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Synchronous Multi-view Neural Diffusion

Yongquan Shi, Weijun Huang, Yueyang Pi, Wendi Zhao, Yiqing Shi, Shiping Wang

arXiv:2609.39019v1cs.LG

TL;DR

Existing multi-view fusion separates within-view evolution from cross-view interactions, leaving cross-view relationships constrained by view-specific structure. SynMDiff models these interactions jointly as diffusion in a unified multi-view space, with sampling and centralized training to reduce computational cost. The paper reports effectiveness on diverse real-world scenarios and best performance across four large-scale datasets.

  • Problem

    Existing fusion methods separate intra-view and inter-view operations, so arbitrary cross-view feature interactions are not explicitly modeled and information may pass through distortion-prone intermediate pathways.

    Source: §1 · p. 1

  • Method

    SynMDiff models pairwise feature interactions as diffusion flows in a joint multi-view space and uses energy-based topological sampling with virtual-anchor centralized training.

    Source: §1 · p. 2, §4.4 · p. 5, §6 · p. 8

  • Results

    SynMDiff achieves the best performance across all four large-scale datasets, and experiments across diverse real-world multi-view scenarios demonstrate effectiveness.

    Source: §1 · p. 2, §5.1 · p. 7

  • Takeaways & Limitations

    The paper concludes that synchronized diffusion can mitigate view-specific structural-bias conflicts while supporting efficient inference in large-scale scenarios.

    Source: §6 · p. 8

    A direct implementation of Eq. (13) has O(V^2N^2) computational and memory complexity because it stores a dense coefficient matrix and exhaustively interacts across the multi-view space.

    Source: §4.2 · p. 4

Abstract

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Multi-view learning seeks to learn more comprehensive representations by exploiting the complementarity and consistency across diverse modalities or views. However, existing multi-view fusion strategies treat intra- and inter-view fusion as independent stages, without simultaneously considering the evolution within views and the dependency across views. Such an asynchronous fusion paradigm inevitably constrains cross-view interactions due to conflicting view-specific structural inductive biases. As a result, information flow is prone to distortion and compression along intermediate pathways, confining the model to learn within a restricted solution space. To address this, we propose Synchronous Multi-view Neural Diffusion (SynMDiff), which conceptualizes the multi-view feature space as a unified dynamical system driven by a diffusion process. By modeling the diffusion flow across arbitrary dyadic feature interactions in a joint space, SynMDiff enables the concurrent and adaptive intra- and inter-view information fusion. While a direct implementation of this synchronized mechanism incurs prohibitive computational costs, we further introduce an energy-based topological sampling strategy and an Ego-Net style centralized training architecture, ensuring both efficiency and scalability during learning and inference. Due to its conceptual elegance and computational efficacy, evaluations on real-world datasets demonstrate that SynMDiff outperforms the baselines by a large margin.

1 Introduction

Existing multi-view fusion commonly separates within-view encoding from cross-view fusion, leaving arbitrary cross-view interactions implicit. SynMDiff proposes joint diffusion-based fusion, with sampling and centralized training to address its computational cost.

1 Introduction

  • Existing methods commonly use independent view encoders followed by post-hoc fusion, separating intra-view and inter-view fusion into two stages.Conflicting view-specific structural biases can constrain cross-view information flow, which may be distorted or compressed along intermediate pathways.Source: §1 · p. 1
  • SynMDiff models arbitrary pairwise feature interactions as adaptive diffusion flows in a unified multi-view space, enabling concurrent intra-view and inter-view fusion.The formulation is described as allowing information to propagate directly across views without view-specific intermediate representations or predefined pathways.Source: §1 · p. 2
  • An energy-based topological sampling mechanism prunes redundant interactions, while an Ego-Net-style centralized architecture supports efficient training and inference at large scale.These components address the prohibitive computational overhead of directly implementing synchronous diffusion.Source: §1 · p. 2
  • Extensive experiments on real-world datasets across diverse multi-view scenarios demonstrate the effectiveness of the proposed method.The introduction does not give a numerical comparison in the supplied passages.Source: §1 · p. 2

2 Related Work

Prior multi-view methods span weighting, shared-subspace, graph-based, and attention approaches, while diffusion research has explored continuous dynamics and graph propagation. The paper positions its contribution as a synchronized diffusion formulation for joint multi-view feature evolution.

2.1 Multi-view Learning

  • Multi-view approaches include weighting, shared-subspace, graph-based, and multi-stage methods, but the cited approaches neglect dynamic cross-view interactions.Recent global-attention methods still follow asynchronous two-stage fusion and remain influenced by view-specific structural biases.Source: §2.1 · p. 2

2.2 Neural Diffusion Models

  • Prior diffusion-based learning commonly uses PDE-governed continuous processes or graph-based information propagation.The cited literature also includes frameworks that adopt a diffusive perspective on representation learning.Source: §2.2 · p. 2
  • This work introduces neural diffusion flows for heterogeneous cross-view interactions and synchronizes intra-view and inter-view feature fusion in a unified dynamical system.The authors describe this as the first formulation of multi-view feature space as a unified dynamical system capturing both interaction types synchronously.Source: §2.2 · p. 2

3 Preliminary

The preliminary section presents diffusion as movement from higher to lower concentration and develops a discrete feature-space formulation. It then introduces forward Euler iteration and states a convergence guarantee for its specified step range.

3 Preliminary

  • Diffusion is introduced as mass moving from regions of higher to lower concentration, with temperature represented by a time-varying scalar function over a system.The system is typically assumed to be a Riemannian manifold.Source: §3 · pp. 2–3
  • In a discrete data space, feature discrepancies between instances are treated as temperature variations, providing a relational inductive bias for exploiting information across instances.The text gives a discrete reformulation after introducing the heat-diffusion process.Source: §3 · p. 3
  • The explicit forward Euler scheme is presented as a numerical iteration for solving the discrete diffusion equation, and the text states convergence for any τ in (0, 1).The supplied passage attributes this convergence guarantee to [46].Source: §3 · p. 3

4 Method

SynMDiff treats multi-view features as a unified dynamical system, jointly modeling interactions across views and instances. It uses topology sampling and virtual anchors to make this coupled diffusion more efficient and scalable.

4.1 Rethinking the Decoupled Paradigm in Multi-view Fusion

  • View-decoupled fusion stages intra-view propagation before cross-view alignment, leaving interactions implicit and exposing them to conflicting view-specific inductive biases.The paper contrasts this with Global Coupled Fusion, which directly models cross-view interactions.Source: §4.1 · p. 3

4.2 Synchronous Multi-view Neural Diffusion

  • Synchronous diffusion assigns dual-coupling weights across views and instances, enabling concurrent intra- and inter-view propagation across the joint space.The paper characterizes asynchronous diffusion as a restricted case of synchronous diffusion.Source: §4.2 · p. 4

4.3 Energy-based Topological Sampling

  • O(N^2V^2) to O(E) space: similarity-based truncation retains informative edges, and under incoherence mismatch probability decays exponentially as feature dimension D increases.The method interprets diffusion as minimizing Dirichlet energy; truncation removes non-essential edges from the complete graph.Source: §4.3 · pp. 4–5

4.4 Efficient Training with Ego-Net Style Architecture

  • Linear time in N is achieved by routing cross-view instance features through virtual anchors in an Ego-Net style centralized architecture.The anchors aggregate and relay information across views, replacing time-consuming cross-view traversal interactions with centralized connectivity.Source: §4.4 · p. 5

5 Empirical Studies

SynMDiff is evaluated across multi-omics cancer subtyping, heterogeneous-graph node classification, general multi-view classification, and large-scale datasets. The reported results favor SynMDiff across these settings, while visualizations and ablations examine its representations and components.

5 Empirical Studies

  • The experiments cover cancer subtyping, heterogeneous-graph node classification, general multi-view classification, and large-scale scalability, with results averaged over five random seeds.The evaluation includes five cancer cohorts, five heterogeneous-graph benchmarks, eight general multi-view datasets, and four scalability datasets.Source: §5 · p. 5

5.1 Performance

  • SynMDiff outperforms baselines on both Macro-F1 and Micro-F1 for BRCA, UCEC, GBMLGG, and TCGA, and is second-best on LGG.The cancer-subtyping results use 10% of labeled samples for training.Source: §5.1 · p. 6, Table 1 · p. 6
  • SynMDiff outperforms baselines on both reported metrics for FreeBase, DBLP, Yelp, and AMiner, and has the best Macro-F1 on IMDB.The node-classification evaluation uses 20% of labeled nodes for training.Source: §5.1 · p. 6, Table 2 · p. 6
  • SynMDiff outperforms multi-view fusion baselines across all evaluated datasets, with clear gains on multimodal YouTube, IAPR, and ESPGame.The evaluation uses 10% of labeled data for training and 10% for validation.Source: §5.1 · p. 6, Table 3 · p. 7
  • SynMDiff remains scalable and achieves the best performance across four large-scale datasets with lower inference latency and memory consumption.The comparison also reports classification results, inference time, and memory usage.Source: §5.1 · p. 7, Table 4 · p. 7

5.2 Visualization

  • SynMDiff embeddings form more compact clusters, show clearer class separation, and score highest on homogeneity and completeness across the three visualized datasets.The advantage is more pronounced on TCGA; Figure 2 shows DBLP, TCGA, and HW.Source: §5.2 · p. 7, Figure 2 · p. 8

5.3 Ablation Study

  • All three ablations underperform SynMDiff across six datasets; inter-view propagation appears more important than intra-view aggregation on most datasets.Removing sampling and centralized training causes a substantial performance drop, which the authors attribute to semantically irrelevant dense connections propagating noise.Source: §5.3 · p. 8, Figure 3 · p. 8

6 Discussion and Conclusion

SynMDiff models pairwise feature interactions as diffusion flows in a joint multi-view space, while energy-based sampling and virtual-anchor centralized training reduce computational overhead. The authors identify more efficient pruning and possible information compression from centralized training as remaining concerns.

6 Discussion and Conclusion

  • SynMDiff jointly models intra- and inter-view propagation as diffusion flows and uses energy-based sampling and virtual anchors to reduce computational overhead.The centralized architecture supports efficient inference in large-scale scenarios.Source: §6 · p. 8
  • More efficient pruning remains a practical deployment challenge, and centralized training may introduce information compression.Source: §6 · p. 8

A.1 Proof of Proposition 1

The proposition characterizes asynchronous multi-view diffusion as view-decoupled fusion: cross-view dependencies arise only indirectly through a two-stage update.

A.1 Proof of Proposition 1

  • Asynchronous diffusion cannot jointly model cross-view and cross-instance dependencies in one update; it instead propagates within views before point-wise cross-view aggregation.The proposition identifies this two-stage structure as View-Decoupled Fusion.Source: §A.1 · p. 11

A.2 Proof of Proposition 2

The proposition characterizes synchronous multi-view diffusion as globally coupled: a single update includes both inter-view dependencies and cross-instance coupling.

A.2 Proof of Proposition 2

  • Synchronous diffusion updates each instance-view representation using features from other views and aggregates over all instance-view pairs in one step.The proposition identifies these properties as View-Joint Evolution and Cross-instance View Interaction, together constituting Global Coupled Fusion.Source: §A.2 · p. 11

A.3 Proof of Corollary 1

The proof characterizes asynchronous diffusion as a restricted synchronous formulation, then states a support-recovery guarantee and compares the two formulations’ computational complexity.

A.3 Proof of Corollary 1

  • Asynchronous diffusion is recovered from synchronous diffusion by restricting cross-view interactions to co-indexed instances and removing cross-instance interactions across views.These two structural restrictions make the asynchronous formulation a restricted case of the synchronous one.Source: §A.3 · p. 12

A.4 Proof of Theorem 1

  • Under an incoherence condition, Theorem 1 bounds the probability that the truncated adjacency differs structurally from the oracle adjacency.The supplied theorem statement does not specify the bound’s expression.Source: §A.4 · p. 12

B.1 Complexity of Asynchronous Multi-view Diffusion

  • With N≫D≫V, asynchronous diffusion has dominant time complexity O(N^2VD) and space complexity O(VN^2).The analysis gives these dominant terms under the stated practical regime.Source: §B.1 · p. 13

B.2 Complexity of Synchronous Multi-view Diffusion

  • With N≫D≫V, synchronous diffusion has dominant time complexity O(V^2N^2D) and space complexity O(V^2N^2).The synchronous update traverses source pairs across the entire multi-view space.Source: §B.2 · p. 13

B.3 Complexity Reduction via Topological Sampling and Ego-Net Architecture

Topological sampling sparsifies the joint topology, while a virtual-anchor architecture supports centralized diffusion; together, they reduce synchronous diffusion to linear-time propagation with sparse topology storage.

B.3 Complexity Reduction via Topological Sampling and Ego-Net Architecture

  • Topological sampling replaces exhaustive traversal of V^2N^2 target-source pairs with diffusion over retained edges in a sparse graph.Each retained edge still requires a D-dimensional message-passing operation.Source: §B.3 · p. 13
  • With bounded average retained degree, E=O(N), and the combined sampling and Ego-Net design reduces synchronous diffusion to linear-time propagation with sparse topology storage.The conclusion states this reduction under the practical sparse regime.Source: §B.3 · p. 14

C Algorithm

  • Algorithm 1 provides the complete procedure for realizing SynMDiff from the main-text formulation.Source: C Algorithm · p. 14

D.1 Dataset Description

The experiments cover multi-omics cancer subtyping, heterogeneous graph node classification, and general multi-view classification, with described datasets, baselines, and a shared implementation configuration.

D.1 Dataset Description

  • Five cancer cohorts—BRCA, LGG, UCEC, GBMLGG, and TCGA—cover multiple omics profiles and subtype or grade classification tasks.The cohorts range from 430 to 9,664 samples after filtering, as described for the individual datasets.Source: §D.1 · p. 14
  • Heterogeneous graph benchmarks include Freebase, DBLP, IMDB, Yelp, and AMiner, with dataset-specific node types and meta-path sets.The descriptions specify graph attributes and meta-paths for several benchmarks.Source: §D.1 · pp. 14–15
  • General multi-view classification uses datasets spanning handwritten digits, images, video, faces, and noisy digit views, with differing feature types and dimensions.The described collection includes Scene15, YouTube, MITIndoor, HW, IAPR, Caltech, Animals, Espgame, VGGFace, CIFAR-10, NoisyMNIST, and YTF.Source: §D.1 · p. 15

D.2 Compared Methods

  • Comparisons use task-specific baselines, including cancer classifiers and multi-omics models, heterogeneous-graph algorithms, and multi-view classification methods.The listed methods include conventional classifiers, graph models, and multi-view fusion approaches.Source: §D.2 · pp. 15–16

D.3 Implementation and Training Details

  • SynMDiff uses kNN truncation, Adam with cross-entropy, a single-layer shared configuration, and five random-seed runs for reported results.The configuration aligns views to 512 dimensions, then uses four attention heads of dimension 128 and an FFN of hidden dimension 256.Source: §D.3 · p. 16

D.4 Additional Ablation Analysis

The section reports component ablations and neighborhood-size sensitivity, illustrates how synchronous fusion handles a missing cross-view relation, and distinguishes SynMDiff’s joint formulation and scope from prior work.

D.4 Additional Ablation Analysis

  • Removing kNN sampling causes the largest performance drop and increases time and memory costs by approximately 6.69× and 56.0×, respectively.The asynchronous variant decreases ACC by 0.94 percentage points and uses approximately 6.78× more time and 53.1× more memory than SynMDiff; removing the virtual anchor decreases ACC by 0.62 points and increases time by approximately 25.4%.Source: Table 9 · p. 17, §D.4 · p. 17

D.5 Sensitivity to the Neighborhood Size

  • 97.25% ACC at k=15 is the highest reported result; k=10 is comparable with slightly lower execution time.As k increases from 5 to 30, execution time rises from 25.76 ms to 30.09 ms while memory stays within 99.52–100.73 MB.Source: Table 10 · p. 17, §D.5 · p. 17

E Further Illustration of Synchronous Fusion

F Relation to Prior Work and Scope

  • SynMDiff models intra-view, inter-view, cross-instance, and cross-view interactions in one diffusion process, unlike the sequential view-specific fusion described for ECMGD.The paper frames its scope as multi-view fusion formulation rather than a new attention mechanism or graph neural-network backbone.Source: F Relation to Prior Work and Scope · p. 18
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