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.

The vocabulary Vconstructed by Algorithm 1 exhibits the following advantageous properties. Prior to the proof, we first present a clear observation of the created vocabulary V: Proposition A.2. Given any F,F V, for any their instances arising on an arbitrary molecule during the extraction process, either they are not spatially intersected F F =, or they contain each other: F F or F F. Now we prove each claim in the above theorem. We prove it by contradiction. If it is the former case, then Fi1 should be firstly extracted and then merged with other fragments to yield Fi2 which means i1 < i2, conflicting with the assumption.

Nevertheless, these methods usually rely on hand-crafted or external subgraph construction, andthesubgraph assembling depends solely onlocal arrangement.

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.

Compared with MHG, our proposed grammars have better generalization ability. In comparison, our grammar is based on neighboring relationships. From the 220,011 training molecules, we obtained 1,775 production rules. Each molecule is associated with 28 production rules on the average. The maximum number of production rules associated with a molecule is 51.