bm\{x\}\_\{T\}\)\)\}\_\{\\text\{prior matching term\}\\ \\mathcal\{L\}\_\{T\}\}−∑k=2T𝔼𝒒​\(𝒙k\|𝒙0\)\[DKL\(q\(𝒙k−1\|𝒙k,𝒙0\)∥pθ\(𝒙k−1\|𝒙k\)\)\]⏟denoising matching term​ℒk−1,\\displaystyle\\quad\-\\sum\_\{k=2\}^\{T\}\\underbrace\{\\mathbb\{E\}\_\{\\bm\{q\}\(\\bm\{x\}\_\{k\}\|\\bm\{x\}\_\{0\}\)\}\[D\_\{\\mathrm\{KL\}\}\(q\(\\bm\{x\}\_\{k\-1\}\|\\bm\{x\}\_\{k\},\\bm\{x\}\_\{0\}\)\\\|p\_\{\\theta\}\(\\bm\{x\}\_\{k\-1\}\|\\bm\{x\}\_\{k\}\)\)\]\}\_\{\\text\{denoising matching term\}\\ \\mathcal\{L\}\_\{k\-1\}\},where there are three terms to resolve:

- •Reconstruction term: Measures fidelity of𝒙0\\bm\{x\}\_\{0\}given state𝒙1\\bm\{x\}\_\{1\}, which can be achieved by mean square error \(MSE\)\.
- •Prior matching term: Ensuresq​\(𝒙T\|𝒙0\)q\(\\bm\{x\}\_\{T\}\|\\bm\{x\}\_\{0\}\)converges to the Gaussian priorp​\(𝒙T\)∼𝒩​\(𝟎,𝑰\)p\(\\bm\{x\}\_\{T\}\)\\sim\\mathcal\{N\}\(\\bm\{0\},\\bm\{I\}\), which is constant with no trainable parameters and usually omitted in optimization\.
- •Denoising matching terms: Minimizes the Kullback\-Leibler \(KL\) divergence between the true probabilityq​\(𝒙k−1\|𝒙k,𝒙0\)q\(\\bm\{x\}\_\{k\-1\}\|\\bm\{x\}\_\{k\},\\bm\{x\}\_\{0\}\)\(analytically tractable\) and the learned probabilitypθ​\(𝒙k−1\|𝒙k\)p\_\{\\theta\}\(\\bm\{x\}\_\{k\-1\}\|\\bm\{x\}\_\{k\}\), allowing iterative generation of𝒙k−1\\bm\{x\}\_\{k\-1\}from𝒙k\\bm\{x\}\_\{k\}\. By simplification\(Hoet al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib233)\), this term can be achieved by∑k=2T𝔼k,ϵ​\[‖ϵ−ϵθ​\(𝒙k,k\)‖22\]\\sum\_\{k=2\}^\{T\}\\mathbb\{E\}\_\{k,\\bm\{\\epsilon\}\}\[\\\|\\bm\{\\epsilon\}\-\\bm\{\\epsilon\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},k\)\\\|\_\{2\}^\{2\}\], whereϵθ​\(𝒙k,k\)\\bm\{\\epsilon\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},k\)is a neural denoiser \(e\.g\., U\-Net\(Hoet al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib233)\), MLP\(Wanget al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib232)\)\) that predicts the added noiseϵ\\bm\{\\epsilon\}at time stepkk\.

#### 2\.2\.4\.Inference & Sampling

With the trained neural denoiserθ\\theta, the DMs can sample𝒙T∼𝒩​\(𝟎,𝑰\)\\bm\{x\}\_\{T\}\\sim\\mathcal\{N\}\(\\bm\{0\},\\bm\{I\}\)and iteratively leveragepθ​\(𝒙k−1\|𝒙k\)p\_\{\\theta\}\(\\bm\{x\}\_\{k\-1\}\|\\bm\{x\}\_\{k\}\)to generate the predicted sample𝒙^0\\hat\{\\bm\{x\}\}\_\{0\}\. Note that all above procedures can be achieved by embeddings for efficiency\(Rombachet al\.,[2022](https://arxiv.org/html/2607.03154#bib.bib236)\)\.

## 3\.Methodology

Our core idea is to generate domain\-general entity embeddings that transfer knowledge from support KGs to enhance the target KG in KGC prediction\. The framework is presented in Figure[3](https://arxiv.org/html/2607.03154#S2.F3)\.

### 3\.1\.Multi\-domain Entity Encoder

#### 3\.1\.1\.Prior Entity Embedding

Prior to KG domain encoding, we obtain entity embeddings via a randomly initialized layer as:

\(4\)𝒆~=Embedding​\(e\),e∈ℰ,\\displaystyle\\tilde\{\\bm\{e\}\}=\\mathrm\{Embedding\}\(e\),e\\in\\mathcal\{E\},where we call𝒆~∈ℝd\\tilde\{\\bm\{e\}\}\\in\\mathbb\{R\}^\{d\}theprior entity embedding\. Here, we share the embeddings for all KGs, whereℰ\\mathcal\{E\}denotes the unified set of entities\. Note that these embeddings are domain\-independent and obtained prior to domain\-specific encoding, making them inherently unbiased toward any domains\.

#### 3\.1\.2\.Domain Entity Embedding

To encode KG domain information, we leverage an effective KG encoder\(Tanget al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib175)\)\. Given a KG𝒢\\mathcal\{G\}\(omit subscript for simplicity\), it encodes an entityeewith its relational neighborhood𝒩​\(e\)\\mathcal\{N\}\(e\)from𝒢\\mathcal\{G\}as:

\(5\)Encoderl​\(𝒆,𝒢\)\\displaystyle\\mathrm\{Encoder\}\_\{l\}\(\\bm\{e\},\\mathcal\{G\}\)=𝒆\+δ​\(∑\{rj,ej\}∈𝒩​\(e\)αl​\(𝒆,𝒓j,𝒆j\)⋅𝑾3l​\[𝒆j⊕𝒓j\]\),\\displaystyle=\\bm\{e\}\+\\delta\(\\\!\\\!\\\!\\\!\\sum\_\{\\\{r\_\{j\},e\_\{j\}\\\}\\in\\mathcal\{N\}\(e\)\}\\\!\\\!\\\!\\\!\\alpha\_\{l\}\(\\bm\{e\},\\bm\{r\}\_\{j\},\\bm\{e\}\_\{j\}\)\\cdot\\bm\{W\}^\{l\}\_\{3\}\[\\bm\{e\}\_\{j\}\\oplus\\bm\{r\}\_\{j\}\]\),αl​\(𝒆,𝒓j,𝒆j\)\\displaystyle\\alpha\_\{l\}\(\\bm\{e\},\\bm\{r\}\_\{j\},\\bm\{e\}\_\{j\}\)=softmax⁡\(scorel​\(𝒆,𝒓j,𝒆j\)\),\\displaystyle=\\operatorname\{softmax\}\(\\mathrm\{score\}\_\{l\}\(\\bm\{e\},\\bm\{r\}\_\{j\},\\bm\{e\}\_\{j\}\)\),scorel​\(𝒆,𝒓j,𝒆j\)\\displaystyle\\mathrm\{score\}\_\{l\}\(\\bm\{e\},\\bm\{r\}\_\{j\},\\bm\{e\}\_\{j\}\)=βrj⋅1d​\(𝑾1l​𝒆⋅𝑾2l​\[𝒆j⊕𝒓j\]\),\\displaystyle=\\beta\_\{r\_\{j\}\}\\cdot\\frac\{1\}\{\\sqrt\{d\}\}\(\\bm\{W\}^\{l\}\_\{1\}\\bm\{e\}\\cdot\\bm\{W\}^\{l\}\_\{2\}\[\\bm\{e\}\_\{j\}\\oplus\\bm\{r\}\_\{j\}\]\),whereδ\\deltais the ReLU activation,⊕\\oplusis the vector concatenation,llis the layer,𝑾1l∈ℝd×d,𝑾2l,𝑾3l∈ℝd×2​d\\bm\{W\}^\{l\}\_\{1\}\\in\\mathbb\{R\}^\{d\\times d\},\\bm\{W\}^\{l\}\_\{2\},\\bm\{W\}^\{l\}\_\{3\}\\in\\mathbb\{R\}^\{d\\times 2d\}are learnable layer weights\. The relation embedding𝒓∈ℝd\\bm\{r\}\\in\\mathbb\{R\}^\{d\}is randomly initialized, and the input𝒆\\bm\{e\}is the prior entity embedding𝒆~\\tilde\{\\bm\{e\}\}from Eq\. \([4](https://arxiv.org/html/2607.03154#S3.E4)\)\. Here, the score considers both the learnable prior weightβr∈ℝ\\beta\_\{r\}\\in\\mathbb\{R\}of relationrr, and also captures the contextual attentive relational relevance\. The encoder output is denoted as𝒛\\bm\{z\}, which we calldomain entity embeddingsas they contain domain\-specific information\.

In the following sections, we use𝒛t\\bm\{z\}\_\{t\}to denote an involved entityeefrom the target KG𝒯=𝒢t\\mathcal\{T\}=\\mathcal\{G\}\_\{t\}, and\{𝒛s\}s\\\{\\bm\{z\}\_\{s\}\\\}\_\{s\}denotes its equivalent entities333FollowingTanget al\.\([2023](https://arxiv.org/html/2607.03154#bib.bib175)\), for simplicity of implementation, we also add virtual isolated entities in the KGs where the equivalent entity doesn’t exist\.from the corresponding support KGs𝒮=\{𝒢s\}s\\mathcal\{S\}=\\\{\\mathcal\{G\}\_\{s\}\\\}\_\{s\}\.

### 3\.2\.Conditional Diffusion Transfer

Unlike existing consistency\-based methods\(Chenet al\.,[2017](https://arxiv.org/html/2607.03154#bib.bib136); Huanget al\.,[2022](https://arxiv.org/html/2607.03154#bib.bib174); He and Yang,[2024](https://arxiv.org/html/2607.03154#bib.bib212)\), we transfer knowledge through conditional diffusion\. To this end, we leverage support KGs as conditional guidance and use the prior entity embeddings as the proxy generation objective to ensure an unbiased generation\. The training will be detailed in Section[3\.3](https://arxiv.org/html/2607.03154#S3.SS3)\.

#### 3\.2\.1\.Forward Process

Given an entityeeand its domain entity embeddings, we expect to generate a domain\-general entity embedding\. To this end, we use the prior embedding𝒆~\\tilde\{\\bm\{e\}\}as the initial state, i\.e\.,𝒙0=𝒆~\\bm\{x\}\_\{0\}=\\tilde\{\\bm\{e\}\}\. As introduced in section[2\.2](https://arxiv.org/html/2607.03154#S2.SS2), the forward process isq​\(xk\|𝒙k−1\)=𝒩​\(𝒙k;1−βk​𝒙k−1,βk​𝑰\)q\(x\_\{k\}\|\\bm\{x\}\_\{k\-1\}\)=\\mathcal\{N\}\(\\bm\{x\}\_\{k\};\\sqrt\{1\-\\beta\_\{k\}\}\\bm\{x\}\_\{k\-1\},\\beta\_\{k\}\\bm\{I\}\), whereβk\\beta\_\{k\}is the noise scale factor\. Using the reparameterization trick\(Kingma and Welling,[2014](https://arxiv.org/html/2607.03154#bib.bib182); Hoet al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib233)\), we can efficiently obtain𝒙k\\bm\{x\}\_\{k\}from𝒙0\\bm\{x\}\_\{0\}as:

\(6\)q​\(𝒙k\|𝒙0\)=𝒩​\(𝒙k;α¯k​𝒙0,\(1−α¯k\)​𝑰\),\\displaystyle q\(\\bm\{x\}\_\{k\}\|\\bm\{x\}\_\{0\}\)=\\mathcal\{N\}\(\\bm\{x\}\_\{k\};\\sqrt\{\\bar\{\\alpha\}\_\{k\}\}\\bm\{x\}\_\{0\},\(1\-\\bar\{\\alpha\}\_\{k\}\)\\bm\{I\}\),whereαk=1−βk\\alpha\_\{k\}=1\-\\beta\_\{k\},α¯k=Πk′=1k​αk\\bar\{\\alpha\}\_\{k\}=\\Pi\_\{k^\{\\prime\}=1\}^\{k\}\\alpha\_\{k\}\. Hence, we can directly obtain the embedding𝒙k=α¯k​𝒙0\+1−α¯k​ϵ,ϵ∼𝒩​\(𝟎,𝑰\)\\bm\{x\}\_\{k\}=\\sqrt\{\\bar\{\\alpha\}\_\{k\}\}\\bm\{x\}\_\{0\}\+\\sqrt\{1\-\\bar\{\\alpha\}\_\{k\}\}\\epsilon,\\epsilon\\sim\\mathcal\{N\}\(\\bm\{0,\\bm\{I\}\}\)at any stepkk\. The last state of the noisy embedding is denoted as𝒙T\{\\bm\{x\}\}\_\{T\}\.

#### 3\.2\.2\.Reverse Process

The reverse process gradually denoises𝒙T\\bm\{x\}\_\{T\}to reconstruct the initial state𝒙0\\bm\{x\}\_\{0\}\. Believing that each KG describes a partial view of the domain\-general entity, we leverage the equivalent entities as condition information for reconstruction\. Thereafter, the reverse process with conditions\(Ho and Salimans,[2022](https://arxiv.org/html/2607.03154#bib.bib246)\)is as follows:

\(7\)pθ​\(𝒙k−1\|𝒙k,𝒄\)=𝒩​\(𝒙k−1;𝝁θ​\(𝒙k,𝒄,k\),σ2​\(k\)​𝑰\),\\displaystyle p\_\{\\theta\}\(\\bm\{x\}\_\{k\-1\}\|\\bm\{x\}\_\{k\},\\bm\{c\}\)=\\mathcal\{N\}\(\\bm\{x\}\_\{k\-1\};\\bm\{\\mu\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},\\bm\{c\},k\),\\sigma^\{2\}\(k\)\\bm\{I\}\),where𝝁θ​\(𝒙k,𝒄,k\)\\bm\{\\mu\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},\\bm\{c\},k\)is learned by a conditional denoiser \(detailed later\)\. Here,𝒄∈ℝd\\bm\{c\}\\in\\mathbb\{R\}^\{d\}is the embedding of one or more equivalent entities to guide the generation \(i\.e\., noise prediction\)\.

#### 3\.2\.3\.Conditional Denoiser

The conditional denoiser learns to predict the added noise at each time stepkk\. To keep it simple, we employ an effective multilayer perceptron \(MLP\) as the denoiser:

\(8\)𝒙^θ​\(𝒙k,𝒄,k\):=MLP⁡\(𝒙k⊕𝒄⊕𝒌;θ\),\\displaystyle\\hat\{\\bm\{x\}\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},\\bm\{c\},k\)=\\operatorname\{MLP\}\(\\bm\{x\}\_\{k\}\\oplus\\bm\{c\}\\oplus\\bm\{k\};\\theta\),where we use a two\-layer MLP with dimensions as3​d→2​d→d3d\\rightarrow 2d\\rightarrow d, and𝒌∈ℝd\\bm\{k\}\\in\\mathbb\{R\}^\{d\}is the time\-step embedding\(Hoet al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib233)\)\. Here, as the condition information can be different, we consider three types of condition𝒄\\bm\{c\}: \(i\) when the condition is not given, we set𝒄=ϕ\\bm\{c\}=\\phiwhereϕ∈ℝd\\phi\\in\\mathbb\{R\}^\{d\}is an initializednullembedding in training\. \(ii\) when an equivalent entity embedding from an arbitrary KG𝒢i\\mathcal\{G\}\_\{i\}is given, the condition is𝒄=𝒛i\\bm\{c\}=\\bm\{z\}\_\{i\}\. \(iii\) when equivalent entities\{𝒛s\}s\\\{\\bm\{z\}\_\{s\}\\\}\_\{s\}from support KGs𝒮\\mathcal\{S\}are given, we fuse them according to their relevance to the entity𝒛t\\bm\{z\}\_\{t\}as

\(9\)𝒄=𝒛s¯\\displaystyle\\bm\{c\}=\\bm\{z\}\_\{\\bar\{s\}\}=∑𝒛s∈\{𝒛s\}sα​\(𝒛t,𝒛s\)⋅𝒛s,\\displaystyle=\\sum\_\{\\bm\{z\}\_\{s\}\\in\\\{\\bm\{z\}\_\{s\}\\\}\_\{s\}\}\\alpha\(\\bm\{z\}\_\{t\},\\bm\{z\}\_\{s\}\)\\cdot\\bm\{z\}\_\{s\},α​\(𝒛t,𝒛s\)\\displaystyle\\alpha\(\\bm\{z\}\_\{t\},\\bm\{z\}\_\{s\}\)=softmax⁡\(score​\(𝒛t,𝒛s\)\),\\displaystyle=\\operatorname\{softmax\}\(\\mathrm\{score\}\(\\bm\{z\}\_\{t\},\\bm\{z\}\_\{s\}\)\),score​\(𝒛t,𝒛s\)\\displaystyle\\mathrm\{score\}\(\\bm\{z\}\_\{t\},\\bm\{z\}\_\{s\}\)=βt​s⋅1d\(𝑼1𝒛t⋅𝑼2𝒛s\]\),\\displaystyle=\\beta\_\{ts\}\\cdot\\frac\{1\}\{\\sqrt\{d\}\}\(\\bm\{U\}\_\{1\}\\bm\{z\}\_\{t\}\\cdot\\bm\{U\}\_\{2\}\\bm\{z\}\_\{s\}\]\),where𝑼1,𝑼2∈ℝd×d\\bm\{U\}\_\{1\},\\bm\{U\}\_\{2\}\\in\\mathbb\{R\}^\{d\\times d\}are learnable weights\. In particular,βt​s∈ℝ\\beta\_\{ts\}\\in\\mathbb\{R\}is a learnable factor to reflect the prior relevance between𝒢t\\mathcal\{G\}\_\{t\}and𝒢s\\mathcal\{G\}\_\{s\}\. This design captures both the prior and contextual relevance of equivalent entities between KGs, aggregating conditions adaptive to the target KG to benefit generation\.

### 3\.3\.Joint Training and Inference

#### 3\.3\.1\.Training

Conventional DMs train the denoiser to predict the added noise at each time step\(Hoet al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib233)\)\. However, it is costly to perform a reverse process in training to obtain the generated domain\-general embedding\. Hence, we look back on ELBO in Eq\. \([3](https://arxiv.org/html/2607.03154#S2.E3)\)\.

Consider the denoising matching termℒk−1\\mathcal\{L\}\_\{k\-1\}, which matchespθ​\(𝒙k−1\|𝒙k\)p\_\{\\theta\}\(\\bm\{x\}\_\{k\-1\}\|\\bm\{x\}\_\{k\}\)withq​\(𝒙k−1\|𝒙k,𝒙0\)q\(\\bm\{x\}\_\{k\-1\}\|\\bm\{x\}\_\{k\},\\bm\{x\}\_\{0\}\)by KL divergence\. By Bayes rules,q​\(𝒙k−1\|𝒙k,𝒙0\)∼𝒩​\(𝒙k−1;𝝁~​\(𝒙k,𝒙0,k\),σ2​\(k\)​𝑰\)q\(\\bm\{x\}\_\{k\-1\}\|\\bm\{x\}\_\{k\},\\bm\{x\}\_\{0\}\)\\\!\\sim\\\!\\mathcal\{N\}\(\\bm\{x\}\_\{k\-1\};\\bm\{\\tilde\{\\mu\}\}\(\\bm\{x\}\_\{k\},\\bm\{x\}\_\{0\},k\),\\sigma^\{2\}\(k\)\\bm\{I\}\)can be written as:

\(10\)𝝁~​\(𝒙k,𝒙0,k\)\\displaystyle\\bm\{\\tilde\{\\mu\}\}\(\\bm\{x\}\_\{k\},\\bm\{x\}\_\{0\},k\)=αk​\(1−α¯k−1\)1−α¯k​𝒙k\+α¯k−1​\(1−αk\)1−α¯k​𝒙0,\\displaystyle=\\frac\{\\sqrt\{\\alpha\_\{k\}\}\(1\-\\bar\{\\alpha\}\_\{k\-1\}\)\}\{1\-\\bar\{\\alpha\}\_\{k\}\}\\bm\{x\}\_\{k\}\+\\frac\{\\sqrt\{\\bar\{\\alpha\}\_\{k\-1\}\}\(1\-\\alpha\_\{k\}\)\}\{1\-\\bar\{\\alpha\}\_\{k\}\}\\bm\{x\}\_\{0\},σ2​\(k\)​𝑰\\displaystyle\\sigma^\{2\}\(k\)\\bm\{I\}=\(1−αk\)​\(1−α¯k−1\)1−α¯k​𝑰\.\\displaystyle=\\frac\{\(1\-\\alpha\_\{k\}\)\(1\-\\bar\{\\alpha\}\_\{k\-1\}\)\}\{1\-\\bar\{\\alpha\}\_\{k\}\}\\bm\{I\}\.whereμ~​\(𝒙k,𝒙0,k\)\\tilde\{\\mu\}\(\\bm\{x\}\_\{k\},\\bm\{x\}\_\{0\},k\)andσ2​\(k\)​𝑰\\sigma^\{2\}\(k\)\\bm\{I\}are mean and covariance\. As suggested\(Yanget al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib237); Wanget al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib232)\), instead of learning the added noiseϵ\\bm\{\\epsilon\}by parameterizingϵθ​\(𝒙k,k\)\\bm\{\\epsilon\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},k\), we directly parameterize𝒙0\\bm\{x\}\_\{0\}, which is:

\(11\)𝝁θ​\(𝒙k,k\)=αk​\(1−α¯k−1\)1−α¯k​𝒙k\+α¯k−1​\(1−αk\)1−α¯k​𝒙^θ​\(𝒙k,k\),\\bm\{\\mu\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},k\)=\\frac\{\\sqrt\{\\alpha\_\{k\}\}\(1\-\\bar\{\\alpha\}\_\{k\-1\}\)\}\{1\-\\bar\{\\alpha\}\_\{k\}\}\\bm\{x\}\_\{k\}\+\\frac\{\\sqrt\{\\bar\{\\alpha\}\_\{k\-1\}\}\(1\-\\alpha\_\{k\}\)\}\{1\-\\bar\{\\alpha\}\_\{k\}\}\\hat\{\\bm\{x\}\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},k\),where𝒙^θ​\(𝒙k,k\)\\hat\{\\bm\{x\}\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},k\)is an approximation of the given true data𝒙0\\bm\{x\}\_\{0\}, based on the situation at the time stepkk\. This is proven to be equal to the vanilla ELBO in DDPM\(Yanget al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib237)\)\. Using the above parameterization, thedenoising matching term\(k≥2k\\geq 2\) can be derived as:

\(12\)ℒk−1\\displaystyle\\mathcal\{L\}\_\{k\-1\}:=𝔼q​\(𝒙k\|𝒙0\)\[DKL\(q\(𝒙k−1\|𝒙k,𝒙0\)∥pθ\(𝒙k−1\|𝒙k\)\)\]\\displaystyle=\\mathbb\{E\}\_\{q\(\\bm\{x\}\_\{k\}\|\\bm\{x\}\_\{0\}\)\}\[D\_\{\\mathrm\{KL\}\}\(q\(\\bm\{x\}\_\{k\-1\}\|\\bm\{x\}\_\{k\},\\bm\{x\}\_\{0\}\)\\\|p\_\{\\theta\}\(\\bm\{x\}\_\{k\-1\}\|\\bm\{x\}\_\{k\}\)\)\]=𝔼q​\(𝒙k\|𝒙0\)​\[12​σ2​\(k\)​‖𝝁θ​\(𝒙k,k\)−𝝁~​\(𝒙k,𝒙0,k\)‖22\]\\displaystyle=\\mathbb\{E\}\_\{q\(\\bm\{x\}\_\{k\}\|\\bm\{x\}\_\{0\}\)\}\[\\frac\{1\}\{2\\sigma^\{2\}\(k\)\}\\\|\\bm\{\\mu\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},k\)\-\\tilde\{\\bm\{\\mu\}\}\(\\bm\{x\}\_\{k\},\\bm\{x\}\_\{0\},k\)\\\|\_\{2\}^\{2\}\]=𝔼q​\(𝒙k\|𝒙0\)​\[12​\(α¯k−11−α¯k−1−α¯k1−α¯k\)​‖𝒙^θ​\(𝒙k,k\)−𝒙0‖22\]\.\\displaystyle=\\mathbb\{E\}\_\{q\(\\bm\{x\}\_\{k\}\|\\bm\{x\}\_\{0\}\)\}\[\\frac\{1\}\{2\}\(\\frac\{\\bar\{\\alpha\}\_\{k\-1\}\}\{1\-\\bar\{\\alpha\}\_\{k\-1\}\}\-\\frac\{\\bar\{\\alpha\}\_\{k\}\}\{1\-\\bar\{\\alpha\}\_\{k\}\}\)\\\|\\hat\{\\bm\{x\}\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},k\)\-\\bm\{x\}\_\{0\}\\\|\_\{2\}^\{2\}\]\.This form is similar to thereconstruction term\(k=0k=0\) with Gaussian log\-likelihood\(Lianget al\.,[2018](https://arxiv.org/html/2607.03154#bib.bib245)\)asℒ0:=𝔼q​\(𝒙1\|𝒙0\)​‖𝒙^θ​\(𝒙1,1\)−𝒙0‖22\\mathcal\{L\}\_\{0\}:=\\mathbb\{E\}\_\{q\(\\bm\{x\}\_\{1\}\|\\bm\{x\}\_\{0\}\)\}\\\!\\\|\\hat\{\\bm\{x\}\}\_\{\\theta\}\(\\bm\{x\}\_\{1\},1\)\-\\bm\{x\}\_\{0\}\\\|\_\{2\}^\{2\}\. Thereafter, we combine them into aunified training term\(k≥1k\\geq 1\) as:

\(13\)ℒk−1:=𝔼q​\(𝒙k\|𝒙0\)​‖𝒙^θ​\(𝒙k,k\)−𝒙0‖22\.\\displaystyle\\mathcal\{L\}\_\{k\-1\}=\\mathbb\{E\}\_\{q\(\\bm\{x\}\_\{k\}\|\\bm\{x\}\_\{0\}\)\}\\\|\\hat\{\\bm\{x\}\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},k\)\-\\bm\{x\}\_\{0\}\\\|\_\{2\}^\{2\}\.In this way, the denoiser actually seeks to predict the initial embedding \(i\.e\., the generation objective\) at each step\. Based on this design, it provides a direct way to impose constraints to manipulate the generated embeddings\. Here, we propose three constraints:

##### \(i\) Domain\-General Embedding Generation

To generate domain\-general entity embeddings, we leverage all equivalent entities from support KGs to guide generation, which is

\(14\)ℒgen:=∑k=1T𝔼q​\(𝒙k\|𝒆~\)​‖𝒙^θ​\(𝒙k,𝒛s¯,k\)−𝒆~‖22,\\displaystyle\\mathcal\{L\}\_\{\\text\{gen\}\}=\\sum\_\{k=1\}^\{T\}\\mathbb\{E\}\_\{q\(\\bm\{x\}\_\{k\}\|\\tilde\{\\bm\{e\}\}\)\}\\\|\\hat\{\\bm\{x\}\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},\\bm\{z\}\_\{\\bar\{s\}\},k\)\-\\tilde\{\\bm\{e\}\}\\\|\_\{2\}^\{2\},where𝒙^θ​\(𝒙k,𝒛s¯,k\)\\hat\{\\bm\{x\}\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},\\bm\{z\}\_\{\\bar\{s\}\},k\)comes from Eq\. \([9](https://arxiv.org/html/2607.03154#S3.E9)\)\. This constraint encourages the generated embeddings to approximate the prior embeddings, ensuring unbiased generation towards conditioned support KGs\. Here, we adopt the classifier\-free guidance \(CFG\) strategy\(Ho and Salimans,[2022](https://arxiv.org/html/2607.03154#bib.bib246)\), which retains a ratiopup\_\{u\}of generation cases without conditions \(i\.e\.,ϕ\\phi\), improving the unconditional generation ability\.

##### \(ii\) Target\-Domain Task Prediction

This constraint ensures the generated domain\-general embedding to be task\-predictive in the KG target𝒢t\\mathcal\{G\}\_\{t\}\. To enrich the entity information, we fuse the generated𝒙^θ\\hat\{\\bm\{x\}\}\_\{\\theta\}, the prior𝒆~\\tilde\{\\bm\{e\}\}, and the target\-domain embedding𝒛t\\bm\{z\}\_\{t\}as:

\(15\)𝒛¯t=𝒙^θ\+𝒆~\+𝒛t,\\displaystyle\\bar\{\\bm\{z\}\}\_\{t\}=\\hat\{\\bm\{x\}\}\_\{\\theta\}\+\\tilde\{\\bm\{e\}\}\+\\bm\{z\}\_\{t\},where𝒙^θ=𝒙^θ​\(𝒙k,𝒛s¯,k\)\\hat\{\\bm\{x\}\}\_\{\\theta\}=\\hat\{\\bm\{x\}\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},\\bm\{z\}\_\{\\bar\{s\}\},k\)\. For a triple\(h,r,o\)\(h,r,o\)sampled444Here, we useooto denote the tail entity, sincettis used to denote the target KG\.in𝒢t\\mathcal\{G\}\_\{t\}, we use the classical triple scoring function\(Bordeset al\.,[2013](https://arxiv.org/html/2607.03154#bib.bib149)\)to predict plausibility:

\(16\)ψ​\(h,r,o\)=−‖𝒛¯t,h\+𝒓−𝒛¯t,o‖2,\\psi\(h,r,o\)=\-\\\|\\bar\{\\bm\{z\}\}\_\{t,h\}\+\\bm\{r\}\-\\bar\{\\bm\{z\}\}\_\{t,o\}\\\|\_\{2\},\(17\)ℒtask:=∑\(h,r,o\)∈ℱt∑\(h,r,o′\)∉ℱt\[λ−ψ​\(h,r,o\)\+ψ​\(h,r,o′\)\]\+,\\mathcal\{L\}\_\{\\text\{task\}\}:=\\\!\\\!\\\!\\sum\_\{\(h,r,o\)\\in\\mathcal\{F\}\_\{t\}\}\\sum\_\{\(h,r,o^\{\\prime\}\)\\notin\\mathcal\{F\}\_\{t\}\}\\\!\\\!\\\!\[\\lambda\-\\psi\(h,r,o\)\+\\psi\(h,r,o^\{\\prime\}\)\]\_\{\+\},where we adopt the margin loss,\[⋅\]\+:=max⁡\(⋅,0\)\[\\cdot\]\_\{\+\}:=\\max\(\\cdot,0\),λ\\lambdais the margin factor, ando′∈ℰto^\{\\prime\}\\in\\mathcal\{E\}\_\{t\}is a negative entity randomly selected\. In this way, the generated embedding𝒙^θ\\hat\{\\bm\{x\}\}\_\{\\theta\}is refined, and together with other embeddings to enhance KGC in the target KG\.

##### \(iii\) Single\-Domain Conditional Regularization

This constraint further emphasizes the unbiased and consistent generation with partial conditions\. Specifically, it seeks to generate consistent domain\-general embedding conditioned on each KG:

\(18\)ℒreg:=∑i=1N∑k=1T𝔼q​\(𝒙k\|𝒆~\)​‖𝒙^θ​\(𝒙k,𝒛i,k\)−𝒆~‖22,\\displaystyle\\mathcal\{L\}\_\{\\text\{reg\}\}=\\sum\_\{i=1\}^\{N\}\\sum\_\{k=1\}^\{T\}\\mathbb\{E\}\_\{q\(\\bm\{x\}\_\{k\}\|\\tilde\{\\bm\{e\}\}\)\}\\\|\\hat\{\\bm\{x\}\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},\\bm\{z\}\_\{i\},k\)\-\\tilde\{\\bm\{e\}\}\\\|\_\{2\}^\{2\},where𝒛i\\bm\{z\}\_\{i\}is a domain entity embedding of equivalent entities from all KGs\. This further ensures generation consistency in practice\.

Based upon the aforementioned constraints, the overall training objective is formulated as:

\(19\)ℒ=ℒtask\+ω1​ℒgen\+ω2​ℒreg,\\displaystyle\\mathcal\{L\}=\\mathcal\{L\}\_\{\\text\{task\}\}\+\\omega\_\{1\}\\mathcal\{L\}\_\{\\text\{gen\}\}\+\\omega\_\{2\}\\mathcal\{L\}\_\{\\text\{reg\}\},whereω1,ω2∈ℝ\\omega\_\{1\},\\omega\_\{2\}\\in\\mathbb\{R\}are harmonic factors to balance training\. The algorithm[1](https://arxiv.org/html/2607.03154#alg1)presents the overall training procedure, where we adopt sampling strategies\(Hoet al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib233)\)to accelerate training for efficiency\.

#### 3\.3\.2\.Inference

In inference, we use the domain\-general entity embedding𝒙^0\\hat\{\\bm\{x\}\}\_\{0\}from𝒙^θ​\(𝒙k,𝒛s¯,k\)\\hat\{\\bm\{x\}\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},\\bm\{z\}\_\{\\bar\{s\}\},k\)to transfer knowledge from the support KGs\. Following the CFG strategy\(Ho and Salimans,[2022](https://arxiv.org/html/2607.03154#bib.bib246)\)to enable conditional generation, we adjust the generation by interpolating the generated conditional and unconditional embedding as:

\(20\)𝒙~θ​\(𝒙k,𝒛s¯,k\)=𝒙^θ​\(𝒙k,ϕ,k\)\+s​\[𝒙^θ​\(𝒙k,𝒛s¯,k\)−𝒙^θ​\(𝒙k,ϕ,k\)\],\\displaystyle\\tilde\{\\bm\{x\}\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},\\bm\{z\}\_\{\\bar\{s\}\},k\)=\\hat\{\\bm\{x\}\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},\\phi,k\)\+s\[\\hat\{\\bm\{x\}\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},\\bm\{z\}\_\{\\bar\{s\}\},k\)\-\\hat\{\\bm\{x\}\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},\\phi,k\)\],wheres∈ℝs\\in\\mathbb\{R\}is a factor in controlling the strength of the condition\. Subsequently, in inference, given𝒙0=𝒆~\\bm\{x\}\_\{0\}=\\tilde\{\\bm\{e\}\}, we first perform the forward process to derive𝒙T\\bm\{x\}\_\{T\}, and then set𝒙^T=𝒙T\\hat\{\\bm\{x\}\}\_\{T\}=\\bm\{x\}\_\{T\}to start the reverse process\. This process holds for both head and tail entities involved \(as in Eq\. \([16](https://arxiv.org/html/2607.03154#S3.E16)\)\)\. For a query\(h,r,?\)\(h,r,?\)in𝒢t\\mathcal\{G\}\_\{t\}, we treat all entities inℰt\\mathcal\{E\}\_\{t\}as candidates\. The entity with the highest score is returned as the result\. The algorithm[2](https://arxiv.org/html/2607.03154#alg2)presents the inference procedure\.

Algorithm 1Training procedureInput: Training data𝒟=\{𝒢i\}i\\mathcal\{D\}=\\\{\\mathcal\{G\}\_\{i\}\\\}\_\{i\}and equivalent entity sets\{𝒜i​j\}i≠j\\\{\\mathcal\{A\}\_\{ij\}\\\}\_\{i\\neq j\}\.Output: Model parametersΘ\\Theta\.

1:Initialize all model parameters\.

2:whilenot convergencedo

3:Sample a target KG

𝒢t\\mathcal\{G\}\_\{t\}and support KGs

𝒮=\{𝒢s\|s≠t\}\\mathcal\{S\}=\\\{\\mathcal\{G\}\_\{s\}\|s\\neq t\\\}\.

4:Sample a triple

\(h,r,o\)\(h,r,o\)from

𝒢t\\mathcal\{G\}\_\{t\}, and a negative entity

o′o^\{\\prime\}from

ℰt\\mathcal\{E\}\_\{t\}\.

5:for

e∈\{h,o,o′\}e\\in\\\{h,o,o^\{\\prime\}\\\}do

6:Obtain prior embedding

𝒆~\\tilde\{\\bm\{e\}\}, and let

𝒙0=𝒆~\\bm\{x\}\_\{0\}=\\tilde\{\\bm\{e\}\};

7:forall

𝒢i∈𝒟\\mathcal\{G\}\_\{i\}\\in\\mathcal\{D\}do

8:Obtain

𝒛i=Encoder​\(𝒆~,𝒢i\)\\bm\{z\}\_\{i\}=\\mathrm\{Encoder\}\(\\tilde\{\\bm\{e\}\},\\mathcal\{G\}\_\{i\}\)by Eq\. \([5](https://arxiv.org/html/2607.03154#S3.E5)\);

9:end for

10:Sample

k∼𝒰​\(1,T\)k\\sim\\mathcal\{U\}\(1,T\),

ϵ∼𝒩​\(0,I\)\\epsilon\\sim\\mathcal\{N\}\(0,I\), and obtain

𝒙k\\bm\{x\}\_\{k\}by Eq\. \([6](https://arxiv.org/html/2607.03154#S3.E6)\);

11:Estimate

𝒙^θ​\(𝒙k,𝒛s¯,k\)\\hat\{\\bm\{x\}\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},\\bm\{z\}\_\{\\bar\{s\}\},k\)with CFG, obtain

ℒgen\\mathcal\{L\}\_\{\\mathrm\{gen\}\}by Eq\. \([14](https://arxiv.org/html/2607.03154#S3.E14)\);

12:Estimate

𝒙^θ​\(𝒙k,𝒛i,k\)\\hat\{\\bm\{x\}\}\_\{\\theta\}\(\\bm\{x\}\_\{k\},\\bm\{z\}\_\{i\},k\)with CFG, obtain

ℒreg\\mathcal\{L\}\_\{\\mathrm\{reg\}\}by Eq\. \([18](https://arxiv.org/html/2607.03154#S3.E18)\);

13:Obtain mixed embedding

𝒛¯t,e=𝒙^θ\+𝒆~\+𝒛t,e\\bar\{\\bm\{z\}\}\_\{t,e\}=\\hat\{\\bm\{x\}\}\_\{\\theta\}\+\\tilde\{\\bm\{e\}\}\+\\bm\{z\}\_\{t,e\};

14:end for

15:Obtain

ℒtask\\mathcal\{L\}\_\{\\mathrm\{task\}\}by Eq\. \([17](https://arxiv.org/html/2607.03154#S3.E17)\);

16:Obtain overall loss

ℒ\\mathcal\{L\}by Eq\. \([19](https://arxiv.org/html/2607.03154#S3.E19)\) to optimize

Θ\\Theta;

17:end while

Algorithm 2Inference procedureInput:Θ\\Theta, query\(h,r,?\)\(h,r,?\)in target𝒯=𝒢t\\mathcal\{T\}=\\mathcal\{G\}\_\{t\}, support𝒮=\{𝒢s\}s≠t\\mathcal\{S\}=\\\{\\mathcal\{G\}\_\{s\}\\\}\_\{s\\neq t\}\.Output: Scoreψ​\(h,r,o′\)\\psi\(h,r,o^\{\\prime\}\)of all candidate entitieso′∈ℰto^\{\\prime\}\\in\\mathcal\{E\}\_\{t\}\.

1:for

e∈\{h\}∪ℰte\\in\\\{h\\\}\\cup\\mathcal\{E\}\_\{t\}do

2:Obtain prior embedding

𝒆~\\tilde\{\\bm\{e\}\}\.

3:forall

𝒢i∈𝒯∪𝒮\\mathcal\{G\}\_\{i\}\\in\\mathcal\{T\}\\cup\\mathcal\{S\}do

4:Obtain

𝒛i=Encoder​\(𝒆~,𝒢i\)\\bm\{z\}\_\{i\}=\\mathrm\{Encoder\}\(\\tilde\{\\bm\{e\}\},\\mathcal\{G\}\_\{i\}\)by Eq\. \([5](https://arxiv.org/html/2607.03154#S3.E5)\)\.

5:end for

6:Sample

ϵ∼𝒩​\(0,I\)\\epsilon\\sim\\mathcal\{N\}\(0,I\), and obtain

𝒙^T\\hat\{\\bm\{x\}\}\_\{T\}by Eq\. \([6](https://arxiv.org/html/2607.03154#S3.E6)\);

7:for

k=T,⋯,1k=T,\\cdots,1do

8:Estimate

𝒙^θ​\(𝒙^k,𝒛s¯,k\)\\hat\{\\bm\{x\}\}\_\{\\theta\}\(\\hat\{\\bm\{x\}\}\_\{k\},\\bm\{z\}\_\{\\bar\{s\}\},k\)and

𝒙^θ​\(𝒙^k,ϕ,k\)\\hat\{\\bm\{x\}\}\_\{\\theta\}\(\\hat\{\\bm\{x\}\}\_\{k\},\\phi,k\)by Eq\. \([8](https://arxiv.org/html/2607.03154#S3.E8)\);

9:Obtain

𝒙~θ​\(𝒙^k,𝒛s¯,k\)\\tilde\{\\bm\{x\}\}\_\{\\theta\}\(\\hat\{\\bm\{x\}\}\_\{k\},\\bm\{z\}\_\{\\bar\{s\}\},k\)by Eq\. \([20](https://arxiv.org/html/2607.03154#S3.E20)\);

10:Obtain

𝒙^k−1=μθ​\(𝒙^k,k\)\\hat\{\\bm\{x\}\}\_\{k\-1\}=\\mu\_\{\\theta\}\(\\hat\{\\bm\{x\}\}\_\{k\},k\)with

𝒙^k\\hat\{\\bm\{x\}\}\_\{k\}and

𝒙~θ​\(𝒙^k,𝒛s¯,k\)\\tilde\{\\bm\{x\}\}\_\{\\theta\}\(\\hat\{\\bm\{x\}\}\_\{k\},\\bm\{z\}\_\{\\bar\{s\}\},k\)by Eq\. \([11](https://arxiv.org/html/2607.03154#S3.E11)\);

11:end for

12:Obtain mixed embedding

𝒛¯t=𝒙^0\+𝒆~\+𝒛t\\bar\{\\bm\{z\}\}\_\{t\}=\\hat\{\\bm\{x\}\}\_\{0\}\+\\tilde\{\\bm\{e\}\}\+\\bm\{z\}\_\{t\};

13:Calculate score

ψ​\(h,r,o′\)\\psi\(h,r,o^\{\\prime\}\)with

𝒛¯t,h\\bar\{\\bm\{z\}\}\_\{t,h\}and

𝒛¯t,o′\\bar\{\\bm\{z\}\}\_\{t,o^\{\\prime\}\}by Eq\. \([16](https://arxiv.org/html/2607.03154#S3.E16)\);

14:end for

## 4\.Experiments

In this section, we address the following research questions:\(Q1\)How effectively does DMKGC perform across diverse benchmark datasets?\(Q2\)Is the proposed knowledge transfer robust to low\-resource data scenarios? For analyzes of parameter sensitivity and computational efficiency, please refer to theAppendix\(Q3\)\.

### 4\.1\.Evaluation Settings

Table 1\.Results \(%\) on DBP\-5L\.†\{\\dagger\}indicates re\-produced results\. The best result isbold\-facedand the runner\-up isunderlined\.MethodELENESFRJAAVGH@1H@10MRRH@1H@10MRRH@1H@10MRRH@1H@10MRRH@1H@10MRRMRRTransE13\.143\.724\.37\.329\.316\.913\.545\.024\.417\.548\.827\.621\.148\.525\.323\.7DistMult8\.911\.39\.88\.830\.018\.37\.422\.413\.26\.123\.814\.59\.327\.515\.814\.3RotatE14\.536\.226\.212\.330\.420\.721\.253\.933\.823\.255\.535\.126\.460\.239\.831\.1KG\-BERT17\.340\.127\.312\.931\.921\.021\.954\.134\.023\.555\.935\.426\.959\.838\.731\.3KEnS28\.156\.9\-15\.139\.8\-23\.660\.1\-25\.562\.9\-32\.165\.3\-\-CG\-MuA21\.544\.832\.813\.133\.522\.222\.355\.434\.324\.257\.136\.127\.361\.140\.133\.1AlignKGC27\.656\.333\.815\.539\.222\.324\.260\.935\.124\.162\.337\.431\.664\.341\.634\.0SS\-AGA30\.858\.635\.316\.341\.323\.125\.561\.936\.627\.165\.538\.334\.666\.942\.935\.2LSMGA33\.189\.954\.516\.861\.732\.425\.674\.842\.831\.281\.348\.633\.579\.149\.845\.6GLKGC†36\.686\.553\.017\.160\.232\.928\.374\.443\.631\.578\.447\.936\.577\.650\.945\.7DMKGC41\.991\.061\.020\.964\.236\.333\.077\.749\.138\.682\.354\.242\.082\.456\.351\.4Table 2\.Results \(%\) on E\-PKG\.†\{\\dagger\}indicates re\-produced results\. The best result isbold\-facedand the runner\-up isunderlined\.MethodDEENESFRITJAAVGH@1H@10MRRH@1H@10MRRH@1H@10MRRH@1H@10MRRH@1H@10MRRH@1H@10MRRMRRTransE21\.265\.537\.423\.267\.539\.417\.258\.433\.020\.866\.937\.522\.063\.837\.825\.172\.743\.638\.1DistMult21\.454\.535\.423\.860\.137\.217\.946\.230\.920\.753\.535\.122\.851\.834\.825\.962\.638\.035\.2RotatE22\.364\.338\.224\.266\.840\.018\.358\.933\.722\.164\.338\.222\.564\.038\.126\.371\.941\.838\.3KG\-BERT21\.864\.738\.424\.366\.439\.618\.758\.833\.222\.367\.238\.322\.963\.737\.226\.972\.444\.138\.5KEnS24\.365\.8\-26\.269\.5\-21\.359\.5\-25\.468\.2\-25\.164\.6\-33\.573\.6\-\-CG\-MuA22\.964\.938\.724\.867\.940\.219\.258\.833\.823\.067\.539\.123\.963\.837\.630\.472\.945\.939\.2AlignKGC22\.165\.138\.525\.668\.340\.519\.459\.134\.222\.867\.238\.824\.263\.437\.331\.272\.346\.239\.3SS\-AGA24\.666\.339\.426\.769\.841\.521\.060\.136\.325\.968\.740\.224\.963\.838\.433\.974\.148\.340\.7LSMGA30\.768\.544\.831\.970\.245\.923\.161\.136\.523\.763\.538\.226\.864\.541\.043\.778\.457\.143\.9GLKGC†24\.163\.637\.727\.158\.439\.424\.661\.036\.822\.162\.336\.427\.063\.740\.444\.176\.457\.541\.4DMKGC30\.969\.145\.033\.370\.346\.826\.763\.739\.726\.068\.840\.731\.266\.344\.650\.179\.161\.846\.4Table 3\.Results \(%\) on DWY\.†\{\\dagger\}indicates re\-produced results\. The best result isbold\-facedand the runner\-up isunderlined\.MethodDBWKYGAVGH@1H@10MRRH@1H@10MRRH@1H@10MRRMRRTransE†4\.352\.920\.33\.048\.617\.32\.242\.213\.116\.9DistMult†8\.636\.517\.68\.441\.718\.44\.632\.512\.716\.2RotatE†13\.257\.427\.99\.952\.526\.43\.542\.713\.822\.7SS\-AGA†5\.861\.822\.66\.652\.218\.59\.052\.322\.921\.3LSGMA†14\.064\.330\.99\.554\.623\.911\.448\.623\.526\.1GLKGC†13\.466\.932\.39\.355\.024\.316\.552\.828\.728\.4DMKGC15\.768\.934\.511\.459\.326\.723\.666\.737\.933\.1#### 4\.1\.1\.Datasets

For evaluation, we use three benchmarks comprising 14 KGs: the multilingualDBP\-5L\(Chenet al\.,[2017](https://arxiv.org/html/2607.03154#bib.bib136)\)andE\-PKG\(Huanget al\.,[2022](https://arxiv.org/html/2607.03154#bib.bib174)\), and a constructed multi\-domainDWY\(Sunet al\.,[2018](https://arxiv.org/html/2607.03154#bib.bib227)\)dataset\. DBP\-5L contains five DBpedia\-based KGs in Greek \(EL\), English \(EN\), Spanish \(ES\), French \(FR\), and Japanese \(JA\)\. Besides, E\-PKG includes industrial e\-commerce mobile phone data in six languages: German \(DE\), English \(EN\), Spanish \(ES\), French \(FR\), Italian \(IT\), and Japanese \(JA\)\. In addition, DWY integrates DBpedia \(DB\), YAGO \(YG\), and Wiki \(WK\), where we adopt the original aligned entities between each two KGs\(Sunet al\.,[2018](https://arxiv.org/html/2607.03154#bib.bib227)\), and take 80%, 10%, 10% triples in each KG for training, validation and testing\. All datasets provide aligned entity pairs between KGs, with unified and shared relations across all KGs\(Chenet al\.,[2017](https://arxiv.org/html/2607.03154#bib.bib136); Tanget al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib175)\)\. The statistics are shown inAppendix\.

#### 4\.1\.2\.Baselines

To evaluate our model, we select the following state\-of\-the\-art methods as baselines: \(i\)Single\-domain methods, which perform inference within individual KGs without knowledge transfer between KGs, includingTransE\(Bordeset al\.,[2013](https://arxiv.org/html/2607.03154#bib.bib149)\),DisMult\(Yanget al\.,[2015](https://arxiv.org/html/2607.03154#bib.bib159)\),RotatE\(Sunet al\.,[2019](https://arxiv.org/html/2607.03154#bib.bib150)\),KG\-BERT\(Yaoet al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib151)\)\. \(ii\)Multi\-domain methods, which mostly attempt consistency\-based modules to transfer knowledge from support KGs for target KG predictions, includingKEnS\(Chenet al\.,[2020c](https://arxiv.org/html/2607.03154#bib.bib222)\),CG\-MuA\(Zhuet al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib133)\),AlignKGC\(Singhet al\.,[2021](https://arxiv.org/html/2607.03154#bib.bib141)\),SS\-AGA\(Huanget al\.,[2022](https://arxiv.org/html/2607.03154#bib.bib174)\),LSMGA\(Tanget al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib175)\)andGLKGC\(He and Yang,[2024](https://arxiv.org/html/2607.03154#bib.bib212)\)\. For details, please refer toAppendix\.

#### 4\.1\.3\.Evaluation Protocol

Following previous studies\(Chenet al\.,[2017](https://arxiv.org/html/2607.03154#bib.bib136); Tanget al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib175)\), we evaluate models in the task oftail entity prediction\. During training, we combine all the training data from the multiple KGs\. In testing, we rank all candidate entities of the target KG to predictttgivenhhandrrfor each triple\(h,r,?\)\(h,r,?\)in the test data\. Three metrics are reported, including Hits@10 \(H@10 for short\), Hits@1 \(H@1\) and mean reciprocal ranks \(MRR\)\. FollowingTanget al\.\([2023](https://arxiv.org/html/2607.03154#bib.bib175)\), the optimal model is selected according to the average MRR of all KGs\.

#### 4\.1\.4\.Implementation Details

Most hyperparameters are shared for all datasets\. The entity and relation embeddings are randomly initialized with dimension 256\. The learning rate is set to 0\.001, and the marginλ\\lambdais set to 0\.5 for all datasets\. The KG encoder has 2 layers\. The diffusion stepTTis selected in\{2,4,⋯,64\}\\\{2,4,\\cdots,64\\\}, and the strengthssin\{1,2,⋯,5\}\\\{1,2,\\cdots,5\\\},ω1,ω2\\omega\_\{1\},\\omega\_\{2\}are tuned in\{1,3,5\}×10−\{4,3,2,1\}\\\{1,3,5\\\}\\\!\\times\\\!10^\{\-\\\{4,3,2,1\\\}\}\. For baselines, most results on DBP\-5L and E\-PKG are obtained from original literature\. On DWY, we re\-implement baselines with the best hyperparameters reported\. We employ a grid search with three trials, and the optimal hyperparameters are reported inAppendix\.

### 4\.2\.Main Results \(RQ1\)

#### 4\.2\.1\.Method Comparison

We present the comparison between our model and existing baselines in Table[1](https://arxiv.org/html/2607.03154#S4.T1),[2](https://arxiv.org/html/2607.03154#S4.T2)and[3](https://arxiv.org/html/2607.03154#S4.T3)\. We find that:First, multi\-domain KGC methods outperform single\-domain methods\.This ensures the effectiveness of using support KGs for target KG prediction, which can help improve inference on entities with limited triples\.Second, our model outperforms all existing methods\.Specifically, our model achieves average improvements in MRR of 5\.7%, 2\.5%, and 4\.7% on DBP\-5L, E\-PKG, and DWY, respectively\. This reflects the effectiveness of using conditional diffusion to achieve knowledge transfer, which produces more informative embeddings than existing multi\-domain KGC methods, such as SS\-AGA, LSGMA and GLKGC\.Third, our model obtains consistent improvements in three datasets with 14 KGs, with an overall 4\.3% MRR improvement\. The results on multilingual DBP\-5L, industrial E\-PKG, and multi\-domain DWY broadly demonstrate the generality of our model\.

Table 4\.Variant analysis on DBP\-5L, where AVG\-H@1, AVG\-H@10 and AVG\-MRR denote the average metrics \(%\)\.Table 5\.Comparison with general knowledge transfer methods\. The results \(%\) are reported on DBP\-5L\.
#### 4\.2\.2\.In\-depth Variant Analysis

To evaluate the unity of the components, we perform variant analysis in Table[4](https://arxiv.org/html/2607.03154#S4.T4)\. We find that:First, repl\. GCN replaces the attentive KG encoder with non\-relational GCN\(Kipf and Welling,[2017](https://arxiv.org/html/2607.03154#bib.bib165)\), indicating the fundamental role of a capable encoder\.Second, w/o cond removes the condition in diffusion, and repl\. mean replaces the attentive condition fuser with simple vector mean\. The results reflect the crucial unity of the condition information\.Third, w/o DM removes the diffusion knowledge transfer and w/o reg removes the regularizationℒreg\\mathcal\{L\}\_\{\\mathrm\{reg\}\}\. This reflects the vital role of learning domain\-general entity embeddings with unbiased generation\.Forth, repl\.ϵ\\epsilon\-ELBO achieves ELBO with DDPM\(Hoet al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib233)\), repl\.ϵ\\epsilon\-init starts the reverse process with a random noise, and repl\. cosine replaces L2\-norm with cosine score in Eq\. \([13](https://arxiv.org/html/2607.03154#S3.E13)\)\.The results reflect that direct parameterizing𝒙0\\bm\{x\}\_\{0\}by𝒙^θ\\hat\{\\bm\{x\}\}\_\{\\theta\}can be helpful in learning the general entity embedding, the initial𝒙T\\bm\{x\}\_\{T\}achieves a better initialization, and cosine depicts relative embedding similarity but can hardly reconstruct the embedding details\.All results indicate the effectiveness of components\.

#### 4\.2\.3\.Analysis on Knowledge Transfer

To evaluate the impact of conditional diffusion transfer, we adapt three general knowledge transfer methods to our KG encoder backbone, and fuse the refined embeddings with mean fusion: \(i\)InfoNCE\(Chenet al\.,[2020a](https://arxiv.org/html/2607.03154#bib.bib253)\)leverages contrastive loss to enhance the consistency between equivalent entities from various KGs\. \(ii\)DA\-DIFF\(Penget al\.,[2024](https://arxiv.org/html/2607.03154#bib.bib251)\)uses the fused support KG embedding as the initial embedding, adds noise to it, and learns to approximate the also noised target KG embedding step by step\. \(iii\)MMD\(Grettonet al\.,[2012](https://arxiv.org/html/2607.03154#bib.bib252)\)adopts the classical maximum mean discrepancy, which measures the distributional relevance between equivalent entities\. The results are shown in Table[5](https://arxiv.org/html/2607.03154#S4.T5)\. We find that our model outperforms the three methods\. Actually, the three methods commonly capture the consistency between equivalent entities in different aspects\. We believe thatour conditional diffusion transfer learns to generate a domain\-general entity embedding, thus allowing more informative embeddings for task prediction in various KGs\.

### 4\.3\.Results in Low\-resource Scenarios \(RQ2\)

![Refer to caption](https://arxiv.org/html/2607.03154v1/x4.png)Figure 4\.Results \(%\) with a limited number of equivalent entities, randomly selected at 20%, 50% and 80% on DBP\-5L\.![Refer to caption](https://arxiv.org/html/2607.03154v1/x5.png)Figure 5\.Results \(%\) with a limited number of support KGs for target KG prediction \(EL\) on DBP\-5L\.Table 6\.Results \(%\) on unseen entity settings conducted on DBP\-5L, where head entities in queries are unseen in training\.#### 4\.3\.1\.Analysis on Limited Equivalent Entities

To investigate robustness, we performed experiments with limited equivalent entities \(20%, 50%, 80%\), shown in Figure[4](https://arxiv.org/html/2607.03154#S4.F4)\. We find thatour model consistently outperforms existing methods\.With fewer equivalent entities, the methods have less supervision to learn knowledge transfer\. In contrast to consistency\-based methods that rely on the given equivalent entities,our model uses prior entity embeddings as the supervision, which learns domain\-general information for generation using all entities in domains, enriching knowledge transfer\.

#### 4\.3\.2\.Analysis on Fewer Support KGs

For investigation, we also explored experiments with various numbers of support KGs, shown in Figure[5](https://arxiv.org/html/2607.03154#S4.F5)\. We find that:First, more support KGs lead to better results in the target KG\.This indicates the significance of the MKGC task in improving low\-resource KGC\.Second, our model achieves better results for all numbers\.We believe that our method learns domain\-general entity information, which produces more informative embeddings than the existing consistency\-based methods\.

#### 4\.3\.3\.Analysis on Unseen Entities

To further investigate generalizability, we conducted experiments on unseen entities in an extrapolation setting\(Chenet al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib254)\)\. Specifically,for a query\(h,r,?\)\(h,r,?\), we suppose thathhis unseen in the target KG, but it has triples in other support KGs\.This setting is useful for new\-coming entities to build connections in the current KG\. To implement it, for head entities in the testing data, we remove their triples in the training data of the located KG, thus, the prediction has to rely on the related triples from other KGs\. The results are shown in Table[6](https://arxiv.org/html/2607.03154#S4.T6)\. We find that our model derives the best results and significantly exceeds the previous baselines LSGMA and GLKGC\. We believe thatthe diffusion generation module learns general information about entities, which is representative for unseen entities\.We leave further studies in future works\.

## 5\.Related Works

### 5\.1\.Knowledge Graph Completion

Knowledge graph completion \(KGC\)aims to predict missing triples based on existing triples in a single KG\. Classical studies proposetriple\-based methods\(Bordeset al\.,[2013](https://arxiv.org/html/2607.03154#bib.bib149); Yanget al\.,[2015](https://arxiv.org/html/2607.03154#bib.bib159); Sunet al\.,[2019](https://arxiv.org/html/2607.03154#bib.bib150); Dettmerset al\.,[2018](https://arxiv.org/html/2607.03154#bib.bib154); Trouillonet al\.,[2016](https://arxiv.org/html/2607.03154#bib.bib220)\)with translation\-based\(Bordeset al\.,[2013](https://arxiv.org/html/2607.03154#bib.bib149); Sunet al\.,[2019](https://arxiv.org/html/2607.03154#bib.bib150)\)or semantic matching\-based score functions\(Yanget al\.,[2015](https://arxiv.org/html/2607.03154#bib.bib159); Dettmerset al\.,[2018](https://arxiv.org/html/2607.03154#bib.bib154)\)\. Later studies proposeGNN\-based methods\(Shanget al\.,[2019](https://arxiv.org/html/2607.03154#bib.bib193); Schlichtkrullet al\.,[2018](https://arxiv.org/html/2607.03154#bib.bib195); Liuet al\.,[2024a](https://arxiv.org/html/2607.03154#bib.bib194)\)to capture relational graph structures\. Recent studies also explore entity textual information\(Xieet al\.,[2016](https://arxiv.org/html/2607.03154#bib.bib202); Yaoet al\.,[2025](https://arxiv.org/html/2607.03154#bib.bib198)\)with PLMs\(Yaoet al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib151); Wanget al\.,[2021](https://arxiv.org/html/2607.03154#bib.bib201)\)or LLMs\(Weiet al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib196); Guoet al\.,[2024](https://arxiv.org/html/2607.03154#bib.bib208); Zhanget al\.,[2024a](https://arxiv.org/html/2607.03154#bib.bib207); Liuet al\.,[2024b](https://arxiv.org/html/2607.03154#bib.bib200); Yaoet al\.,[2025](https://arxiv.org/html/2607.03154#bib.bib198); Liet al\.,[2024](https://arxiv.org/html/2607.03154#bib.bib197); Yaoet al\.,[2025](https://arxiv.org/html/2607.03154#bib.bib198)\), which are not designed in our task setting\. Overall, these studies attempt to achieve KGC in an individual KG, which cannot be directly used for multi\-domain and low\-resource scenarios\.

### 5\.2\.Multi\-domain KG Completion

Multi\-domain KG completion \(MKGC\)aims to fully utilize multiple KG triples to improve KGC\. Early studies explore it exclusively in multilingual scenarios, namelymultilingual KGC\(Huanget al\.,[2022](https://arxiv.org/html/2607.03154#bib.bib174); Tanget al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib175)\)\. For generality, we term it as multi\-domain KGC beyond languages\. For the methods, MTransE\(Chenet al\.,[2017](https://arxiv.org/html/2607.03154#bib.bib136)\)first extends the KG embeddings from one to multiple KGs\. Later studies\(Zhanget al\.,[2019](https://arxiv.org/html/2607.03154#bib.bib203); Zhuet al\.,[2021](https://arxiv.org/html/2607.03154#bib.bib204); Sunet al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib216); Yanget al\.,[2025b](https://arxiv.org/html/2607.03154#bib.bib205)\)focus mainly on entity alignment \(EA\) for knowledge fusion\. Further studies\(Zhuet al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib133); Singhet al\.,[2021](https://arxiv.org/html/2607.03154#bib.bib141); Huanget al\.,[2022](https://arxiv.org/html/2607.03154#bib.bib174); He and Yang,[2024](https://arxiv.org/html/2607.03154#bib.bib212); Shenget al\.,[2026](https://arxiv.org/html/2607.03154#bib.bib265)\)explore KGC with the other related KGs\. They encode KGs with relational GNNs, and leverage EA for consistency to transfer knowledge for the target KGC\. However, consistency\-based methods can limit entity representation in knowledge transfer, impeding domain\-specific information\. To our knowledge, few studies have explored generation\-based transfer for MKGC\.

### 5\.3\.Diffusion Models

Diffusion models \(DMs\)have achieved remarkable success in generative tasks such as image\(Podellet al\.,[2024](https://arxiv.org/html/2607.03154#bib.bib235); Hoet al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib233)\)and text generation\(Gulrajani and Hashimoto,[2023](https://arxiv.org/html/2607.03154#bib.bib256); Lovelaceet al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib255)\), and also reflect potential in discriminative tasks\(Rahmanet al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib257); Wanget al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib232); Yanget al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib237); Jianget al\.,[2024](https://arxiv.org/html/2607.03154#bib.bib239)\)\. Recent KGC studies attempt DMs to model the generative distribution of triples\(Longet al\.,[2024a](https://arxiv.org/html/2607.03154#bib.bib259),[b](https://arxiv.org/html/2607.03154#bib.bib248); Huanget al\.,[2025](https://arxiv.org/html/2607.03154#bib.bib249)\)and graph structures\(Caoet al\.,[2024](https://arxiv.org/html/2607.03154#bib.bib260)\)for triple prediction\. Our paper exploresknowledge transfer for multi\-domain KGC, which has a different research focus\. For knowledge transfer, existing studies explore DMs for knowledge distillation\(Huanget al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib264); Heet al\.,[2025](https://arxiv.org/html/2607.03154#bib.bib262)\)or domain adaptation\(Penget al\.,[2024](https://arxiv.org/html/2607.03154#bib.bib251)\), which transfer knowledge mainly through a denoising process using the diffusion path as a bridge\. Unlike them, our paper leverages diffusion models to pioneer the unbiased generation from support domains and simultaneously allows target information for prediction, making a more informative knowledge transfer\.

## 6\.Conclusion

This paper addresses MKGC, which transfers knowledge from support KGs to improve KGC in a target KG\. Existing studies mainly leverage consistency\-based methods, potentially surpassing domain\-specific KG information\. To address this, we propose a novel generation\-based paradigm\. Our framework, DMKGC, uses conditional diffusion models to generate domain\-general entity embeddings, effectively integrating support KG knowledge while preserving domain\-specific information\. By treating each KG as a partial view of entities and using domain\-agnostic embeddings as unbiased generation targets, DMKGC learns rich generalizable representations\. Experiments on 14 KGs show that DMKGC achieves significant gains and consistently excels in low\-resource scenarios\.

## Acknowledgments

The authors thank the reviewers for their helpful feedback\. This work was supported by the National Natural Science Foundation of China \(No\. 62406319\)\.

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## Appendix AAppendix

In this appendix, we provide: \(i\) the dataset details, \(ii\) baselines, \(iii\) the evaluation protocol, and \(iv\) optimal hyper\-parameters\.

### A\.1\.Dataset Details

For evaluation, we adopt three benchmarks with 14 KGs in our experiments: two multilingual datasets DBP\-5L\(Chenet al\.,[2017](https://arxiv.org/html/2607.03154#bib.bib136)\), E\-PKG\(Huanget al\.,[2022](https://arxiv.org/html/2607.03154#bib.bib174)\), and a constructed multi\-domain dataset DWY\(Sunet al\.,[2018](https://arxiv.org/html/2607.03154#bib.bib227)\)\.

- •TheDBP\-5Ldataset consists of 5 KGs extracted from DBpedia constructed in Greek \(EL\), English \(EN\), Spanish \(ES\), French \(FR\) and Japanese \(JA\)\.
- •TheE\-PKGdataset is an e\-commerce dataset about the mobile phone\-related product information in 6 languages, including German \(DE\), English \(EN\), Spanish \(ES\), French \(FR\), Italian \(IT\) and Japanese \(JA\)\.
- •TheDWYdataset is a multi\-domain dataset constructed in this paper based onSunet al\.\([2018](https://arxiv.org/html/2607.03154#bib.bib227)\), which includes DBpedia \(DB\), YAGO \(YG\) and Wiki \(WK\)\. We select 80%, 10%, 10% triples of each KG as training, validation, testing data, respectively\. To connect different KGs in the MKGC setting, we adopt the original aligned entities between paired KGs, and prepare equivalent entities between DB\-YG, DB\-WK and YG\-WK\. We will release this dataset for future public research\.

For all datasets, the equivalent entities are given to connect each of two KGs\. The relations are unified in a scheme across all KGs\(Chenet al\.,[2017](https://arxiv.org/html/2607.03154#bib.bib136); Tanget al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib175)\)\. Detailed statistics of all datasets are shown in Table[7](https://arxiv.org/html/2607.03154#A1.T7)\.

Table 7\.Statistics of DBP\-5L\(Chenet al\.,[2017](https://arxiv.org/html/2607.03154#bib.bib136)\), E\-PKG\(Huanget al\.,[2022](https://arxiv.org/html/2607.03154#bib.bib174)\)and DWY\(Sunet al\.,[2018](https://arxiv.org/html/2607.03154#bib.bib227)\)\.DatasetKG\# Ent\.\# Rel\.\# Tra\.\# Val\.\# Tes\.DBP\-5LEL5,2311118,6704,1521,017EN13,99683148,65224,0517,464ES12,38214433,03616,2204,810FR13,17617830,13914,7054,171JA11,80512817,9798,6332,162E\-PKGDE17,2232145,51522,7537,602EN16,5442160,31039,15010,071ES9,5952118,0909,0393,034FR17,0682147,99923,9948022IT15,6702142,76721,3777,148JA2,6422110,0135,0021,688DYWDB23,31518085,50610,68810,780YG13,8642791,17911,39811,410WK17,7439082,04710,25510,296
### A\.2\.Baselines

To evaluate our model, we select the following state\-of\-the\-art methods as baselines:

\(i\)Single\-domain methods, which learn and perform KGC independently on each KG:

- •TransE\(Bordeset al\.,[2013](https://arxiv.org/html/2607.03154#bib.bib149)\)models relations as translation in Euclidean space\.
- •DisMult\(Yanget al\.,[2015](https://arxiv.org/html/2607.03154#bib.bib159)\)uses a bilinear function for semantic matching\.
- •RotatE\(Sunet al\.,[2019](https://arxiv.org/html/2607.03154#bib.bib150)\)represents relations as rotations in complex space\.
- •KG\-BERT\(Yaoet al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib151)\)leverages pre\-trained language models for KGC using textual descriptions of entities and relations\.

These methods perform inference within individual KGs without knowledge transfer between KGs\.

\(ii\)Multi\-domain methods, which jointly leverage multiple KGs to enhance KGC through knowledge transfer:

- •KEnS\(Chenet al\.,[2020b](https://arxiv.org/html/2607.03154#bib.bib131)\)learns a unified embedding space across KGs and employs ensemble\-based knowledge transfer\.
- •CG\-MuA\(Zhuet al\.,[2020](https://arxiv.org/html/2607.03154#bib.bib133)\)aligns KGs through a GNN with collective aggregation and adapts loss functions for multi\-domain KGC\.
- •AlignKGC\(Singhet al\.,[2021](https://arxiv.org/html/2607.03154#bib.bib141)\)jointly performs KGC, entity alignment, and relation alignment across KGs\.
- •SS\-AGA\(Huanget al\.,[2022](https://arxiv.org/html/2607.03154#bib.bib174)\)enhances multi\-domain KGC by dynamically generating potential entity alignments\.
- •LSMGA\(Tanget al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib175)\)encodes KGs with an attentive relational graph encoder and fuses equivalent entities via attention mechanisms\.
- •GLKGC\(He and Yang,[2024](https://arxiv.org/html/2607.03154#bib.bib212)\)uses a transformer\-based GNN for encoding, trained with KGC and entity alignment losses\.

These models mostly attempt consistency\-based modules to align equivalent entities, and thus transfer knowledge from support KGs to benefit target KG predictions\.

### A\.3\.Evaluation Protocol

For generality, we evaluate the KGC model with the task of predicting tail entities\. For a query\(h,r,?\)\(h,r,?\), we place all candidate tail entities in the query to form triples and measure the plausibility scores of the triples\. The tail entity in the triple with the highest score is treated as the final prediction of the tail entity\. Note that the entity set of a target KG serves as the corresponding candidate tail entities\. The testing data of all KGs are used to test the model, and we use the averaged metrics of all KGs to measure the overall performance\(Tanget al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib175)\)\. In detail, the following metrics are used:

- •Hits@N: Hits@N \(H@N for short\) is the proportion of true entities that appear in the firstNNentities of the sorted rank list\. Hits@N can be defined as: \(21\)Hits​@​N=1\|𝒬\|​∑qi∈𝒬𝕀​\[rank​\(i\)≤N\],\\displaystyle\\mathrm\{Hits@N\}=\\frac\{1\}\{\|\\mathcal\{Q\}\|\}\\sum\_\{q\_\{i\}\\in\\mathcal\{Q\}\}\\mathbb\{I\}\[\\mathrm\{rank\}\(i\)\\leq N\],where𝒬\\mathcal\{Q\}denotes all query triples\(h,r,?\)\(h,r,?\)in the testing data,ranki\\mathrm\{rank\}\_\{i\}denotes the rank position of the correct entity in the candidates for theii\-th query, and𝕀​\[rank​\(i\)≤N\]\\mathbb\{I\}\[\\mathrm\{rank\}\(i\)\\leq N\]yields 1 ifiiis ranked within top\-NN, and 0 otherwise\. This metric is bounded in the range \[0, 1\], where the higher, the better\. Note that Hits@1 is equivalent to the precision in conventional classification tasks\.
- •MRR: Mean reciprocal rank \(MRR\) measures the overall performance of the ranking, which is the average of the reciprocal ranks of results for all queries as: \(22\)MRR=1\|𝒬\|​∑qi∈𝒬1rank​\(i\),\\displaystyle\\mathrm\{MRR\}=\\frac\{1\}\{\|\\mathcal\{Q\}\|\}\\sum\_\{q\_\{i\}\\in\\mathcal\{Q\}\}\\frac\{1\}\{\\mathrm\{rank\}\(i\)\},where𝒬\\mathcal\{Q\}also refers to the query triples\(h,r,?\)\(h,r,?\)\. MRR is a useful metric since it reflects the overall ranks of all query triples\. Higher MRR values indicate better performance, with 1 being the maximum achievable value\.

### A\.4\.Optimal Hyper\-parameters

We implement our model with Pytorch555https://docs\.pytorch\.org/docs/stable/index\.htmlbased on the PyG666https://pytorch\-geometric\.readthedocs\.io/en/latest/architecture\. Experiments are conducted on a server with Tesla T4 GPUs\. The optimal model is selected according to the average MRR of all KGs on their validation sets by grid\-search with three trials\(Tanget al\.,[2023](https://arxiv.org/html/2607.03154#bib.bib175)\)\. We use Adam\(Kingma and Ba,[2014](https://arxiv.org/html/2607.03154#bib.bib170)\)to learn the model\. The tuning ranges of hyper\-parameters are reported in the main text\. Here, we report the hyper\-parameters used in Table[8](https://arxiv.org/html/2607.03154#A1.T8)for re\-implementation\.

Table 8\.Detailed hyper\-parameters of our DMKGC model\.
### A\.5\.Further Analysis \(RQ3\)

![Refer to caption](https://arxiv.org/html/2607.03154v1/x6.png)![Refer to caption](https://arxiv.org/html/2607.03154v1/x7.png)![Refer to caption](https://arxiv.org/html/2607.03154v1/x8.png)![Refer to caption](https://arxiv.org/html/2607.03154v1/x9.png)Figure 6\.Impact of timestep numberTT, condition strengthss, and harmonic factorsω1,ω2\\omega\_\{1\},\\omega\_\{2\}\. Averaged MRR \(%\) is reported with±\\pmstd of the 5 KGs on DBP\-5L\.#### A\.5\.1\.Impact on Hyper\-parameters

We show the impact of diffusion time stepTT, conditional strength factorss, and training balance factorsω1\\omega\_\{1\}andω2\\omega\_\{2\}, in Figure[6](https://arxiv.org/html/2607.03154#A1.F6)\. We find that too largeTTmay not be helpful for relatively simplistic embedding generation\. A lower strengthssis better, in agreement with the expectation that the generation is unbiased towards the conditions\. Factorsω1\\omega\_\{1\}andω2\\omega\_\{2\}require the taking of trade\-off values to balance unbiased generation/regularization and the target task prediction\.

#### A\.5\.2\.Comparison on Time Consuming

To evaluate efficiency, we analyze the running time on DBP\-5L\. In training, LSGMA, GLKGC and DMKGC \(w/ 16 diffusion steps\) spend 3\.80, 4\.87 and 4\.71ms per triple, and achieve the best results at 49, 47, 16 training rounds, respectively\. This reflects thatour diffusion\-based model is still training\-efficient, but can also accelerate convergence\. In test time, LSGMA, GLKGC and DMKGC cost 5\.80, 6\.19, 6\.64ms per triple, respectively\. We believethe few reverse steps are controllable and acceptable considering remarkable accuracy improvements\.