The paper studies the stability of graph-aware continuous‑time generative models that use a graph filter combined with a learned graph neural network. It derives explicit Wasserstein bounds showing how relative graph perturbations affect the generated distributions, and proposes a principled framework for designing stable graph filters that preserve heat‑diffusion smoothing while improving structural stability. Experiments on synthetic and fMRI data demonstrate that these stable filters enhance robustness and match or surpass the generative quality of a heat‑equation baseline.
Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations. While favorable stability properties of Graph Neural Networks (GNNs) have been well documented, it is unclear how structural errors propagate through the dynamics of continuous generative flow models that are gaining traction for graph signal generation.
arXiv:2607. 07510v1 Announce Type: cross Abstract: Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations.
arXiv:2609.39739v1 Announce Type: new Abstract: Graph generative models increasingly rely on Graph Transformers (GT) to capture complex dependencies among nodes and edges. While deeper architectures...
arXiv:2608. 19914v1 Announce Type: new Abstract: Network topology inference from graph signals is central to graph signal processing with applications in neuroscience, sensor, and social networks.
arXiv:2402. 17500v2 Announce Type: replace-cross Abstract: A central question of network science is how functional properties of systems emerge from their structure.
The article reviews the problem of learning graph structures from data, noting that research has traditionally split into two paths: inferring the topology of a single graph from observations on it, and learning a generative distribution from multiple observed graphs to sample new ones. It proposes a unified framework that treats both as inverse problems of a common graph generation process, reviews key methods, and discusses their interrelations, strengths, and limitations. The review highlights opportunities for cross‑paradigm integration and outlines future research directions.
arXiv:2601. 22107v2 Announce Type: replace Abstract: We introduce \textit{Prior-Informed Flow Matching (PIFM)}, a conditional flow model for graph reconstruction.
The paper explores how information propagates in Deep Graph Networks (DGNs) for both static and dynamic graphs, treating DGNs as dynamical systems. It presents new architectures that better preserve long‑term node dependencies and learn complex spatio‑temporal patterns from irregular, sparsely sampled dynamic graphs. The work combines theoretical analysis with empirical results to demonstrate the effectiveness of these designs.
arXiv:2608. 07161v1 Announce Type: cross Abstract: Simulating complex fluid flows requires capturing full equilibrium distributions rather than just mean trajectories, yet high-fidelity solvers remain computationally prohibitive.
arXiv:2606. 17684v1 Announce Type: cross Abstract: Graph-based learning methods have become increasingly prominent due to their strong performance across diverse applications.
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.
arXiv:2607. 07232v1 Announce Type: cross Abstract: Diffusion models represent a leading paradigm for graph generation, with notable impact in domains such as molecular design.