Graph Diffusion that can Insert and Delete

2025-06-06

arXiv.org

AI Summary

Existing discrete denoising diffusion probabilistic models (DDPMs) for graph generation assume fixed node counts, limiting their applicability to property-driven molecular design—where target properties often strongly correlate with molecular size. This work proposes the first graph diffusion generative model supporting dynamic node insertion and deletion, thereby overcoming the static graph-structure constraint inherent in conventional DDPM-based approaches. Our core innovation is the integration of a monotonic node insertion/deletion mechanism into the discrete graph diffusion framework, which necessitates a reformulation of both the noise scheduling and reverse sampling procedures, while jointly optimizing discrete graph operations and a differentiable surrogate objective. Experiments demonstrate that our model matches or surpasses state-of-the-art graph diffusion methods on attribute-conditioned molecular generation, and achieves performance comparable to specialized molecular optimization algorithms. It significantly enhances flexibility and practicality for size-sensitive conditional generation.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

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.

Problem

• Overcoming graph size limitations in diffusion models for molecules
• Enabling dynamic node insertion and deletion during graph generation
• Improving conditional molecular generation with size adaptation capability

Innovation

• Monotonic node insertion and deletion processes
• Dynamic graph size adjustment during generation
• Size-adaptive diffusion model for molecular graphs