Alex M. Tseng

Nathaniel Diamant, Alex M. Tseng, Kangway V. Chuang et al.

Deep graph generative modeling has proven capable of learning the distribution of complex, multi-scale structures characterizing real-world graphs. However, one of the main limitations of existing methods is their large output space, which limits generation scalability and hinders accurate modeling of the underlying distribution. To overcome these limitations, we propose a novel approach that significantly reduces the output space of existing graph generative models. Specifically, starting from the observation that many real-world graphs have low graph bandwidth, we restrict graph bandwidth during training and generation. Our strategy improves both generation scalability and quality without increasing architectural complexity or reducing expressiveness. Our approach is compatible with existing graph generative methods, and we describe its application to both autoregressive and one-shot models. We extensively validate our strategy on synthetic and real datasets, including molecular graphs. Our experiments show that, in addition to improving generation efficiency, our approach consistently improves generation quality and reconstruction accuracy. The implementation is made available.

Alex M. Tseng, Nathaniel Diamant, Tommaso Biancalani et al.

Diffusion models achieve state-of-the-art performance in generating realistic objects and have been successfully applied to images, text, and videos. Recent work has shown that diffusion can also be defined on graphs, including graph representations of drug-like molecules. Unfortunately, it remains difficult to perform conditional generation on graphs in a way which is interpretable and controllable. In this work, we propose GraphGUIDE, a novel framework for graph generation using diffusion models, where edges in the graph are flipped or set at each discrete time step. We demonstrate GraphGUIDE on several graph datasets, and show that it enables full control over the conditional generation of arbitrary structural properties without relying on predefined labels. Our framework for graph diffusion can have a large impact on the interpretable conditional generation of graphs, including the generation of drug-like molecules with desired properties in a way which is informed by experimental evidence.

Alex M. Tseng, Nathaniel Diamant, Tommaso Biancalani et al.

Diffusion models have achieved state-of-the-art performance in generating many different kinds of data, including images, text, and videos. Despite their success, there has been limited research on how the underlying diffusion process and the final convergent prior can affect generative performance; this research has also been limited to continuous data types and a score-based diffusion framework. To fill this gap, we explore how different discrete diffusion kernels (which converge to different prior distributions) affect the performance of diffusion models for graphs. To this end, we developed a novel formulation of a family of discrete diffusion kernels which are easily adjustable to converge to different Bernoulli priors, and we study the effect of these different kernels on generative performance. We show that the quality of generated graphs is sensitive to the prior used, and that the optimal choice cannot be explained by obvious statistics or metrics, which challenges the intuitions which previous works have suggested.

Alex M. Tseng, Max Shen, Tommaso Biancalani et al.

Class-labeled datasets, particularly those common in scientific domains, are rife with internal structure, yet current class-conditional diffusion models ignore these relationships and implicitly diffuse on all classes in a flat fashion. To leverage this structure, we propose hierarchically branched diffusion models as a novel framework for class-conditional generation. Branched diffusion models rely on the same diffusion process as traditional models, but learn reverse diffusion separately for each branch of a hierarchy. We highlight several advantages of branched diffusion models over the current state-of-the-art methods for class-conditional diffusion, including extension to novel classes in a continual-learning setting, a more sophisticated form of analogy-based conditional generation (i.e. transmutation), and a novel interpretability into the generation process. We extensively evaluate branched diffusion models on several benchmark and large real-world scientific datasets spanning many data modalities.