Graph Diffusion that can Insert and Delete

TL;DR

This paper introduces GrIDDD, a graph diffusion model that can dynamically insert and delete nodes, enabling size-adaptive molecular generation and improving performance in property-driven design tasks.

Contribution

We reformulate graph diffusion processes to support monotonic node insertion and deletion, allowing size flexibility during molecular generation.

Findings

GrIDDD matches or exceeds existing models in property targeting.

It effectively supports size adaptation in molecular generation.

Competitive performance in molecular optimization tasks.

Abstract

Generative models of graphs based on discrete Denoising Diffusion Probabilistic Models (DDPMs) offer a principled approach to molecular generation by systematically removing structural noise through iterative atom and bond adjustments. However, existing formulations are fundamentally limited by their inability to adapt the graph size (that is, the number of atoms) during the diffusion process, severely restricting their effectiveness in conditional generation scenarios such as property-driven molecular design, where the targeted property often correlates with the molecular size. In this paper, we reformulate the noising and denoising processes to support monotonic insertion and deletion of nodes. The resulting model, which we call GrIDDD, dynamically grows or shrinks the chemical graph during generation. GrIDDD matches or exceeds the performance of existing graph diffusion models on molecular property targeting despite being trained on a more difficult problem. Furthermore, when applied to molecular optimization, GrIDDD exhibits competitive performance compared to specialized optimization models. This work paves the way for size-adaptive molecular generation with graph diffusion.