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Conditional Diffusion Guided Knowledge Transfer for Multi-Domain Knowledge Graph Completion
Jiawei Sheng, Taoyu Su, Xixun Lin, Xiaodong Li, Tingwen Liu
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Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 94%
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Summary
The paper introduces DMKGC, a generation-based framework for Multi-Domain Knowledge Graph Completion (MKGC) that leverages conditional diffusion models to transfer knowledge from support KGs to a target KG. By treating each KG as a partial view and using domain-agnostic prior embeddings as a proxy objective, DMKGC generates informative domain-general entity embeddings while preserving domain-specific information. This approach overcomes the limitations of consistency-based methods that suppress contextual details, achieving a 4.3% average MRR improvement across 14 KGs and demonstrating robust performance in low-resource scenarios.
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Relation Signals (8)
DMKGC → addresses → Multi-Domain Knowledge Graph Completion
confidence 98% · Multi-domain knowledge graph completion (MKGC) aims to improve missing triple prediction in a target KG by transferring knowledge from other support KGs.
DMKGC → uses → Diffusion Models
confidence 97% · we employ diffusion models (DMs), which generate such embeddings conditioned on the entity information from the support KGs.
DMKGC → utilizes → Support KGs
confidence 96% · fuse equivalent entities from support KGs as the conditional diffusion generation guidance.
DMKGC → generates → Domain-general entity embeddings
confidence 95% · generate informative domain-general entity embeddings through diffusion models conditioned on support KGs.
DMKGC → targets → Target KG
confidence 95% · predict missing triples in a target KG by using other related support KGs.
DMKGC → leverages → Equivalent entities
confidence 94% · entities that appear simultaneously among multiple KGs (e.g. BillGates) are called equivalent entities, which are previously aligned and connect across these KGs
DMKGC → achieves → MRR
confidence 93% · demonstrate a 4.3% average MRR improvement in tail entity prediction over state-of-the-art methods
DMKGC → →
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Abstract
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.
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- Source: https://arxiv.org/abs/2607.03154v1
- Canonical: https://arxiv.org/abs/2607.03154v1
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by Conditional Diffusion Guided Knowledge Transfer for Multi-Domain Knowledge Graph Completion Jiawei Sheng Institute of Information Engineering, Chinese Academy of SciencesBeijingChina shengjiawei@iie.ac.cn 0000-0002-4865-982X , Taoyu Su Institute of Information Engineering, Chinese Academy of SciencesBeijingChina sutaoyu@iie.ac.cn 0009-0003-1674-7635 , Xixun Lin Institute of Information Engineering, Chinese Academy of SciencesBeijingChina linxixun@iie.ac.cn 0009-0004-6645-0597 , Xiaodong Li Institute of Information Engineering, Chinese Academy of Sciences School of Cyber Security, UCASBeijingChina lixiaodong@iie.ac.cn 0009-0008-7374-5413 and Tingwen Liu Institute of Information Engineering, Chinese Academy of Sciences School of Cyber Security, UCASBeijingChina liutingwen@iie.ac.cn 0000-0002-0750-6923 (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: c†conference: Proceedings of the ACM Web Conference 2026; April 13–17, 2026; Dubai, United Arab Emirates†booktitle: Proceedings of the ACM Web Conference 2026 (W ’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 (Liu et al., 2023; Zhang et al., 2025; Liang et al., 2025). However, their practical utility is often hampered by inherent incompleteness, prompting the task of KG completion (KGC) (Pan et al., 2024; Wang et al., 2017). 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 (Luo et al., 2024; Sheng et al., 2020). 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 on multi-domain KG completion (MKGC)111Here, we use the term domain to generally denote a KG constructed from various sources, such as different languages or platforms (Chen et al., 2017; Sun et al., 2023; Zhang et al., 2024b; Yang et al., 2025a)., a practical task that aims to predict missing triples in a target KG by using other related support KGs. As shown in Figure 1, the task is to predict (Microsoft, Founder, ?) in the target KG (EL), but the contextual triples of BillGates are 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 called equivalent entities, which are previously aligned and connect across these KGs (Huang et al., 2022; Tang et al., 2023). 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 (Chen et al., 2020c; Zhu et al., 2020; Singh et al., 2021; Huang et al., 2022; Tang et al., 2023; He and Yang, 2024) follow a consistency-based paradigm for solutions. They learn entity embeddings within individual KGs, and then enforce consistency constraints (Chen et al., 2017; Huang et al., 2022; He and Yang, 2024) between equivalent entities to ensure semantic alignment of KGs (shown in Figure 2(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). To overcome this limitation, we propose a generation-based knowledge transfer paradigm (Figure 2(b)). The core idea is to learn to generate domain-general entity embeddings that effectively preserve rich domain-specific information while remaining unbiased across domains. To achieve this, we employ diffusion models (DMs) (Ho et al., 2020), 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; Podell et al., 2024). In contrast to existing consistency-based methods (Chen et al., 2017; Huang et al., 2022; He and Yang, 2024; Tang et al., 2023), 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-agnostic prior entity embeddings as 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 conditional Diffusion guided knowledge transfer framework for MKGC. 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. 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. Figure 2. Paradigm of consistency-based and our generation-based knowledge transfer. Here, ,S,T are the support and target KG, 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, let =ii=1ND=\G_i\_i=1^N be a set of KGs, where each KG i=(ℰi,ℛi,ℱi)G_i=(E_i,R_i,F_i) involves entities ℰiE_i, relations ℛiR_i and factual triples ℱiF_i. For any two KGs iG_i and jG_j, a small set of equivalent entity pairs is given: ij=(ei,ej)∣ei≡ej,ei∈ℰi,ej∈ℰjA_ij=\(e_i,e_j) e_i≡ e_j,e_i _i,\ e_j _j\. Additionally, all KGs adhere to a unified relation schema ℛR, meaning each ℛi⊆ℛR_i . The task is to predict query triples =(h,r,?)Q\!=\!\(h,r,?)\ for a target KG =t,t∈T=G_t,G_t , leveraging existing triples from both the target KG T and all other support KGs =s|s∈,s≠tS=\G_s|G_s ,s≠ t\. 2.2. Diffusion Model In this paper, we leverage diffusion models (DMs) (Ho et al., 2020; Sohl-Dickstein et al., 2015) to transfer knowledge, which contains a forward and a reverse process. Figure 3. The overview of our proposed framework, DMKGC. It contains (a) multi-domain entity encoder to extract KG features, (b) conditional diffusion transfer to generate entity embeddings, and (c) joint training and inference to achieve the task. 2.2.1. Forward Process Given an input data sample 0∼q(x0) x_0 q(x_0), the forward process constructs a series of latent variables 1:T x_1:T through a Markov chain by gradually adding Gaussian noise across T steps. Specifically, the transition at each time step k is defined by: (1) q(xk|k−1)=(k;1−βkk−1,βk), q(x_k| x_k-1)=N( x_k; 1- _k x_k-1, _k I), where k∈1,2,…,Tk∈\1,2,...,T\, N denotes a Gaussian distribution, and factor βk∈(0,1) _k∈(0,1) controls the scale of noise added at step k. The factors ensure that, when T→∞T→∞, the variable k 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 state T∼(0,1) x_T (0,1), DMs parameterize a Markov chain that transitions from k x_k to k−1 x_k-1 via: (2) pθ(k−1|k)=(k−1;θ(k,k),Σθ(k,k)), p_θ( x_k-1| x_k)=N( x_k-1; μ_θ( x_k,k), _θ( x_k,k)), where k∈T,T−1,…,1k∈\T,T-1,...,1\ denotes the reversed time step, θ(k,k) μ_θ( x_k,k) and θ(k,k) _θ( x_k,k) are the mean and covariance of the Gaussian distribution generated by a neural network θ. For simplicity and training stability, Σθ(k,k) _θ( x_k,k) is usually set to constants σ2(k)σ^2(k) I varying over time steps (Ho et al., 2020). 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 data 0 x_0 to enable data generation (Ho et al., 2020), which is: (3) logp(0) p( x_0) =log∫p(0:T)d1:T=log(1:T|0)[p(0:T)q(1:T|0)] = p( x_0:T)d x_1:T= _ q( x_1:T| x_0)[ p( x_0:T)q( x_1:T| x_0)] ≥(1|0)[logpθ(0|1)]⏟reconstruction termℒ0−DKL(q(T|0)∥p(T))⏟prior matching termℒT ≥ E_ q( x_1| x_0)[ p_θ( x_0| x_1)]_reconstruction term\ L_0- D_KL(q( x_T| x_0)\|p( x_T))_prior matching term\ L_T −∑k=2T(k|0)[DKL(q(k−1|k,0)∥pθ(k−1|k))]⏟denoising matching termℒk−1, - _k=2^T E_ q( x_k| x_0)[D_KL(q( x_k-1| x_k, x_0)\|p_θ( x_k-1| x_k))]_denoising matching term\ L_k-1, where there are three terms to resolve: • Reconstruction term: Measures fidelity of 0 x_0 given state 1 x_1, which can be achieved by mean square error (MSE). • Prior matching term: Ensures q(T|0)q( x_T| x_0) converges to the Gaussian prior p(T)∼(,)p( x_T) ( 0, 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 probability q(k−1|k,0)q( x_k-1| x_k, x_0) (analytically tractable) and the learned probability pθ(k−1|k)p_θ( x_k-1| x_k), allowing iterative generation of k−1 x_k-1 from k x_k. By simplification (Ho et al., 2020), this term can be achieved by ∑k=2Tk,ϵ[‖ϵ−ϵθ(k,k)‖22] _k=2^TE_k, ε[\| ε- ε_θ( x_k,k)\|_2^2], where ϵθ(k,k) ε_θ( x_k,k) is a neural denoiser (e.g., U-Net (Ho et al., 2020), MLP (Wang et al., 2023)) that predicts the added noise ϵ ε at time step k. 2.2.4. Inference & Sampling With the trained neural denoiser θ, the DMs can sample T∼(,) x_T ( 0, I) and iteratively leverage pθ(k−1|k)p_θ( x_k-1| x_k) to generate the predicted sample ^0 x_0. Note that all above procedures can be achieved by embeddings for efficiency (Rombach et al., 2022). 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. 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) ~=Embedding(e),e∈ℰ, e=Embedding(e),e , where we call ~∈ℝd e ^d the prior entity embedding. Here, we share the embeddings for all KGs, where ℰE 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 (Tang et al., 2023) . Given a KG G (omit subscript for simplicity), it encodes an entity e with its relational neighborhood (e)N(e) from G as: (5) Encoderl(,) _l( e,G) =+δ(∑rj,ej∈(e)αl(,j,j)⋅3l[j⊕j]), = e+δ(\!\!\!\! _\r_j,e_j\ (e)\!\!\!\! _l( e, r_j, e_j)· W^l_3[ e_j r_j]), αl(,j,j) _l( e, r_j, e_j) =softmax(scorel(,j,j)), =softmax(score_l( e, r_j, e_j)), scorel(,j,j) _l( e, r_j, e_j) =βrj⋅1d(1l⋅2l[j⊕j]), = _r_j· 1 d( W^l_1 e· W^l_2[ e_j r_j]), where δ is the ReLU activation, ⊕ is the vector concatenation, l is the layer, 1l∈ℝd×d,2l,3l∈ℝd×2d W^l_1 ^d× d, W^l_2, W^l_3 ^d× 2d are learnable layer weights. The relation embedding ∈ℝd r ^d is randomly initialized, and the input e is the prior entity embedding ~ e from Eq. (4). Here, the score considers both the learnable prior weight βr∈ℝ _r of relation r, and also captures the contextual attentive relational relevance. The encoder output is denoted as z, which we call domain entity embeddings as they contain domain-specific information. In the following sections, we use t z_t to denote an involved entity e from the target KG =tT=G_t, and ss\ z_s\_s denotes its equivalent entities333Following Tang et al. (2023), for simplicity of implementation, we also add virtual isolated entities in the KGs where the equivalent entity doesn’t exist. from the corresponding support KGs =ssS=\G_s\_s. 3.2. Conditional Diffusion Transfer Unlike existing consistency-based methods (Chen et al., 2017; Huang et al., 2022; He and Yang, 2024), 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. 3.2.1. Forward Process Given an entity e and its domain entity embeddings, we expect to generate a domain-general entity embedding. To this end, we use the prior embedding ~ e as the initial state, i.e., 0=~ x_0= e. As introduced in section 2.2, the forward process is q(xk|k−1)=(k;1−βkk−1,βk)q(x_k| x_k-1)=N( x_k; 1- _k x_k-1, _k I), where βk _k is the noise scale factor. Using the reparameterization trick (Kingma and Welling, 2014; Ho et al., 2020), we can efficiently obtain k x_k from 0 x_0 as: (6) q(k|0)=(k;α¯k0,(1−α¯k)), q( x_k| x_0)=N( x_k; α_k x_0,(1- α_k) I), where αk=1−βk _k=1- _k, α¯k=Πk′=1kαk α_k= _k =1^k _k. Hence, we can directly obtain the embedding k=α¯k0+1−α¯kϵ,ϵ∼(,) x_k= α_k x_0+ 1- α_kε,ε ( 0, I) at any step k. The last state of the noisy embedding is denoted as T x_T. 3.2.2. Reverse Process The reverse process gradually denoises T x_T to reconstruct the initial state 0 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) is as follows: (7) pθ(k−1|k,)=(k−1;θ(k,,k),σ2(k)), p_θ( x_k-1| x_k, c)=N( x_k-1; μ_θ( x_k, c,k),σ^2(k) I), where θ(k,,k) μ_θ( x_k, c,k) is learned by a conditional denoiser (detailed later). Here, ∈ℝd c ^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 step k. To keep it simple, we employ an effective multilayer perceptron (MLP) as the denoiser: (8) ^θ(k,,k):=MLP(k⊕;θ), x_θ( x_k, c,k)=MLP( x_k c k;θ), where we use a two-layer MLP with dimensions as 3d→2d→d3d→ 2d→ d, and ∈ℝd k ^d is the time-step embedding (Ho et al., 2020). Here, as the condition information can be different, we consider three types of condition c: (i) when the condition is not given, we set =ϕ c=φ where ϕ∈ℝdφ ^d is an initialized null embedding in training. (i) when an equivalent entity embedding from an arbitrary KG iG_i is given, the condition is =i c= z_i. (i) when equivalent entities ss\ z_s\_s from support KGs S are given, we fuse them according to their relevance to the entity t z_t as (9) =s¯ c= z_ s =∑s∈ssα(t,s)⋅s, = _ z_s∈\ z_s\_sα( z_t, z_s)· z_s, α(t,s) α( z_t, z_s) =softmax(score(t,s)), =softmax(score( z_t, z_s)), score(t,s) ( z_t, z_s) =βts⋅1d(1t⋅2s]), = _ts· 1 d( U_1 z_t· U_2 z_s]), where 1,2∈ℝd×d U_1, U_2 ^d× d are learnable weights. In particular, βts∈ℝ _ts is a learnable factor to reflect the prior relevance between tG_t and sG_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 (Ho et al., 2020). 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). Consider the denoising matching term ℒk−1L_k-1, which matches pθ(k−1|k)p_θ( x_k-1| x_k) with q(k−1|k,0)q( x_k-1| x_k, x_0) by KL divergence. By Bayes rules, q(k−1|k,0)∼(k−1;~(k,0,k),σ2(k))q( x_k-1| x_k, x_0)\! \!N( x_k-1; μ( x_k, x_0,k),σ^2(k) I) can be written as: (10) ~(k,0,k) μ( x_k, x_0,k) =αk(1−α¯k−1)1−α¯kk+α¯k−1(1−αk)1−α¯k0, = _k(1- α_k-1)1- α_k x_k+ α_k-1(1- _k)1- α_k x_0, σ2(k) σ^2(k) I =(1−αk)(1−α¯k−1)1−α¯k. = (1- _k)(1- α_k-1)1- α_k I. where μ~(k,0,k) μ( x_k, x_0,k) and σ2(k)σ^2(k) I are mean and covariance. As suggested (Yang et al., 2023; Wang et al., 2023), instead of learning the added noise ϵ ε by parameterizing ϵθ(k,k) ε_θ( x_k,k), we directly parameterize 0 x_0, which is: (11) θ(k,k)=αk(1−α¯k−1)1−α¯kk+α¯k−1(1−αk)1−α¯k^θ(k,k), μ_θ( x_k,k)= _k(1- α_k-1)1- α_k x_k+ α_k-1(1- _k)1- α_k x_θ( x_k,k), where ^θ(k,k) x_θ( x_k,k) is an approximation of the given true data 0 x_0, based on the situation at the time step k. This is proven to be equal to the vanilla ELBO in DDPM (Yang et al., 2023). Using the above parameterization, the denoising matching term (k≥2k≥ 2) can be derived as: (12) ℒk−1 _k-1 :=q(k|0)[DKL(q(k−1|k,0)∥pθ(k−1|k))] =E_q( x_k| x_0)[D_KL(q( x_k-1| x_k, x_0)\|p_θ( x_k-1| x_k))] =q(k|0)[12σ2(k)‖θ(k,k)−~(k,0,k)‖22] =E_q( x_k| x_0)[ 12σ^2(k)\| μ_θ( x_k,k)- μ( x_k, x_0,k)\|_2^2] =q(k|0)[12(α¯k−11−α¯k−1−α¯k1−α¯k)‖^θ(k,k)−0‖22]. =E_q( x_k| x_0)[ 12( α_k-11- α_k-1- α_k1- α_k)\| x_θ( x_k,k)- x_0\|_2^2]. This form is similar to the reconstruction term (k=0k=0) with Gaussian log-likelihood (Liang et al., 2018) as ℒ0:=q(1|0)‖^θ(1,1)−0‖22L_0:=E_q( x_1| x_0)\!\| x_θ( x_1,1)- x_0\|_2^2. Thereafter, we combine them into a unified training term (k≥1k≥ 1) as: (13) ℒk−1:=q(k|0)‖^θ(k,k)−0‖22. _k-1=E_q( x_k| x_0)\| x_θ( x_k,k)- 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=1Tq(k|~)‖^θ(k,s¯,k)−~‖22, _gen= _k=1^TE_q( x_k| e)\| x_θ( x_k, z_ s,k)- e\|_2^2, where ^θ(k,s¯,k) x_θ( x_k, z_ s,k) comes from Eq. (9). 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), which retains a ratio pup_u of generation cases without conditions (i.e., ϕφ), improving the unconditional generation ability. (i) Target-Domain Task Prediction This constraint ensures the generated domain-general embedding to be task-predictive in the KG target tG_t. To enrich the entity information, we fuse the generated ^θ x_θ, the prior ~ e, and the target-domain embedding t z_t as: (15) ¯t=^θ+~+t, z_t= x_θ+ e+ z_t, where ^θ=^θ(k,s¯,k) x_θ= x_θ( x_k, z_ s,k). For a triple (h,r,o)(h,r,o) sampled444Here, we use o to denote the tail entity, since t is used to denote the target KG. in tG_t, we use the classical triple scoring function (Bordes et al., 2013) to predict plausibility: (16) ψ(h,r,o)=−‖¯t,h+−¯t,o‖2,ψ(h,r,o)=-\| z_t,h+ r- z_t,o\|_2, (17) ℒtask:=∑(h,r,o)∈ℱt∑(h,r,o′)∉ℱt[λ−ψ(h,r,o)+ψ(h,r,o′)]+,L_task:=\!\!\! _(h,r,o) _t _(h,r,o ) _t\!\!\![λ-ψ(h,r,o)+ψ(h,r,o )]_+, where we adopt the margin loss, [⋅]+:=max(⋅,0)[·]_+:= (·,0), λ is the margin factor, and o′∈ℰto _t is a negative entity randomly selected. In this way, the generated embedding ^θ x_θ is refined, and together with other embeddings to enhance KGC in the target KG. (i) 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=1Tq(k|~)‖^θ(k,i,k)−~‖22, _reg= _i=1^N _k=1^TE_q( x_k| e)\| x_θ( x_k, z_i,k)- e\|_2^2, where i 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+ω1ℒgen+ω2ℒreg, =L_task+ _1L_gen+ _2L_reg, where ω1,ω2∈ℝ _1, _2 are harmonic factors to balance training. The algorithm 1 presents the overall training procedure, where we adopt sampling strategies (Ho et al., 2020) to accelerate training for efficiency. 3.3.2. Inference In inference, we use the domain-general entity embedding ^0 x_0 from ^θ(k,s¯,k) x_θ( x_k, z_ s,k) to transfer knowledge from the support KGs. Following the CFG strategy (Ho and Salimans, 2022) to enable conditional generation, we adjust the generation by interpolating the generated conditional and unconditional embedding as: (20) ~θ(k,s¯,k)=^θ(k,ϕ,k)+s[^θ(k,s¯,k)−^θ(k,ϕ,k)], x_θ( x_k, z_ s,k)= x_θ( x_k,φ,k)+s[ x_θ( x_k, z_ s,k)- x_θ( x_k,φ,k)], where s∈ℝs is a factor in controlling the strength of the condition. Subsequently, in inference, given 0=~ x_0= e, we first perform the forward process to derive T x_T, and then set ^T=T x_T= x_T to start the reverse process. This process holds for both head and tail entities involved (as in Eq. (16)). For a query (h,r,?)(h,r,?) in tG_t, we treat all entities in ℰtE_t as candidates. The entity with the highest score is returned as the result. The algorithm 2 presents the inference procedure. Algorithm 1 Training procedure Input: Training data =iiD=\G_i\_i and equivalent entity sets iji≠j\A_ij\_i≠ j.Output: Model parameters Θ . 1: Initialize all model parameters. 2: while not convergence do 3: Sample a target KG tG_t and support KGs =s|s≠tS=\G_s|s≠ t\. 4: Sample a triple (h,r,o)(h,r,o) from tG_t, and a negative entity o′o from ℰtE_t. 5: for e∈h,o,o′e∈\h,o,o \ do 6: Obtain prior embedding ~ e, and let 0=~ x_0= e; 7: for all i∈G_i do 8: Obtain i=Encoder(~,i) z_i=Encoder( e,G_i) by Eq. (5); 9: end for 10: Sample k∼(1,T)k (1,T), ϵ∼(0,I)ε (0,I), and obtain k x_k by Eq. (6); 11: Estimate ^θ(k,s¯,k) x_θ( x_k, z_ s,k) with CFG, obtain ℒgenL_gen by Eq. (14); 12: Estimate ^θ(k,i,k) x_θ( x_k, z_i,k) with CFG, obtain ℒregL_reg by Eq. (18); 13: Obtain mixed embedding ¯t,e=^θ+~+t,e z_t,e= x_θ+ e+ z_t,e; 14: end for 15: Obtain ℒtaskL_task by Eq. (17); 16: Obtain overall loss ℒL by Eq. (19) to optimize Θ ; 17: end while Algorithm 2 Inference procedure Input: Θ , query (h,r,?)(h,r,?) in target =tT=G_t, support =ss≠tS=\G_s\_s≠ t.Output: Score ψ(h,r,o′)ψ(h,r,o ) of all candidate entities o′∈ℰto _t. 1: for e∈h∪ℰte∈\h\ _t do 2: Obtain prior embedding ~ e. 3: for all i∈∪G_i do 4: Obtain i=Encoder(~,i) z_i=Encoder( e,G_i) by Eq. (5). 5: end for 6: Sample ϵ∼(0,I)ε (0,I), and obtain ^T x_T by Eq. (6); 7: for k=T,⋯,1k=T,·s,1 do 8: Estimate ^θ(^k,s¯,k) x_θ( x_k, z_ s,k) and ^θ(^k,ϕ,k) x_θ( x_k,φ,k) by Eq. (8); 9: Obtain ~θ(^k,s¯,k) x_θ( x_k, z_ s,k) by Eq. (20); 10: Obtain ^k−1=μθ(^k,k) x_k-1= _θ( x_k,k) with ^k x_k and ~θ(^k,s¯,k) x_θ( x_k, z_ s,k) by Eq. (11); 11: end for 12: Obtain mixed embedding ¯t=^0+~+t z_t= x_0+ e+ z_t; 13: Calculate score ψ(h,r,o′)ψ(h,r,o ) with ¯t,h z_t,h and ¯t,o′ z_t,o by Eq. (16); 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 the Appendix (Q3). 4.1. Evaluation Settings Table 1. Results (%) on DBP-5L. † indicates re-produced results. The best result is bold-faced and the runner-up is underlined. Method EL EN ES FR JA AVG H@1 H@10 MRR H@1 H@10 MRR H@1 H@10 MRR H@1 H@10 MRR H@1 H@10 MRR MRR TransE 13.1 43.7 24.3 7.3 29.3 16.9 13.5 45.0 24.4 17.5 48.8 27.6 21.1 48.5 25.3 23.7 DistMult 8.9 11.3 9.8 8.8 30.0 18.3 7.4 22.4 13.2 6.1 23.8 14.5 9.3 27.5 15.8 14.3 RotatE 14.5 36.2 26.2 12.3 30.4 20.7 21.2 53.9 33.8 23.2 55.5 35.1 26.4 60.2 39.8 31.1 KG-BERT 17.3 40.1 27.3 12.9 31.9 21.0 21.9 54.1 34.0 23.5 55.9 35.4 26.9 59.8 38.7 31.3 KEnS 28.1 56.9 - 15.1 39.8 - 23.6 60.1 - 25.5 62.9 - 32.1 65.3 - - CG-MuA 21.5 44.8 32.8 13.1 33.5 22.2 22.3 55.4 34.3 24.2 57.1 36.1 27.3 61.1 40.1 33.1 AlignKGC 27.6 56.3 33.8 15.5 39.2 22.3 24.2 60.9 35.1 24.1 62.3 37.4 31.6 64.3 41.6 34.0 S-AGA 30.8 58.6 35.3 16.3 41.3 23.1 25.5 61.9 36.6 27.1 65.5 38.3 34.6 66.9 42.9 35.2 LSMGA 33.1 89.9 54.5 16.8 61.7 32.4 25.6 74.8 42.8 31.2 81.3 48.6 33.5 79.1 49.8 45.6 GLKGC† 36.6 86.5 53.0 17.1 60.2 32.9 28.3 74.4 43.6 31.5 78.4 47.9 36.5 77.6 50.9 45.7 DMKGC 41.9 91.0 61.0 20.9 64.2 36.3 33.0 77.7 49.1 38.6 82.3 54.2 42.0 82.4 56.3 51.4 Table 2. Results (%) on E-PKG. † indicates re-produced results. The best result is bold-faced and the runner-up is underlined. Method DE EN ES FR IT JA AVG H@1 H@10 MRR H@1 H@10 MRR H@1 H@10 MRR H@1 H@10 MRR H@1 H@10 MRR H@1 H@10 MRR MRR TransE 21.2 65.5 37.4 23.2 67.5 39.4 17.2 58.4 33.0 20.8 66.9 37.5 22.0 63.8 37.8 25.1 72.7 43.6 38.1 DistMult 21.4 54.5 35.4 23.8 60.1 37.2 17.9 46.2 30.9 20.7 53.5 35.1 22.8 51.8 34.8 25.9 62.6 38.0 35.2 RotatE 22.3 64.3 38.2 24.2 66.8 40.0 18.3 58.9 33.7 22.1 64.3 38.2 22.5 64.0 38.1 26.3 71.9 41.8 38.3 KG-BERT 21.8 64.7 38.4 24.3 66.4 39.6 18.7 58.8 33.2 22.3 67.2 38.3 22.9 63.7 37.2 26.9 72.4 44.1 38.5 KEnS 24.3 65.8 - 26.2 69.5 - 21.3 59.5 - 25.4 68.2 - 25.1 64.6 - 33.5 73.6 - - CG-MuA 22.9 64.9 38.7 24.8 67.9 40.2 19.2 58.8 33.8 23.0 67.5 39.1 23.9 63.8 37.6 30.4 72.9 45.9 39.2 AlignKGC 22.1 65.1 38.5 25.6 68.3 40.5 19.4 59.1 34.2 22.8 67.2 38.8 24.2 63.4 37.3 31.2 72.3 46.2 39.3 S-AGA 24.6 66.3 39.4 26.7 69.8 41.5 21.0 60.1 36.3 25.9 68.7 40.2 24.9 63.8 38.4 33.9 74.1 48.3 40.7 LSMGA 30.7 68.5 44.8 31.9 70.2 45.9 23.1 61.1 36.5 23.7 63.5 38.2 26.8 64.5 41.0 43.7 78.4 57.1 43.9 GLKGC† 24.1 63.6 37.7 27.1 58.4 39.4 24.6 61.0 36.8 22.1 62.3 36.4 27.0 63.7 40.4 44.1 76.4 57.5 41.4 DMKGC 30.9 69.1 45.0 33.3 70.3 46.8 26.7 63.7 39.7 26.0 68.8 40.7 31.2 66.3 44.6 50.1 79.1 61.8 46.4 Table 3. Results (%) on DWY. † indicates re-produced results. The best result is bold-faced and the runner-up is underlined. Method DB WK YG AVG H@1 H@10 MRR H@1 H@10 MRR H@1 H@10 MRR MRR TransE† 4.3 52.9 20.3 3.0 48.6 17.3 2.2 42.2 13.1 16.9 DistMult† 8.6 36.5 17.6 8.4 41.7 18.4 4.6 32.5 12.7 16.2 RotatE† 13.2 57.4 27.9 9.9 52.5 26.4 3.5 42.7 13.8 22.7 S-AGA† 5.8 61.8 22.6 6.6 52.2 18.5 9.0 52.3 22.9 21.3 LSGMA† 14.0 64.3 30.9 9.5 54.6 23.9 11.4 48.6 23.5 26.1 GLKGC† 13.4 66.9 32.3 9.3 55.0 24.3 16.5 52.8 28.7 28.4 DMKGC 15.7 68.9 34.5 11.4 59.3 26.7 23.6 66.7 37.9 33.1 4.1.1. Datasets For evaluation, we use three benchmarks comprising 14 KGs: the multilingual DBP-5L (Chen et al., 2017) and E-PKG (Huang et al., 2022), and a constructed multi-domain DWY (Sun et al., 2018) 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 (Sun et al., 2018), 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 (Chen et al., 2017; Tang et al., 2023). The statistics are shown in Appendix. 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, including TransE (Bordes et al., 2013), DisMult (Yang et al., 2015), RotatE (Sun et al., 2019), KG-BERT (Yao et al., 2020). (i) Multi-domain methods, which mostly attempt consistency-based modules to transfer knowledge from support KGs for target KG predictions, including KEnS (Chen et al., 2020c), CG-MuA (Zhu et al., 2020), AlignKGC (Singh et al., 2021), S-AGA (Huang et al., 2022), LSMGA (Tang et al., 2023) and GLKGC (He and Yang, 2024). For details, please refer to Appendix. 4.1.3. Evaluation Protocol Following previous studies (Chen et al., 2017; Tang et al., 2023), we evaluate models in the task of tail 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 predict t given h and r for 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). Following Tang et al. (2023), 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 margin λ is set to 0.5 for all datasets. The KG encoder has 2 layers. The diffusion step T is selected in 2,4,⋯,64\2,4,·s,64\, and the strength s in 1,2,⋯,5\1,2,·s,5\, ω1,ω2 _1, _2 are tuned in 1,3,5×10−4,3,2,1\1,3,5\\!×\!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 in Appendix. 4.2. Main Results (RQ1) 4.2.1. Method Comparison We present the comparison between our model and existing baselines in Table 1, 2 and 3. 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 S-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 (%). Variant AVG-H@1 AVG-H@10 AVG-MRR Δ -MRR Entire 35.3 79.5 51.4 - repl. GCN 23.2 69.8 39.7 ↓ 11.7 w/o cond 27.0 76.3 44.9 ↓ 6.5 repl. mean 32.6 71.6 46.4 ↓ 5.0 w/o DM 31.6 68.9 44.4 ↓ 7.0 w/o reg 32.9 77.8 49.2 ↓ 2.2 repl. ϵε-ELBO 18.8 70.8 37.3 ↓ 14.1 repl. ϵε-init 28.1 77.2 45.9 ↓ 5.5 repl. cosine 25.7 74.2 43.0 ↓ 8.4 Table 5. Comparison with general knowledge transfer methods. The results (%) are reported on DBP-5L. Method AVG-H@1 AVG-H@10 AVG-MRR InfoNCE† 31.5 71.4 45.3 DA-DIFF† 32.6 71.4 46.3 MMD† 34.6 74.3 48.4 DMKGC 35.3 79.5 51.4 4.2.2. In-depth Variant Analysis To evaluate the unity of the components, we perform variant analysis in Table 4. We find that: First, repl. GCN replaces the attentive KG encoder with non-relational GCN (Kipf and Welling, 2017), 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 regularization ℒregL_reg. This reflects the vital role of learning domain-general entity embeddings with unbiased generation. Forth, repl. ϵε-ELBO achieves ELBO with DDPM (Ho et al., 2020), repl. ϵε-init starts the reverse process with a random noise, and repl. cosine replaces L2-norm with cosine score in Eq. (13). The results reflect that direct parameterizing 0 x_0 by ^θ x_θ can be helpful in learning the general entity embedding, the initial T 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 (Chen et al., 2020a) leverages contrastive loss to enhance the consistency between equivalent entities from various KGs. (i) DA-DIFF (Peng et al., 2024) 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. (i) MMD (Gretton et al., 2012) adopts the classical maximum mean discrepancy, which measures the distributional relevance between equivalent entities. The results are shown in Table 5. 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 that our 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) Figure 4. Results (%) with a limited number of equivalent entities, randomly selected at 20%, 50% and 80% on DBP-5L. 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. Methods EL EN ES FR JA AVG H@1 H@10 MRR H@1 H@10 MRR H@1 H@10 MRR H@1 H@10 MRR H@1 H@10 MRR MRR LSGMA† 7.1 48.8 21.7 4.5 26.0 12.0 7.5 37.5 17.6 7.8 42.3 20.2 7.0 33.8 16.7 17.7 GLKGC† 15.9 57.6 31.5 5.3 29.9 14.0 9.7 42.2 21.3 13.6 47.3 26.0 10.0 40.1 21.2 22.8 InfoNCE† 21.6 57.8 34.0 9.3 28.6 15.8 13.4 39.5 22.4 19.8 46.3 29.2 17.2 39.5 25.1 25.3 DA-DIFF† 12.2 54.8 27.5 5.9 31.3 14.8 11.0 45.7 22.6 15.9 50.2 29.5 9.4 43.0 22.0 23.3 MMD† 22.1 55.3 33.9 9.6 28.1 16.1 13.8 39.1 22.5 20.7 46.1 30.0 17.3 39.3 25.2 25.5 DMKGC 24.9 61.8 39.0 12.4 32.1 19.4 19.0 46.2 28.8 23.4 50.4 33.4 19.3 43.3 27.6 29.6 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. We find that our 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. 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 (Chen et al., 2023). Specifically, for a query (h,r,?)(h,r,?), we suppose that h is 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. We find that our model derives the best results and significantly exceeds the previous baselines LSGMA and GLKGC. We believe that the 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 propose triple-based methods (Bordes et al., 2013; Yang et al., 2015; Sun et al., 2019; Dettmers et al., 2018; Trouillon et al., 2016) with translation-based (Bordes et al., 2013; Sun et al., 2019) or semantic matching-based score functions (Yang et al., 2015; Dettmers et al., 2018). Later studies propose GNN-based methods (Shang et al., 2019; Schlichtkrull et al., 2018; Liu et al., 2024a) to capture relational graph structures. Recent studies also explore entity textual information (Xie et al., 2016; Yao et al., 2025) with PLMs (Yao et al., 2020; Wang et al., 2021) or LLMs (Wei et al., 2023; Guo et al., 2024; Zhang et al., 2024a; Liu et al., 2024b; Yao et al., 2025; Li et al., 2024; Yao et al., 2025), 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, namely multilingual KGC (Huang et al., 2022; Tang et al., 2023). For generality, we term it as multi-domain KGC beyond languages. For the methods, MTransE (Chen et al., 2017) first extends the KG embeddings from one to multiple KGs. Later studies (Zhang et al., 2019; Zhu et al., 2021; Sun et al., 2023; Yang et al., 2025b) focus mainly on entity alignment (EA) for knowledge fusion. Further studies (Zhu et al., 2020; Singh et al., 2021; Huang et al., 2022; He and Yang, 2024; Sheng et al., 2026) 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 (Podell et al., 2024; Ho et al., 2020) and text generation (Gulrajani and Hashimoto, 2023; Lovelace et al., 2023), and also reflect potential in discriminative tasks (Rahman et al., 2023; Wang et al., 2023; Yang et al., 2023; Jiang et al., 2024). Recent KGC studies attempt DMs to model the generative distribution of triples (Long et al., 2024a, b; Huang et al., 2025) and graph structures (Cao et al., 2024) for triple prediction. Our paper explores knowledge transfer for multi-domain KGC, which has a different research focus. For knowledge transfer, existing studies explore DMs for knowledge distillation (Huang et al., 2023; He et al., 2025) or domain adaptation (Peng et al., 2024), 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. 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Dataset Details For evaluation, we adopt three benchmarks with 14 KGs in our experiments: two multilingual datasets DBP-5L (Chen et al., 2017), E-PKG (Huang et al., 2022), and a constructed multi-domain dataset DWY (Sun et al., 2018). • The DBP-5L dataset consists of 5 KGs extracted from DBpedia constructed in Greek (EL), English (EN), Spanish (ES), French (FR) and Japanese (JA). • The E-PKG dataset 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). • The DWY dataset is a multi-domain dataset constructed in this paper based on Sun et al. (2018), 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 (Chen et al., 2017; Tang et al., 2023). Detailed statistics of all datasets are shown in Table 7. Table 7. Statistics of DBP-5L (Chen et al., 2017), E-PKG (Huang et al., 2022) and DWY (Sun et al., 2018). Dataset KG # Ent. # Rel. # Tra. # Val. # Tes. DBP-5L EL 5,231 111 8,670 4,152 1,017 EN 13,996 831 48,652 24,051 7,464 ES 12,382 144 33,036 16,220 4,810 FR 13,176 178 30,139 14,705 4,171 JA 11,805 128 17,979 8,633 2,162 E-PKG DE 17,223 21 45,515 22,753 7,602 EN 16,544 21 60,310 39,150 10,071 ES 9,595 21 18,090 9,039 3,034 FR 17,068 21 47,999 23,994 8022 IT 15,670 21 42,767 21,377 7,148 JA 2,642 21 10,013 5,002 1,688 DYW DB 23,315 180 85,506 10,688 10,780 YG 13,864 27 91,179 11,398 11,410 WK 17,743 90 82,047 10,255 10,296 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 (Bordes et al., 2013) models relations as translation in Euclidean space. • DisMult (Yang et al., 2015) uses a bilinear function for semantic matching. • RotatE (Sun et al., 2019) represents relations as rotations in complex space. • KG-BERT (Yao et al., 2020) 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. (i) Multi-domain methods, which jointly leverage multiple KGs to enhance KGC through knowledge transfer: • KEnS (Chen et al., 2020b) learns a unified embedding space across KGs and employs ensemble-based knowledge transfer. • CG-MuA (Zhu et al., 2020) aligns KGs through a GNN with collective aggregation and adapts loss functions for multi-domain KGC. • AlignKGC (Singh et al., 2021) jointly performs KGC, entity alignment, and relation alignment across KGs. • S-AGA (Huang et al., 2022) enhances multi-domain KGC by dynamically generating potential entity alignments. • LSMGA (Tang et al., 2023) encodes KGs with an attentive relational graph encoder and fuses equivalent entities via attention mechanisms. • GLKGC (He and Yang, 2024) 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 (Tang et al., 2023). 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 first N entities of the sorted rank list. Hits@N can be defined as: (21) Hits@N=1||∑qi∈[rank(i)≤N], @N= 1|Q| _q_i I[rank(i)≤ N], where Q denotes all query triples (h,r,?)(h,r,?) in the testing data, rankirank_i denotes the rank position of the correct entity in the candidates for the i-th query, and [rank(i)≤N]I[rank(i)≤ N] yields 1 if i is ranked within top-N, 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||∑qi∈1rank(i), = 1|Q| _q_i 1rank(i), where 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.html based 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 (Tang et al., 2023). We use Adam (Kingma and Ba, 2014) 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 for re-implementation. Hyper-parameters DBP-5L E-PKG DWY batch size 300 300 300 learning rate 1×10−31× 10^-3 1×10−31× 10^-3 1×10−31× 10^-3 margin λ 0.5 0.5 0.5 epoch 30 50 30 embedding size d 256 256 256 hidden dimension 256 256 256 encoder layer number L 2 2 2 ratio pup_u 0.1 0.1 0.1 strength s 2 1 2 diffusion step T 16 32 16 factor ω1 _1 1×10−21× 10^-2 1×10−21× 10^-2 1×10−21× 10^-2 factor ω2 _2 1×10−31× 10^-3 1×10−31× 10^-3 1×10−31× 10^-3 Table 8. Detailed hyper-parameters of our DMKGC model. A.5. Further Analysis (RQ3) Figure 6. Impact of timestep number T, condition strength s, and harmonic factors ω1,ω2 _1, _2. Averaged MRR (%) is reported with ± std of the 5 KGs on DBP-5L. A.5.1. Impact on Hyper-parameters We show the impact of diffusion time step T, conditional strength factor s, and training balance factors ω1 _1 and ω2 _2, in Figure 6. We find that too large T may not be helpful for relatively simplistic embedding generation. A lower strength s is better, in agreement with the expectation that the generation is unbiased towards the conditions. Factors ω1 _1 and ω2 _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 that our 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 believe the few reverse steps are controllable and acceptable considering remarkable accuracy improvements.