SeaDAG: Semi-autoregressive Diffusion for Conditional Directed Acyclic Graph Generation

TL;DR

SeaDAG is introduced, a semi-autoregressive diffusion model for conditional generation of Directed Acyclic Graphs (DAGs), and explicitly train the model to learn graph conditioning with a condition loss, which enhances the diffusion model's capacity to generate graphs that are both realistic and aligned with specified properties.

Abstract

We introduce SeaDAG, a semi-autoregressive diffusion model for conditional generation of Directed Acyclic Graphs (DAGs). Considering their inherent layer-wise structure, we simulate layer-wise autoregressive generation by designing different denoising speed for different layers. Unlike conventional autoregressive generation that lacks a global graph structure view, our method maintains a complete graph structure at each diffusion step, enabling operations such as property control that require the full graph structure. Leveraging this capability, we evaluate the DAG properties during training by employing a graph property decoder. We explicitly train the model to learn graph conditioning with a condition loss, which enhances the diffusion model's capacity to generate graphs that are both realistic and aligned with specified properties. We evaluate our method on two representative conditional DAG generation tasks: (1) circuit generation from truth tables, where precise DAG structures are crucial for realizing circuit functionality, and (2) molecule generation based on quantum properties. Our approach demonstrates promising results, generating high-quality and realistic DAGs that closely align with given conditions.

Figures (10)

• Figure 1: The overview of proposed layer-wise semi-autoregressive diffusion of SeaDAG. Layers are denoised at different speeds depending on their levels in DAG. A complete graph structure is maintained at very step.
• Figure 2: (a) Example AIG and its truth table. (b) Example molecule and its junction tree, where each node represents a chemical substructure. The tree will be further transformed into a DAG.
• Figure 3: Training pipeline. SeaDAG predicts the node and edge type distribution in the clean graph. Apart from the cross-entropy loss, we employ a condition loss to incorporate explicit condition learning during training.
• Figure 4: Sampled AIG and molecules by SeaDAG and the one-shot diffusion baseline DiGress.
• Figure 5: Distribution of maximum levels in generated AIGs. SeaDAG with semi-autoregressive diffusion generates AIGs with maximum levels similar to ground truth AIGs, while other two one-shot methods produce significantly shallower AIGs.