The paper identifies a limitation of discrete graph diffusion models: independent edge updates combined with exchangeability force the terminal prior to be an Erdős–Rényi graph, which hampers denoising and leads to loss of node heterogeneity. To overcome this, the authors propose a Latent Sociability Prior (LSP) and a joint diffusion process that co‑evolves latent sociability variables with graph structure, eliminating edge independence while maintaining exchangeability. Experiments on several graph generation datasets show that this approach better captures graph distributions than baseline methods that lack node features.
By Adarsh Jamadandi, Nicolas Keriven, Aline Roumy
arXiv:2607. 14398v1 Announce Type: cross Abstract: Constrained generative models aim to produce samples that satisfy complex feasibility constraints while remaining faithful to the data distribution.
By Xiaoxuan Liang, Saeid Naderiparizi, Berend Zwartsenberg, Frank Wood
The paper introduces Logic-Guided Graph Denoising Diffusion Models, which integrate First Order Logic (FOL) constraints into graph diffusion models via classifier guidance. By conditioning the denoising trajectory on a fuzzy, differentiable relaxation of logical rules, the method steers generation toward graphs that satisfy domain-specific structural constraints. Experiments on knowledge graph generation show a significant increase in the proportion of outputs that comply with ontological rules.
By Samuel Cognolato, Luciano Serafini, Alessandro Sperduti, Andrea Cavallaro
The paper explores using denoising diffusion generative models as plug‑and‑play priors for high‑dimensional inference problems. By combining a pre‑trained diffusion prior with a differentiable auxiliary constraint, the authors enable approximate inference through iterative differentiation across multiple noisy versions of the data. This framework opens possibilities for conditional generation, image segmentation, and novel combinatorial optimization algorithms.
By Alexandros Graikos, Esmeralda S. Whitammer, Nebojsa Jojic, Dimitris Samaras
The paper introduces simplex denoising, a generative framework that operates on the probability simplex rather than directly in the discrete state space. It employs a non‑Markovian noising scheme where noisy representations at different times are conditionally independent, preserving theoretical guarantees while removing unnecessary constraints. Empirical results show that unrestrained simplex denoising outperforms strong discrete diffusion and flow‑matching baselines on both synthetic and real‑world graph benchmarks.
By Yoann Boget, Alexandros Kalousis
arXiv:2603. 08825v2 Announce Type: replace-cross Abstract: Discrete graph generation has emerged as a powerful paradigm for modeling graph-structured data, yet state of the art models often rely on Graph Transformers or higher order architectures.
By Jay Revolinsky, Harry Shomer, Jiliang Tang
arXiv:2607. 23226v1 Announce Type: new Abstract: Despite the empirical success of score-based diffusion models, a complete theoretical understanding of how finite-sample learning, network parameterization, and numerical discretization jointly dictate generative quality remains underdeveloped.
By Jinshu Huang, Yiming Jiang, Chunlin Wu
arXiv:2610.22763v1 Announce Type: new
Abstract: Bayesian optimization (BO) over discrete spaces is challenging due to missing gradients and the sparsity of valid solutions. Latent-space BO sidesteps...
By Tommaso Ancilli, Thomas Wedenig, Henry Moss, Robert Peharz
arXiv:2605. 30747v2 Announce Type: replace Abstract: Logical rules constitute a cornerstone of knowledge graph (KG) reasoning, valued for their interpretability and ability to model relational patterns.
By Haoxiang Cheng, Yunfei Wang, Chao Chen, Kewei Cheng, Zhipeng Lin, Haoxuan Li, Changjun Fan, Shixuan Liu
GRIFDIR is a new architecture for score-based diffusion models that operates directly on unstructured meshes, enabling function-space diffusion over irregular domains. By representing generalized graph convolutional kernels as finite element functions, the model achieves resolution invariance and can handle complex, non-convex, and multiply-connected geometries. Experiments demonstrate that GRIFDIR maintains high fidelity in both unconditional and conditional sampling across diverse shapes.
By James Rowbottom, Elizabeth L. Baker, Nick Huang, Ben Adcock, Carola-Bibiane Sch\"onlieb, Alexander Denker
The paper introduces Variational Bayesian Flow Network (VBFN), a graph generation model that lifts Bayesian updates to a joint Gaussian belief family with structured precisions, enabling coupled node and edge updates in a single fusion step. By constructing sample‑agnostic sparse precisions from a representation‑induced dependency graph, VBFN avoids label leakage while enforcing node‑edge consistency. Experiments on synthetic and molecular graph datasets show that VBFN improves fidelity and diversity over baseline methods.
By Yida Xiong, Jiameng Chen, Xiuwen Gong, Jia Wu, Shirui Pan, Wenbin Hu
arXiv:2607. 13431v1 Announce Type: cross Abstract: Discrete denoising diffusion models (DDMs) have recently emerged as a compelling alternative to autoregressive (AR) modeling for discrete data, offering parallel generation and iterative global refinement capabilities.
By Ye Yuan, Weien Li, Rui Song, Zeyu Li, Haochen Liu, Xiangyu Kong, Zixuan Dong, Linfeng Du, Zipeng Sun, Weixu Zhang, Jiaxin Huang, Changjiang Han, Yonghan Yang, Zichen Zhao, Xiuyuan Hu, Haolun Wu, Yankai Chen, Fengran Mo, Jikun Kang, Bowei He, Philip S. Yu, Xue Liu