Weshowthat GDC isclosely related to spectral-based models and thus combines the strengths ofboth spatial (message passing) and spectral methods.

Predicting the effect of amino acid mutations on enzyme thermodynamic stability (DDG) is fundamental to protein engineering and drug design. While recent deep learning approaches have shown promise, they often process sequence and structure information independently, failing to capture the intricate coupling between local structural geometry and global sequential patterns. We present DGTN (Diffused Graph-Transformer Network), a novel architecture that co-learns graph neural network (GNN) weights for structural priors and transformer attention through a diffusion mechanism. Our key innovation is a bidirectional diffusion process where: (1) GNN-derived structural embeddings guide transformer attention via learnable diffusion kernels, and (2) transformer representations refine GNN message passing through attention-modulated graph updates. We provide rigorous mathematical analysis showing this co-learning scheme achieves provably better approximation bounds than independent processing. On ProTherm and SKEMPI benchmarks, DGTN achieves state-of-the-art performance (Pearson Rho = 0.87, RMSE = 1.21 kcal/mol), with 6.2% improvement over best baselines. Ablation studies confirm the diffusion mechanism contributes 4.8 points to correlation. Our theoretical analysis proves the diffused attention converges to optimal structure-sequence coupling, with convergence rate O(1/sqrt(T) ) where T is diffusion steps. This work establishes a principled framework for integrating heterogeneous protein representations through learnable diffusion.

Graph diffusion, which iteratively propagates real-valued substances among the graph, is used in numerous graph/network-involved applications.

Generating molecular graphs is a challenging task due to their discrete nature and the competitive objectives involved. Diffusion models have emerged as SOTA approaches in data generation across various modalities. For molecular graphs, graph neural networks (GNNs) as a diffusion backbone have achieved impressive results. Latent space diffusion, where diffusion occurs in a low-dimensional space via an autoencoder, has demonstrated computational efficiency. However, the literature on latent space diffusion for molecular graphs is scarce, and no commonly accepted best practices exist. In this work, we explore different approaches and hyperparameters, contrasting generative flow models (denoising diffusion, flow matching, heat dissipation) and architectures (GNNs and E(3)-equivariant GNNs). Our experiments reveal a high sensitivity to the choice of approach and design decisions. Code is made available at github.com/Prashanth-Pombala/Molecule-Generation-using-Latent-Space-Graph-Diffusion.

Generative models such as diffusion models have achieved remarkable success in state-of-the-art image and text tasks. Recently, score-based diffusion models have extended their success beyond image generation, showing competitive performance with discriminative methods in image {\em classification} tasks~\cite{zimmermann2021score}. However, their application to classification in the {\em graph} domain, which presents unique challenges such as complex topologies, remains underexplored. We show how graph diffusion models can be applied for graph classification. We find that to achieve competitive classification accuracy, score-based graph diffusion models should be trained with a novel training objective that is tailored to graph classification. In experiments with a sampling-based inference method, our discriminative training objective achieves state-of-the-art graph classification accuracy.

Alzheimer's disease (AD) is a complex neurodegenerative disorder that affects millions of people worldwide. Due to the heterogeneous nature of AD, its diagnosis and treatment pose critical challenges. Consequently, there is a growing research interest in identifying homogeneous AD subtypes that can assist in addressing these challenges in recent years. In this study, we aim to identify subtypes of AD that represent distinctive clinical features and underlying pathology by utilizing unsupervised clustering with graph diffusion and similarity learning. We adopted SIMLR, a multi-kernel similarity learning framework, and graph diffusion to perform clustering on a group of 829 patients with AD and mild cognitive impairment (MCI, a prodromal stage of AD) based on their cortical thickness measurements extracted from magnetic resonance imaging (MRI) scans. Although the clustering approach we utilized has not been explored for the task of AD subtyping before, it demonstrated significantly better performance than several commonly used clustering methods. Specifically, we showed the power of graph diffusion in reducing the effects of noise in the subtype detection. Our results revealed five subtypes that differed remarkably in their biomarkers, cognitive status, and some other clinical features. To evaluate the resultant subtypes further, a genetic association study was carried out and successfully identified potential genetic underpinnings of different AD subtypes. Our source code is available at: https://github.com/PennShenLab/AD-SIMLR.