Graph Diffusion

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6 papers in the last four weeks, up 100% on the four weeks before. 0.1% of all new papers.

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Latest papers 52

Oct 1, 2026cs.LG

Graph Representation via Elements of Discrete Morse and Cobordism Theories

Topology is, by its nature and design, suited to structure that is nonlinear, multiscale, and nonstationary - however, within machine learning, its use remains largely confined to topological data analysis. We advocate that tools from low-dimensional topology which have remained almost exclusively contained within the domain of pure mathematics (such as Morse theory) offer a strong, complementary, and yet virtually unexplored perspective on the hidden structure of data-generating processes and learning tasks built upon them. Here we introduce concepts from cobordism theory and harness tools from discrete Morse theory to improve the performance of graph diffusion models through our pipeline MG-Diff. Further, we derive theoretical guarantees and sufficient conditions so that under a positive decision-gap, the Morse-theoretic tools and their application for induced diffusion guidance are stable under small perturbations. Finally, we illustrate the utility of discrete Morse theory in application to graph diffusion models for spatio-temporal graph forecasting and graph regeneration, and argue that these applications are only a small window into the part of what low-dimensional topology can offer to the field of machine learning.

Jennifer Rozenblit, Chenguang Yang, Yuxin Liu +2

Department of Mathematics; University of Texas, Austin · Department of Statistics; University of California, Riverside · Department of Statistics; Virginia Tech

Diffusion Model Guidance Topological Representation Learning Graph Diffusion

Oct 1, 2026cs.AI

Network World Models as Environments for Algorithm Design on Complex Systems

World models, which simulate an environment and predict how it changes under actions, are increasingly used in real-world applications such as robotics. Complex systems call for the same tool because the effect of an action is not immediate. Seeding nodes for a campaign, or immunizing nodes against an epidemic, changes little on its own; what matters is the outcome that unfolds over the steps that follow. Designing an algorithm that selects such actions to maximize expected performance on a task is inherently iterative, and every candidate must be scored by the outcome it produces. Obtaining that outcome has relied on simulation, whose cost becomes a bottleneck when candidates are evaluated over many sampled trajectories. We propose an action-conditioned Network World Model that learns a network's diffusion dynamics under interventions over time, applies each action to the network, and predicts the outcome that follows. It serves as a fast evaluator inside an algorithm design loop in which a coding agent designs and refines executable algorithms using feedback from full rollouts, action-level credit, and counterfactual probes over alternative interventions. Across eight network tasks and five diffusion models, the designed algorithms match or exceed the strongest reported baseline in 138 of 141 settings while enabling up to 14.5 times faster rollouts than Monte Carlo simulation. Code will be released upon acceptance.

Rishab Alagharu, Hongji Pu, Zeeshan Memon +3

Emory University · University of Illinois Urbana-Champaign

Automated Algorithm Discovery World Model-Based Planning Action-Conditioned World Models Graph Diffusion

Sep 30, 2026cs.LG

Graph Residual Conjugate Diffusion: SNR-Equalized Heat Flow for Graph Signals

Diffusion models generate data by reversing a forward corruption process that typically approaches a simple Gaussian prior. Recent work has extended this framework to signals supported on fixed graphs, e.g., road-network traffic and sensor-network measurements. Many graph signals have nonuniform spectral energy, whereas isotropic corruption adds the same conditional noise variance to every graph-frequency mode. Driving all modes to near-zero terminal signal-to-noise ratio (SNR) requires strong corruption, which increases the noise range that must be covered under a fixed sampling budget. We introduce Graph Residual Conjugate Diffusion (GRCD), which replaces the shared clock of graph heat diffusion with a mode-dependent clock that gives every graph-Fourier mode the same conditional SNR. GRCD fits a zero-mean graph-spectral Gaussian reference on the training split and stops at a finite terminal SNR at which the propagated reference still carries the fitted spectral variances. The Gaussian component has an exact modewise propagator in the probability-flow ODE, so sampling advances it analytically and integrates only the learned residual score numerically. We evaluate GRCD on five settings (METR-LA traffic, Molene weather, and three stochastic block models) against seven comparators under a matched protocol: Graph-Aware Diffusion (GAD), EDM (graph backbone), two adaptations of Whitened Score Diffusion (WSD), and three preconditioning controls. At four function evaluations (NFEs), GRCD lowers averaged maximum mean discrepancy (aMMD) by 22 to 36 times over the best comparator on all five settings, reaching 0.054 on METR-LA, where it clears an aMMD 0.1 target with 87% less sampling wall-clock time than the cheapest comparator that reaches it. Fitting the terminal reference reduces aMMD by 2.7 to 7.3 times at finite terminal SNR, while the factors shrink to 1.00 to 1.01 near zero.

Jinwei Li, Daniel Tenbrinck

Department of Data Science Friedrich-Alexander-Universität Erlangen-Nürnberg Erlangen, Germany

Graph Signal Processing Diffusion Model Inference Acceleration Graph Diffusion

Sep 28, 2026cs.LG

Propagate, Then Sharpen: Post-Hoc Refinement of Frozen Node Classifiers

We study post-hoc refinement of frozen node classifiers: given only the graph

G

and class distributions

Q

predicted by a frozen model, can we improve accuracy without access to node features, model parameters, or gradients? APPNP answers this by propagating logits with a restart towards the initial predictions, minimizing the anchored Dirichlet energy. Instead, we consider the Potts energy, and decompose it into a Dirichlet term, which penalizes disagreement between neighbouring nodes, and a Gini term, which penalizes indecision within each node. This decomposition motivates Propagate, Then Sharpen (PtS), which alternates between propagation of class probabilities and node-wise, mass-preserving sharpening, with only one additional hyperparameter selected using labelled validation nodes. Across nine homophilic graphs, with a frozen MLP backbone, PtS improves mean test accuracy over independently tuned APPNP by

1.71

percentage points on clean inputs and

3.90

under severe Gaussian feature corruption. Gains over APPNP become smaller, but remain positive with frozen GCN and GraphSAGE backbones. Sharpening also removes most of the accuracy loss of deep propagation: on clean inputs without restart, accuracy falls by

2.2

points between

2

and

100

propagation steps under PtS, compared with

33.8

for APPNP.

Preben Johnsen Bentdal, Nello Blaser, Xue-Cheng Tai

Department of Informatics, University of Bergen · Norwegian Research Centre (NORCE)

Graph-Based Semi-Supervised Learning Classification Node Classification Graph Diffusion

Sep 24, 2026cs.LG

From Graphs to Feeders: Constraint-Guided Diffusion for Rule-Compliant Feeder Generation

Generative modeling approaches often focus on recovering broad statistical characteristics from the training data. In the context of graph generation, this may refer to degree distributions, clustering coefficients, or spectral properties. However, generating usable distribution feeders when detailed feeder models are unavailable requires more than matching generic graph statistics: the sampled topology must also obey electrical compatibility and radiality rules. We therefore formulate feeder synthesis as a constraint-guided graph generation problem and propose the Power-Grid-constrained Discrete Denoising Diffusion model, PG-DiGress, which learns categorical node and edge patterns from feeder data, while respecting domain-specific rules. Specifically, it injects feeder constraints into the reverse diffusion process through soft masks that suppress incompatible edge classes during denoising, followed by a final projection step that rebuilds a connected, rule-compliant feeder graph. We evaluate PG-DiGress using graph-distribution similarity, feeder-rule satisfaction, structural validity, and downstream model construction. Compared with the unconstrained baseline, PG-DiGress increases the strict feeder pass rate from 13.7% to 96.8%. We also successfully convert the generated graphs into executable feeder models for downstream analysis.

Yu Qin, Andrew Glaws, Aadil Latif +1

National Laboratory of the Rockies, Golden, Colorado, USA

Constrained Generative Modeling Diffusion Models Graph Diffusion Power Systems

Sep 14, 2026cs.LG

ProtoGuide: Prototype-Driven Guidance for Class-Conditional Graph Generation

Discrete diffusion models are a prominent family for graph generation, but standard class-conditional mechanisms embed the class signal in the denoiser during training, tying the conditioning mechanism to the trained model. Classifier guidance avoids this coupling in continuous domains by steering a frozen model with a classifier's gradient, but discrete graph diffusion samples discrete edge states, so gradients cannot propagate through the sampled graph. We introduce ProtoGuide, a post-hoc, backbone-agnostic framework that recovers an analogous mechanism. At each reverse step the denoiser's per-edge output is relaxed into a differentiable soft adjacency, embedded by a frozen Siamese graph neural network, and scored against a target-class prototype and its nearest competitor; the resulting per-edge gradient, damped by a cosine schedule, is injected back into the denoiser output. All components stay frozen, so guidance is retargeted by supplying a different prototype. On five classes of real-world networks and two architecturally different backbones, EDGE and DiGress, ProtoGuide raises macro classification accuracy from 50.7% to 73.5% and from 73.6% to 83.8%, and outperforms DiGress's built-in conditional training under our configuration. Gains are largest where the unguided models are weakest, and are not uniform across classes. Per-graph coverage remains high in most settings, while distributional effects are class-dependent. A Best-of-N selection baseline matches this accuracy given enough oversampling, but at a substantial cost in graph diversity. An independently initialized classifier, a directionality test, and a few-shot analysis support target-directed steering and robustness to very small support sets.

Salvatore Romano, Marco Grassia, Pietro Liò +1

Department of Electrical, Electronic and Computer Engineering, University of Catania, Italy · Department of Computer Science and Technology, University of Cambridge, UK · University Campus Bio-Medico of Rome, Italy

Graph Generation Diffusion Guidance Graph Diffusion

Aug 28, 2026cs.RO

Generation of High-Level Concepts in 3D Scene Graphs via Autoregressive Diffusion

Indoor 3D Scene Graphs (3DSGs) represent environments as multi-layer hierarchies that connect observed geometric primitives (e.g., planes) to higher-level metric-semantic concepts (e.g., rooms, floors, buildings), enabling incremental spatial reasoning for robotic perception and SLAM. However, classical high-level concept generation approaches rely on hand-crafted rules for specific concept classes, while learning-based methods require separate models for graph structure and spatial node features (e.g., centroids), which limits scalability to novel classes and more complex hierarchies. We propose a unified autoregressive diffusion-based graph generative model that jointly learns structure and features, constructing complete 3DSGs bottom-up from observed vertical planes across arbitrary hierarchy depths. Our method consistently surpasses all learning-based and random baselines across 3DSG datasets spanning synthetic scenes, real architectural floor plans, and robotic sensor data, with varying layout complexity and hierarchy depth, and surpasses a one-shot model with oracle access to the target graph size on the largest hierarchy and on real single-floor data. Finally, we propose an adaptation of the Fused Gromov--Wasserstein distance for principled graph-level evaluation of generated 3DSGs against ground truth.

Jose Andres Millan-Romera, Samuel Cognolato, Holger Voos +2

Automation and Robotics Research Group, SnT University of Luxembourg, Luxembourg · University of Padova, Padova, Italy · Fondazione Bruno Kessler, Trento, Italy +1

3D SGG Autoregressive Generation Graph Diffusion

Aug 12, 2026cs.LG

Faithful, Sufficient and Understandable: Rethinking Graph Counterfactual Explanations via Discrete Diffusion Inversion

Graph Neural Networks (GNNs) achieve strong predictive performance on graph-structured data across domains such as chemistry, biology, and network analysis, yet they provide no intrinsic explanation of their predictions. This limits their adoption in high-stakes and safety-critical settings. Counterfactual explanations address this by revealing the minimal structural modifications that would change a model's prediction. On graphs, however, such a modification is hard to produce. The search space is discrete and combinatorial, and a valid answer must respect categorical node and edge types together with domain rules such as chemical valency in the case of molecular graphs. Existing explainers give up one of two things. Either edits are not held on the data manifold, or the search does not span the full edit space. We propose Graph Diffusion Counterfactual Explanation via Inversion (GDCE-I), which gives up neither. A discrete denoising diffusion model with a novel discrete inversion scheme enables distribution-aware edits leveraging the whole domain edit space. We further address the incomplete and inconsistent evaluation of graph counterfactuals by deriving a framework of explanation desiderata and applying it to every method under one shared protocol. Across four benchmarks, GDCE-I outperforms related work by a large margin on the defined framework. For the molecular domain, we further qualitatively show that GDCE-I attains interpretable in-distribution solutions.

David Bechtoldt, Sidney Bender

Machine Learning Group, TU Berlin, 10587 Berlin, Germany · BIFOLD–Berlin Institute for the Foundations of Learning and Data, Berlin, Germany

Counterfactual Evaluation Counterfactual Explanations GNN Explainability Graph Diffusion

Aug 12, 2026cs.CV

ProBAG: Prototype-Guided Boundary-Aware Graph Diffusion for Weakly Supervised Histopathology Segmentation

Weakly supervised semantic segmentation enables histopathology tissue segmentation from image-level annotations, avoiding costly pixel-level labeling by expert pathologists. However, CAM-based methods often localize only highly discriminative regions and remain unreliable near tissue interfaces. We propose ProBAG, a stage-1 pseudo-mask generator that combines dataset-specific visual prototypes with pathology-aligned CONCH text prototypes over multi-scale frozen UNI features. ProBAG introduces two complementary mechanisms: class-wise power recalibration that reshapes inter-class competition while preserving the total foreground activation mass at each pixel, and one-step graph diffusion in which feature affinities are penalized by a late-transformer attention-context discrepancy used as a soft structural boundary cue. The resulting stage-1 pseudo-masks require neither CRF nor an external segmentation model; for complete two-stage comparison, they additionally supervise a downstream Phikon-FPN segmenter. Experiments on BCSS-WSSS and LUAD-HistoSeg show consistent gains over recent WSSS approaches, while ablations indicate that pathology-aligned text semantics provide the largest improvement and graph refinement provides a smaller complementary gain. The code is available at: https://github.com/wterrr/WSSS

Duy-Dong Nguyen, Le-Van Thai, Hoai Nhan Pham +3

AI VIETNAM Lab, Vietnam · Department of Mechanical System Engineering, Jeonbuk National University, Republic of Korea · Washington University School of Medicine, Saint Louis, MO, USA +1

Histopathology Image Segmentation Weakly Supervised Semantic Segmentation Boundary-Aware Segmentation Semantic Segmentation Graph Diffusion

Jul 28, 2026cs.LG

HeAD-CP: Heterophily-Aware Diffused Conformal Prediction Sets for Graph Neural Networks

Conformal prediction (CP) provides distribution-free uncertainty quantification, and its extension to graphs is an active research direction. Diffused Adaptive Prediction Sets (DAPS) is a widely used graph-aware diffusion baseline, propagating Adaptive Prediction Sets (APS) non-conformity scores along edges with a uniform coefficient

λ

. We identify a fundamental shortcoming of this design: the uniform low-pass diffusion presupposes graph homophily and proves detrimental on heterophilic graphs, enlarging the mean prediction-set size by up to 10.6% relative to plain APS. To mitigate this, we propose HeAD-CP, a family of node-wise diffusion variants whose coefficients are determined by a label-free local-homophily estimate derived from the GNN softmax. Three variants, namely signed-

γ

, edge-compatibility, and a DAPS-baseline-with-correction, are most effective at extreme heterophily, intermediate heterophily, and moderate-to-high homophily, respectively, and all preserve the marginal coverage guarantee. On ten benchmarks, the HeAD-CP family stays at or below plain APS on every dataset, while DAPS exceeds APS on six. The post-hoc oracle over the family improves over DAPS on 8/10 datasets at

p<0.01

(paired Wilcoxon), with the largest gains on heterophilic graphs (10.3% on Texas); on the two homophilic datasets where DAPS still wins (CiteSeer, PubMed), it retains a marginal advantage of at most 0.002, statistically insignificant on CiteSeer (

p=0.23

). Designing a calibrated label-free selector that approaches this oracle is the main outstanding empirical question.

Phan Binh Nguyen Lam, Nguyen Thai Anh

Faculty of Information Technology, University of Science, Vietnam National University, Ho Chi Minh City, Vietnam · Faculty of Information Technology, Van Lang School of Technology, Van Lang University, Ho Chi Minh City, Vietnam

Graph Neural Networks Conformal Prediction Graph Heterophily Graph Diffusion

Jul 20, 2026cs.LG

MotifRole-Diff: Risk-Optimal Role-Aware Corruption for Masked Molecular Graph Diffusion

Masked discrete diffusion for molecular graph generation typically applies a uniform corruption schedule to all tokens in a lossless graph-to-sequence representation, implicitly treating structurally heterogeneous molecular components as equally difficult and equally important to reconstruct. However, different molecular graph token roles exhibit substantial variation in denoising difficulty and their influence on the decoded molecule, motivating role-specific corruption strategies. We introduce MotifRole-Diff, a role-aware corruption process that allocates masking rates according to empirically measured denoising difficulty and graph-level perturbation impact while preserving the model architecture, clean sequence space, and lossless molecular-graph decoder. We formulate schedule selection as the risk-optimal allocation of a fixed masking budget across token roles. Our theorem characterizes optimality for the modeled role-weighted residual risk, while downstream generation performance is evaluated empirically. Under matched architecture, training budget, and sampling compute, MotifRole-Diff improves validity on QM9 from 0.905 to 0.944 while reducing FCD from 1.701 to 1.609, and on MOSES improves validity from 0.920 to 0.938 while reducing FCD from 2.125 to 1.850. Role-wise diagnostics further show improved reconstruction across molecular graph token categories. Together, these matched-compute results indicate that structurally informed corruption is a more effective masking strategy than uniform schedules for serialized molecular graph diffusion.

Tasfia Nuzhat Ornee, Elias Hossain, Ivan Garibay +1

University of Central Florida

Masked Diffusion Models Molecular Graph Generation Molecular Generation Graph Diffusion

Jul 17, 2026cs.LG

From Diffusion to Reaction-Diffusion: A Dynamical-Systems View of Oversmoothing in Hypergraph Neural Networks

Higher-order couplings enhance the expressive power of hypergraph neural networks (HGNNs), but they also intensify representation collapse in deep propagation due to strong multi-way feature mixing. This work investigates hypergraph oversmoothing from a dynamical-systems perspective and develops a reaction--diffusion framework for depth-resistant hypergraph learning. By defining hypergraph gradient and divergence operators, we interpret message passing as an incidence-level diffusion process. The analysis of pure diffusion shows that its continuous semiflow exponentially contracts the null-mode-free component of node representations and drives the Dirichlet energy to zero, revealing hypergraph oversmoothing as an intrinsic transverse-energy dissipation phenomenon. Motivated by this analysis, we propose Hypergraph Neural Reaction--Diffusion (HNRD), which introduces a reaction mechanism acting on the transverse component to compensate diffusion-induced dissipation and stabilize discriminative variations. We establish global well-posedness of the proposed dynamics and prove that the null-mode-free Dirichlet energy remains bounded away from zero. A forward-Euler discretization provides a practical HNRD layer with a stability condition for deep propagation. Experiments on benchmark and synthetic heterophilic hypergraphs demonstrate that HNRD consistently improves over representative hypergraph baselines. Depth, robustness, and efficiency analyses further show that HNRD preserves stable performance and nonzero Dirichlet energy under deep propagation and perturbations. These results provide a principled dynamical framework for designing deep hypergraph architectures that maintain higher-order expressiveness without representation collapse.

Zhiheng Zhou, Mengyao Zhou, Yancheng Chen +3

School of Mathematics and Statistics, Shandong University, Weihai, Shandong 264209, China · Academy of Mathematics and Systems Science, Chinese Academy of Sciences and also with the University of Chinese Academy of Sciences, Beijing 100190, China

Hypergraph Neural Networks Hypergraph Learning Graph Diffusion

Jul 17, 2026cs.AI

MGDT: MLLM-Guided Diffusion Transformer with Relation-Adaptive Mixture-of-Experts for Multimodal Knowledge Graph Completion

Multimodal Knowledge Graph Completion (MKGC) requires inferring missing entities from structural, textual, and visual cues. Existing diffusion-based MKGC methods usually denoise directly on raw multimodal features. Such a design forces the denoiser to simultaneously perform relation-dependent cue selection, cross-modal semantic alignment, and structure-aware entity generation, which introduces noisy and semantically inconsistent conditions for diffusion and consequently leads to suboptimal completion performance. To address this limitation, we propose MGDT: MLLM-Guided Diffusion Transformer with Relation-Adaptive Mixture-of-Experts (MGDT), a novel MKGC framework built on an align-then-diffuse paradigm. MGDT first employs a Relation-Adaptive Semantic Routing Mixture-of-Experts (RASR-MoE) module to select relation-relevant multimodal semantic transformation paths and suppress irrelevant modality interference. MGDT then uses a frozen Multimodal Large Language Model (MLLM) as a semantic anchor to align the routed multimodal representations into a unified latent space and reduce cross-modal semantic heterogeneity. Finally, a Knowledge Graph Diffusion Transformer (KGDT) performs graph-conditioned denoising generation in the aligned space to produce the missing entity representation. Experiments on three benchmark datasets show that MGDT consistently outperforms strong baselines.

Xu Hou, Meiyu Liang, Wei Huang +6

Beijing University of Posts and Telecommunications · School of Computer Science, Beijing University of Posts and Telecommunications · Zhejiang University +3

Multimodal KGs KG Completion Graph Diffusion Multimodal Diffusion Models

Jul 16, 2026cs.CV

DAPGNet: Dynamic Adaptive Physics-Guided Graph Diffusion Network for Hyperspectral Image Classification

Hyperspectral image (HSI) classification requires reliable pixel-relation modeling under spectral variability, mixed pixels, and heterogeneous boundaries. Existing graph-based HSI classifiers usually construct graph topology from spatial proximity, superpixel connectivity, or learned feature affinity. However, the spectral physical prior carried by contiguous bands has limited influence on topology estimation and message propagation. This paper presents DAPGNet, a dynamic adaptive physics-guided graph diffusion network that injects a structure-constrained physical prior into relation-level graph learning. DAPGNet first encodes contiguous spectral responses into node-wise multiscale physical-prior representations. A two-stage graph constructor then combines spectral-spatial affinity, physical-prior consistency, and spatial distance to form a physical-prior-aware sparse topology. During graph diffusion, learned edge weights are transformed into additive attention biases, while a physical gate performs node-wise and feature-wise interpolation between graph-aggregated features and projected physical-prior features. Cross-scale fusion integrates node states from different diffusion depths, and the network is optimized with main classification, auxiliary supervision, and second-order spectral smoothness regularization. Experiments on Indian Pines, WHU-Hi-LongKou, Houston2013, and Houston2018 show that DAPGNet achieves the best OA, AA, and Kappa among representative CNN-, Transformer-, Mamba-, and graph-based baselines. It improves AA over the strongest competing method by 3.64 to 7.31 percentage points across the four datasets. Ablation and sensitivity analyses further support the complementary effects of physical-prior extraction, prior-aware topology construction, physics-gated propagation, and spectral smoothness regularization.

Pengkun Wang, Weijia Cao, Ning Wang +1

National Engineering Laboratory for Satellite Remote Sensing Applications, Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China · Aerospace Information Research Institute, Chinese Academy of Sciences, Beijing 100094, China · Guangzhou University, Guangzhou 510006, China

Graph Structure Learning Hyperspectral Imaging Physics-Informed ML Hyperspectral Image Classification Graph Diffusion

Jul 16, 2026math.ST

Measuring Spatial Clustering via Metropolis-Hastings Diffusion Distance

We propose a novel measure of the discrepancy between two probability distributions

f

and

g

on a graph - which we call the diffusion distance - that measures the rate of convergence of

f

to

g

under a graph-constrained Markov chain with stationary distribution

g

. As a default choice for this Markov chain, we use the Metropolis-Hastings transition matrix targeting

g

with proposals given by a random walk on the graph. Our primary case of interest is when the second distribution

g

is uniform, in which case the diffusion distance becomes a measure of spatial clustering in

f

. Used in this way, (Metropolis-Hastings) diffusion distance to uniformity extends Moran's

I

-type measures of spatial autocorrelation by incorporating global graph geometry rather than just local patterns. Indeed, Moran's

I

, the most well-known measure of spatial autocorrelation, can be viewed as a one-step heuristic for diffusion distance, so long as specific spatial weights are used. We establish theoretical bounds and a stability result for our measure, connecting it to graph spectra and optimal transport. We then turn our attention to outlining a statistical test for spatial clustering using diffusion distance. Under permutation null models, we derive high-probability bounds on diffusion distance underpinned by exact spectral formulas for convergence of distributions, enabling an efficient statistical test for spatial clustering on large datasets. We empirically compare diffusion distance to Moran's

I

both as a numerical measure and as a statistical test. We show that diffusion distance exhibits higher power on synthetic data using a stochastic block model. Empirical analysis of Black population distributions for 100 U.S. cities shows that diffusion distance detects subtle differences in urban segregation patterns that Moran's

I

does not.

Thomas Weighill, Chidinma Williams

Department of Mathematics and Statistics, University of North Carolina at Greensboro, Greensboro, NC 27402

Clustering Graph Diffusion Statistical Hypothesis Testing

Jul 8, 2026stat.ML

DiPhon: Diffusion on Graphons for Scalable Graph Generation

Diffusion models represent a leading paradigm for graph generation, with notable impact in domains such as molecular design. Yet, scaling these models to large graphs remains an open problem. We approach this question in the dense-graph setting through the lens of graphons, the size-agnostic limit objects of dense graph sequences, to study how structural graph statistics behave across node-size scales. This perspective leads to DiPhon, a diffusion framework for size-scalable graph generation. Specifically, we formulate a continuous diffusion process on the graphon space via a Jacobi stochastic differential equation (SDE), and propose DiPhon, a discretized graph-level process that mimics these dynamics on finite graphs. We further derive the corresponding reverse-time process, which requires access to the marginal score. For the Jacobi process, this score interestingly admits a tractable form, which we estimate from data via graph denoising and plug into the reverse process to generate graph samples. We prove that DiPhon matches exactly the first moment of the marginal distributions induced by the continuous graphon process, and approximates the second moment up to a closed-form discrepancy. Thus, DiPhon inherits key size-agnostic statistical properties of the graphon dynamics, providing a principled route toward scalable graph generation. Empirically, we demonstrate this scalability by training on small graphs and generating progressively larger graphs at inference time, without retraining, while preserving their core topological properties.

Sergio Rozada, Yiming Qin, Manuel Madeira +2

King Juan Carlos University · EPFL, Lausanne, Switzerland · University of Pennsylvania

Graph Generation Graph Diffusion

Jul 7, 2026cs.LG

Generative Diffusion Models of Stochastic Graph Signals

Sampling stochastic signals supported on a graph underlies many graph machine learning tasks, including recommender systems, forecasting in financial markets, and wireless network optimization. In these settings, the target signals are realizations of unknown conditional distributions. However, prevailing approaches rely mostly on intricate, application-tailored designs that often regress to a conditional mean instead of sampling from the conditional law. This paper unifies such problems as conditional graph signal generative modeling and tackles them with a single denoising diffusion framework. We learn a reverse diffusion process, parametrized by graph neural networks (GNNs), that draws graph signals conditioned directly on the graph topology and on node-feature side information. The reverse process is realized by a novel architecture, the U-Graph Neural Network (U-GNN), which generalizes the image-convolutional U-Net to graph-structured signals. The U-GNN performs multi-resolution encoder--decoder processing in which pooling and unpooling reduce to a learned node selection, expressed by nested selection matrices, and a zero-padded lifting of coarse signals back to the full node set. The graph convolutions are carried out on the original graph, with a stride that sets their hop reach, so the U-GNN bypasses explicit graph coarsening at every resolution. We demonstrate our method on two generative tasks: stock price forecasting and optimal wireless resource allocation, with extensive numerical results in both domains.

Yiğit Berkay Uslu, Samar Hadou, Sergio Rozada +2

Dept. of Electrical and Systems Eng., University of Pennsylvania, Philadelphia, PA 19104 USA · Department of Signal Processing and Communications, King Juan Carlos University, Madrid, Spain

Graph Neural Networks Financial Forecasting Conditional Diffusion Models Graph Diffusion

Jul 7, 2026cs.LG

Graph Convolutional Attention: A Spectral Perspective on Graph Denoising and Diffusion

Denoising graphs is a fundamental problem in graph learning and the core operation of graph diffusion models. Attention-based architectures like graph transformers have recently shown promise in denoising graphs. However, our principled understanding of attention-based graph denoising remains limited, making it unclear whether standard attention is the right mechanism for this task. Here we show that, under a denoising objective, linear attention is suboptimal and can only learn an average spectral denoising filter over the training distribution. This creates a fundamental limitation as graphs often vary spectrally across the distribution. To overcome this limitation, we introduce Spectral Attention, which directly utilizes the input graph spectrum and provably outperforms linear attention by a margin governed by the spectral diversity of the distribution. We then derive Graph Convolutional Attention (GCA), a practical and permutation-equivariant realization of this idea that implements spectral denoising through graph-filtered queries and keys. For stochastic block models, GCA provably matches the idealized Spectral Attention mechanism. We further show that the softmax operation, that follows the attention, provides additional denoising by approximately projecting noisy eigenvectors onto the clean eigenspace. Empirically, replacing linear attention with GCA consistently improves graph denoising and diffusion on synthetic and real datasets, with gains strongly correlated with spectral diversity. In DiGress, GCA matches standard graph-transformer performance without computing expensive structural features, and when combined with the recently proposed PEARL positional encodings, avoids explicit eigendecomposition computations resulting in faster inference without degrading quality. The code can be found here: github.com/shervinkhalafi/graph_conv_att

Shervin Khalafi, Igor Krawczuk, Sergio Rozada +3

University of Pennsylvania · King Juan Carlos University · Stanford University

Graph Attention Networks Graph Transformer Graph Diffusion

Jun 29, 2026cs.LG

Curvature-Guided Sheaf Diffusion for Unsupervised Community Detection on Heterophilic Graphs

Detecting communities in heterophilic graphs -- where connected nodes often belong to different classes -- is hard for unsupervised methods: classical modularity and spectral methods are feature agnostic, while deep graph-clustering methods rely on contrastive or generative machinery that is opaque. We propose Curvature-Guided Sheaf Diffusion (CGSD), a fully unsupervised community-detection algorithm that uses the discrete Forman--Ricci curvature of each edge as its single topological signal, propagated through every stage of an end-to-end pipeline. CGSD makes three concrete contributions: (i)~a curvature-gated sheaf-diffusion encoder that gates edge messages by

σ(κ_e)

and is trained from three label-free structural losses (modularity, anti-collapse, curvature-weighted reconstruction); (ii)~a curvature-aware spectral clusterer (CSpec) that re-weights the

k

-NN affinity of the embedding by

σ(ακ_{e^*})

before Ng--Jordan--Weiss; and (iii)~a unified label-free evaluation against nine truly-unsupervised baselines. On five heterophilic benchmarks (Cora, Cornell, Texas, Wisconsin, Chameleon), CGSD wins outright on Wisconsin and Chameleon and is competitive on the remaining three against nine unsupervised baselines. The gain over the strongest baseline is driven by the clusterer, not the encoder: on the same embedding, CSpec improves mean NMI from

0.091

with

K

-Means to

0.107

(

+15\%

, paired

t

-test

p=0.008

). The mechanism is interpretable: intra-community and inter-community curvature distributions are visibly separated. Code is open-sourced at https://github.com/woodywff/cgsd.

Feifan Wang

School of Artificial Intelligence Xiamen Institute of Technology No. 1251, Sunban South Road, Jimei District Xiamen, Fujian 361021, China

Graph Representation Learning Graph Clustering Graph Heterophily Graph Diffusion

Jun 28, 2026cs.LG

PCGD: Physics-Guided Conditional Graph Diffusion for TCAD Device Simulation

Technology computer-aided design (TCAD) semiconductor device simulation is fundamentally constrained by the high computational cost of iteratively solving coupled drift-diffusion equations. Existing ML surrogates either reduce internal physics to macroscopic scalar regressions, or rely on single-step mappings that lack the iterative refinement required to resolve stiff, coupled fields. To address this, we introduce PCGD, a Physics-Guided Conditional Graph Diffusion framework operating natively on unstructured TCAD meshes to predict coupled electrostatic and carrier density fields. PCGD employs a Condition-Aware MeshGraphNet denoiser that explicitly injects boundary conditions and device structure context via global cross-attention. By augmenting data-driven denoising with a physics-guided hybrid objective that integrates exponent-free quasi-Fermi gradient matching with noise-aware PDE residuals, PCGD progressively enforce physical constraints in the iterative diffusion trajectory. This strategy successfully bypasses the numerical instabilities typical of stiff drift-diffusion equations. Evaluated on a challenging mixed PN/MOS benchmark, PCGD significantly outperforms deterministic one-step regression (1.207% error) and local diffusion (1.585% error) baselines by achieving a sub-percent mean relative field error of 0.835%, while concurrently reducing maximum PDE residual errors by nearly three orders of magnitude compared to pure diffusion. It also transfers robustly to unseen SOI topologies (0.815% error) via LoRA adaptation, using 5.30

\times

less data and 14.34

\times

fewer parameters than full fine-tuning. Ultimately, PCGD bridges the computational efficiency of generative surrogates with the rigorous physical fidelity of traditional TCAD, unlocking highly scalable, field-level analysis for robust device engineering.

Yihan Zhang, Zhiteng Zhang, Kun Chen +1

PDE Surrogate Modeling Physics-Informed ML Conditional Diffusion Models Physics-Based Simulation Graph Diffusion

Jun 27, 2026stat.ML

Connectivity Estimation using Stochastic Graph Heat Modelling

A growing number of techniques leverage the spatial structures that underlie many real-world datasets. Despite these advances, the complementary task of estimating spatial structures and understanding their role within these techniques has often been overlooked. In neurophysiological data analysis specifically, numerous methods exist to estimate brain connectivity, but most are not explicitly model-based, dynamic, multivariate, or directed. To address these limitations, we previously introduced noise-driven heat modelling on graphs for neurophysiological connectivity estimation. In this study, we extend this framework by relaxing earlier noise assumptions and adding regularisation to improve robustness. We also develop a simulation procedure to characterise and evaluate our technique in a controlled setting. Finally, we demonstrate that the technique is able to capture meaningful spatial structure across two experiments, each using two real-world datasets. The explicit model formulation of our connectivity estimator has the potential to improve the interpretability of graph-based techniques across a wide range of applications. The code implementing our method is available at https://github.com/sgoerttler/Heat_Connectivity.

Stephan Goerttler, Min Wu, Fei He

Centre for Computational Science and Mathematical Modelling, Coventry University, Coventry CV1 5FB, UK · Institute for Infocomm Research, A*STAR, Singapore

Graph Structure Learning Neuroimaging Graph Diffusion Brain Network Analysis

Jun 17, 2026cs.LG

AGDN: Learning to Solve Traveling Salesman Problem with Anisotropic Graph Diffusion Network

The Traveling Salesman Problem (TSP) is a cornerstone of combinatorial optimization and arises in many practical scenarios. Although graph-based learning approaches have been explored for TSP, the question of how to exploit graph structure more effectively remains open. We present the Anisotropic Graph Diffusion Network (AGDN), a new Graph Neural Network framework designed to solve TSP. Our method tackles two central difficulties: (1) the lack of informative topological prior in fully connected TSP graphs, and (2) losing connected nodes in the optimal solution after the commonly used graph sparsification techniques. To overcome these issues, we construct a MixScore transition matrix that merges node similarity with pairwise distance, and we develop an anisotropic graph diffusion strategy that supports efficient information exchange across multiple hops. Comprehensive experiments spanning diverse instance sizes and node distributions show that AGDN consistently outperforms existing methods while keeping computation time competitive. Furthermore, AGDN generalizes well to problem sizes and distributions beyond those seen during training. The implementation is publicly available at: https://github.com/LabRAI/AGDN.

Bolin Shen, Ziwei Huang, Zhiguang Cao +1

Florida State University · Tallahassee, United States · Singapore Management University +1

Traveling Salesperson Problem Graph Neural Networks Combinatorial Optimization Neural Combinatorial Optimization Graph Diffusion

Jun 16, 2026cs.LG

Enhanced Graph Neural Networks using K-Hop Gaussian Diffusion

Most graph neural network (GNN) cores rely on graph convolutions, typically implemented as message passing between direct (single-hop) neighbors. In many real-world graphs, edges can be noisy or poorly defined, limiting information propagation to local neighborhoods. Existing diffusion kernels, such as Personalized PageRank (PPR) and Heat Kernel, alleviate this issue through global propagation, but still struggle with complex local structures and distant node noise. To address these limitations, we propose a K-Hop Gaussian (KHG) diffusion kernel as a preprocessing module for graph data. KHG introduces multi-hop diffusion with Gaussian weighting for remote nodes, balancing local and global information propagation before applying standard GNNs. Experiments on multiple benchmark datasets demonstrate that KHG significantly outperforms traditional message-passing GNNs, as well as PPR and Heat Kernel diffusion, particularly in noisy or structurally complex graphs.

Xuling Zhang, Peng Wang, Daiyan Li +3

Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China · Southern University of Science and Technology, Shenzhen, China

Graph Neural Networks Graph Diffusion

Jun 16, 2026stat.ML

Geometrical fairness in graph neural networks

Graph-based learning methods have become increasingly prominent due to their strong performance across diverse applications. Among these, recent frameworks grounded in diffusion processes provide a unifying perspective that extends traditional graph neural network formulations while addressing limitations of standard message-passing mechanisms. Despite these advances, concerns remain regarding the fairness of such models, as they may propagate or amplify biases present in the data. In this work, we introduce a fairness-aware adaptation of graph-based diffusion by modifying the underlying Laplacian operator. Our approach incorporates multiple complementary transformations, including subspace projections, spectral adjustments, and frequency-based filtering, to mitigate bias-related components. Leveraging the intrinsic smoothing properties of graph diffusion, we provide a principled analysis of the resulting behavior and establish theoretical insights into fairness properties. We evaluate the proposed framework on both synthetic and real-world datasets, demonstrating that it achieves competitive performance while improving fairness metrics with limited additional computational cost.

Arturo Pérez-Peralta, Sandra Benítez-Peña, Blas Kolic +1

Department of Statistics, University Carlos III of Madrid, Spain · uc3m-Santander Big Data Institute

Graph Neural Networks Graph Representation Learning Algorithmic Fairness Spectral Methods Graph Diffusion

Jun 12, 2026cs.LG

Graph Diffusion Residuals for Control-Function Instrumental Variables

Control-function instrumental variable estimators need a first-stage residual, not merely a first-stage prediction. High-capacity first stages can interpolate treatment and leave too little residual information for the outcome equation. We study Adaptive Anisotropic Instrumental Heat Flow (A-IHF), a deterministic graph-diffusion residual extractor for flexible control functions. A-IHF treats treatment as a signal on a graph of first-stage features, uses pilot diffusion to detect large treatment jumps, attenuates conductance across those jumps, and computes the generated control with a sparse graph resolvent. Its observational selection rule uses only

(Z,X)

, combining graph generalized cross-validation, roughness, residualized-treatment relevance, and graph-admissibility filtering. The analysis decomposes error into structural leakage, residual attenuation, and residualized treatment variation, yielding finite-sample bounds, graph-admissibility rates under latent piecewise-smooth geometry, and finite-path selection calibration. Across 54 synthetic benchmark cells with tuned graph, kernel, tree, boosting, series, and neural control-function baselines, guarded observational A-IHF has the lowest average structural-response MSE; the A-IHF family beats the best non-A-IHF baseline in 32 cells. Performance is strongest when the graph captures piecewise-smooth first-stage structure.

Rui Wu, Zongyuan Chen, Hong Xie +2

School of Computer Science and Engineering University of Science and Technology of China

Causal Effect Estimation Instrumental Variable Estimation Causal Inference Graph Diffusion

Jun 10, 2026cs.LG

Net-Ev $^2$ : A Generative Simulator for Network Event Evolution

Reducing real-world trial and error has long been a central goal of decision making, and generative simulators advance this goal by modeling the evolution of future states. An even more challenging yet meaningful task is simulating how disturbance events (e.g., accidents) propagate their impacts across real-world networks. The existing approaches fall short of modeling both structured attributes and unstructured semantics of events, and capturing topological structures in simulating network event evolution. Therefore, we are motivated to propose Net-Ev

^2

(

\underline{\textbf{Net}}

work

\underline{\textbf{Ev}}

ent

\underline{\textbf{Ev}}

olution), a novel generative simulator that jointly leverages event cues while preserving network topology in simulations. Specifically, the framework consists of two stages, namely structure-guided masked pre-training and topology-aware diffusion process, which is achieved by U-Net-like graph downsampling and upsampling during denoising. At inference time, Net-Ev

^2

can generate simulations using natural-language event input only, with greater flexibility for practical usage. Furthermore, we introduce Net-Ev

^2

-6.5M, a multimodal benchmark of aligned event and network traffic data across four large-scale road networks, as well as a new topology-aware metric, namely JL-MMD, to evaluate topological fidelity in generated network dynamics. Extensive experiments demonstrate the state-of-the-art performance and strong generalization ability of Net-Ev

^2

. Code is made available at https://github.com/Guangyu4/Net-Ev-2.

Guangyu Wang, Zhaonan Wang

NYU Shanghai Shanghai, China · NYU Shanghai Center for Data Science Shanghai Key Laboratory of Urban Design and Urban Science

Intelligent Transportation Systems Synthetic Benchmark Generation Conditional Generative Modeling Graph Diffusion

Jun 2, 2026cs.LG

Multi-Modal Graph Neural Network with Transformer-Guided Adaptive Diffusion for Preclinical Alzheimer Classification

The graphical representation of the brain offers critical insights into diagnosing and prognosing neurodegenerative disease via relationships between regions of interest (ROIs). Despite recent emergence of various Graph Neural Networks (GNNs) to effectively capture the relational information, there remain inherent limitations in interpreting the brain networks. Specifically, convolutional approaches ineffectively aggregate information from distant neighborhoods, while attention-based methods exhibit deficiencies in capturing node-centric information, particularly in retaining critical characteristics from pivotal nodes. These shortcomings reveal challenges for identifying disease-specific variation from diverse features from different modalities. In this regard, we propose an integrated framework guiding diffusion process at each node by a downstream transformer where both short- and long-range properties of graphs are aggregated via diffusion-kernel and multi-head attention respectively. We demonstrate the superiority of our model by improving performance of pre-clinical Alzheimer's disease (AD) classification with various modalities. Also, our model adeptly identifies key ROIs that are closely associated with the preclinical stages of AD, marking a significant potential for early diagnosis and prevision of the disease.

Jaeyoon Sim, Minjae Lee, Guorong Wu +1

Pohang University of Science and Technology, Pohang, South Korea · University of North Carolina at Chapel Hill, Chapel Hill, USA

Graph Neural Networks Alzheimer's Disease Classification Multimodal Graph Learning Graph Transformer Graph Diffusion

Jun 1, 2026cs.AI

Structure-Guided Adaptive Propagation for Protein-Protein Interaction Site Prediction

Accurate prediction of protein-protein interaction sites (PPIS) is essential for understanding cellular processes, disease mechanisms, and therapeutic target discovery. Graph-based deep learning has advanced PPIS prediction by incorporating residue-level structural context. However, most graph-based models still rely on fixed propagation schemes that treat all residues similarly, despite the structural and functional heterogeneity of protein interfaces. Such propagation may limit the ability to adapt information diffusion to local geometric environments, making it difficult to distinguish true interaction sites from structurally similar non-interacting neighbors. We present SGAP-PPIS, a structure-guided adaptive propagation model for PPIS prediction. Rather than using a fixed propagation mechanism, SGAP-PPIS leverages multi-scale geometric states from an equivariant graph neural network to generate residue-wise propagation coefficients. This design allows each residue to adaptively balance local feature preservation and neighborhood diffusion according to its geometric microenvironment. Experimental results show that SGAP-PPIS achieves competitive performance among the state-of-the-art methods on Test_60. Ablation studies show that geometry-conditioned adaptive propagation, scale-aligned geometric guidance, and multi-step propagation-state representation jointly drive these improvements.

Enqiang Zhu, Yizi Liu, Yilong Luo +3

Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, Guangdong, China · School of Computer Science, Peking University, Beijing 100871, China · Information Science & Technology Department, Beijing Capital International Airport Co., Ltd., Beijing 101317, China +1

Protein-Protein Interaction Prediction Graph Diffusion

May 25, 2026stat.ML

Learning manifold diffusion semigroups from graph transition matrices

We consider graph diffusion processes constructed from finite i.i.d. samples drawn from an unknown manifold embedded in ambient Euclidean space, where the graph affinity is defined by an ambient Gaussian kernel matrix. We show that the manifold heat semigroup

Q_t = e^{tΔ}

can be approximated directly by iterating the graph transition matrix

P

, under only low regularity assumptions on the test function

f

, including the case

f \in L^\infty

. We bound

\| P^n f - Q_t f \|

in

\infty

-norm, with the operator application to

f

properly defined, and we recover the classical graph-Laplacian pointwise rate

O(N^{-2/(d+6)})

up to logarithmic factors, for diffusion times

t

up to

O(1)

and longer. The rate holds for in-sample error as well as out-of-sample generalization, where the estimator of

Q_t f

at a new point is defined via kernel convolution. To handle non-uniform sampling densities on the manifold, we introduce a right-normalization of the graph transition matrix; under the assumption that the sampling density

p

is

C^3

and bounded away from zero, the same convergence rates hold. We numerically demonstrate the performance of the proposed estimator on simulated data.

Xiuyuan Cheng, Nan Wu

Department of Mathematics, Duke University · Department of Mathematical Sciences, The University of Texas at Dallas

Manifold Learning Graph Diffusion

May 24, 2026cs.LG

Revisiting Pre-Propagation GNNs: Robust Diffusion Operators and Hidden-State Re-Propagation

Pre-propagation graph neural networks (PPGNNs) decouple node feature propagation from transformation: graph diffusion is performed once as preprocessing, and training reduces to dense per-node transformations. This design enables mini-batch training without inter-node dependencies, avoids repeated sparse matrix--matrix multiplications, and better matches modern accelerators optimized for dense compute. However, their expressivity remains unclear, and empirical results show a gap between PPGNNs and their message-passing counterparts on commonly used graph benchmarks, especially heterophilic ones. In this paper, we propose a suite of robust graph diffusion operators for preprocessing and a few-shot hidden-state re-propagation scheme during training. Our methods improve the validation and test accuracy of PPGNNs, enabling them to match the accuracy of message-passing GNNs while maintaining training efficiency.

Zichao Yue, Zhiru Zhang

School of Electrical and Computer Engineering, Cornell University, Ithaca, New York, USA.

Graph Neural Networks Graph Diffusion