Discrete Diffusion Schrödinger Bridge Matching for Graph Transformation

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 Schr\"odinger 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.

Predicting quantum chemical property with easy-to-obtain geometry via positional denoising

As quantum chemical properties have a significant 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 in real-world problems. To tackle this, we propose a method to accurately predict the properties with relatively easy-to-obtain geometries (e.g., optimized geometries from the molecular force field). In this method, the input geometry, regarded as the corrupted geometry of the correct one, gradually approaches the correct one as it passes through the stacked denoising layers. We investigated the performance of the proposed method using 3D message-passing architectures for two prediction tasks: molecular properties and chemical reaction property. The reduction of positional errors through the denoising process contributed to performance improvement by increasing the mutual information between the correct and corrupted geometries. Moreover, our analysis of the correlation between denoising power and predictive accuracy demonstrates the effectiveness of the denoising process.