Transporting between arbitrary distributions is a fundamental goal in generative modeling. Recently proposed diffusion bridge models provide a potential solution, but they rely on a joint distribution that is difficult to obtain in practice. Furthermore, formulations based on continuous domains limit their applicability to discrete domains such as graphs. To overcome these limitations, we propose Discrete Diffusion Schrödinger Bridge Matching (DDSBM), a novel framework that utilizes continuous-time Markov chains to solve the SB problem in a high-dimensional discrete state space. Our approach extends Iterative Markovian Fitting to discrete domains, and we have proved its convergence to the SB. Furthermore, we adapt our framework for the graph transformation, and show that our design choice of underlying dynamics characterized by independent modifications of nodes and edges can be interpreted as the entropy-regularized version of optimal transport with a cost function described by the graph edit distance. To demonstrate the effectiveness of our framework, we have applied DDSBM to molecular optimization in the field of chemistry. Experimental results demonstrate that DDSBM effectively optimizes molecules' property-of-interest with minimal graph transformation, successfully retaining other features. Source code is available [here](https://github.com/junhkim1226/DDSBM).

MOTIVATION: Transcriptome data from gene knock-out (KO) experiments in mice provide crucial insights into the intricate interactions between genotype and phenotype. Differentially expressed gene (DEG) analysis and network propagation (NP) are well-established methods for analysing transcriptome data. To determine genes related to phenotype changes from a KO experiment, we need to choose a cutoff value for the corresponding criterion based on the specific method. Using a rigorous cutoff value for DEG analysis and NP is likely to select mostly positive genes related to the phenotype, but many will be rejected as false negatives. On the other hand, using a loose cutoff value for either method is prone to include a number of genes that are not phenotype-related, which are false positives. Thus, the research problem at hand is how to deal with the trade-off between false negatives and false positives. RESULTS: We propose a novel framework called PONYTA for gene prioritization via positive-unlabeled (PU) learning on biological networks. Beginning with the selection of true phenotype-related genes using a rigorous cutoff value for DEG analysis and NP, we address the issue of handling false negatives by rescuing them through PU learning. Evaluations on transcriptome data from multiple studies show that our approach has superior gene prioritization ability compared to benchmark models. Therefore, PONYTA effectively prioritizes genes related to phenotypes derived from gene KO events and guides in vitro and in vivo gene KO experiments for increased efficiency. AVAILABILITY AND IMPLEMENTATION: The source code of PONYTA is available at https://github.com/Jun-Hyeong-Kim/PONYTA.

As quantum chemical properties have a dependence on their geometries, graph neural networks (GNNs) using 3D geometric information have achieved high prediction accuracy in many tasks. However, they often require 3D geometries obtained from high-level quantum mechanical calculations, which are practically infeasible, limiting their applicability to real-world problems. To tackle this, we propose a new training framework, GeoTMI, that employs denoising process to predict properties accurately using easy-to-obtain geometries (corrupted versions of correct geometries, such as those obtained from low-level calculations). Our starting point was the idea that the correct geometry is the best description of the target property. Hence, to incorporate information of the correct, GeoTMI aims to maximize mutual information between three variables: the correct and the corrupted geometries and the property. GeoTMI also explicitly updates the corrupted input to approach the correct geometry as it passes through the GNN layers, contributing to more effective denoising. We investigated the performance of the proposed method using 3D GNNs for three prediction tasks: molecular properties, a chemical reaction property, and relaxed energy in a heterogeneous catalytic system. Our results showed consistent improvements in accuracy across various tasks, demonstrating the effectiveness and robustness of GeoTMI.