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.

翻译：我们提出了SeaDAG，一种用于条件生成有向无环图（DAGs）的半自回归扩散模型。考虑到其固有的分层结构，我们通过为不同层设计不同的去噪速度来模拟分层自回归生成。与缺乏全局图结构视角的传统自回归生成方法不同，我们的方法在扩散过程的每一步都保持完整的图结构，从而能够执行诸如需要完整图结构的属性控制等操作。利用这一能力，我们通过采用图属性解码器在训练期间评估DAG属性。我们通过引入条件损失，显式地训练模型学习图的条件生成，这增强了扩散模型生成既真实又符合指定属性的图的能力。我们在两个代表性的条件DAG生成任务上评估了我们的方法：（1）从真值表生成电路，其中精确的DAG结构对于实现电路功能至关重要；（2）基于量子性质的分子生成。我们的方法展示了有希望的结果，生成了高质量、真实且与给定条件高度吻合的DAG。