Graph diffusion models have emerged as state-of-the-art techniques in graph
generation, yet integrating domain knowledge into these models remains
challenging. Domain knowledge is particularly important in real-world
scenarios, where invalid generated graphs hinder deployment in practical
applications. Unconstrained and conditioned graph generative models fail to
guarantee such domain-specific structural properties. We present ConStruct, a
novel framework that allows for hard-constraining graph diffusion models to
incorporate specific properties, such as planarity or acyclicity. Our approach
ensures that the sampled graphs remain within the domain of graphs that verify
the specified property throughout the entire trajectory in both the forward and
reverse processes. This is achieved by introducing a specific edge-absorbing
noise model and a new projector operator. ConStruct demonstrates versatility
across several structural and edge-deletion invariant constraints and achieves
state-of-the-art performance for both synthetic benchmarks and attributed
real-world datasets. For example, by leveraging planarity in digital pathology
graph datasets, the proposed method outperforms existing baselines and enhances
generated data validity by up to 71.1 percentage points.

通过引入特定的边吸收噪声模型和新的投影算子，ConStruct 是一种允许硬约束图扩散模型以包含特定属性（如平面性或非循环性）的新框架。它在合成基准和属性现实数据集中展示了多功能性和最先进的性能，例如在数字病理学图数据集中，利用平面性的提出方法提高了生成数据的有效性高达 71.1 个百分点。

结构约束图的生成建模

Generative Modelling of Structurally Constrained Graphs

Models of street networks underlie research in urban travel behavior,
accessibility, design patterns, and morphology. These models are commonly
defined as planar, meaning they can be represented in two dimensions without
any underpasses or overpasses. However, real-world urban street networks exist
in three-dimensional space and frequently feature grade separation such as
bridges and tunnels: planar simplifications can be useful but they also impact
the results of real-world street network analysis. This study measures the
nonplanarity of drivable and walkable street networks in the centers of 50
cities worldwide, then examines the variation of nonplanarity across a single
city. It develops two new indicators - the Spatial Planarity Ratio and the Edge
Length Ratio - to measure planarity and describe infrastructure and
urbanization. While some street networks are approximately planar, we
empirically quantify how planar models can inconsistently but drastically
misrepresent intersection density, street lengths, routing, and connectivity.

本研究测量了全球 50 个城市中心的可行驶和可步行街道网络的非平面性，并开发了两个新指标（空间平面比和边长度比）来测量规划性和描述基础设施和城市化，实证量化了规划模型如何不一致地但极大地误表示交叉口密度、街道长度、路径和连接性。