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