Generative Diffusion Models on Graphs: Methods and Applications (2302.02591v3)

Abstract: Diffusion models, as a novel generative paradigm, have achieved remarkable success in various image generation tasks such as image inpainting, image-to-text translation, and video generation. Graph generation is a crucial computational task on graphs with numerous real-world applications. It aims to learn the distribution of given graphs and then generate new graphs. Given the great success of diffusion models in image generation, increasing efforts have been made to leverage these techniques to advance graph generation in recent years. In this paper, we first provide a comprehensive overview of generative diffusion models on graphs, In particular, we review representative algorithms for three variants of graph diffusion models, i.e., Score Matching with Langevin Dynamics (SMLD), Denoising Diffusion Probabilistic Model (DDPM), and Score-based Generative Model (SGM). Then, we summarize the major applications of generative diffusion models on graphs with a specific focus on molecule and protein modeling. Finally, we discuss promising directions in generative diffusion models on graph-structured data. For this survey, we also created a GitHub project website by collecting the supporting resources for generative diffusion models on graphs, at the link: https://github.com/ChengyiLIU-cs/Generative-Diffusion-Models-on-Graphs

Generative Diffusion Models on Graphs: Methods and Applications

The field of generative diffusion models, which has found significant applicability in image generation tasks, is progressively being applied to graph-structured data. This includes various domains like social networks, molecular structures, and recommender systems, where understanding the inherent relationships within the data is crucial. The paper "Generative Diffusion Models on Graphs: Methods and Applications" offers a comprehensive examination of the methodologies and applications of generative diffusion models on graphs, emphasizing their emerging role and potential in complex data representations like molecules and proteins.

Overview of Generative Diffusion Models

Diffusion models primarily operate through a two-step process: a forward diffusion that systematically introduces noise to the data, and a reverse diffusion that aims to recapture the original data distribution from the noise. These models have demonstrated efficacy in capturing intricate dependencies and generating data that aligns with the complexity of the original input. The paper categorizes these models on graphs into three archetypes:

1. Score Matching with Langevin Dynamics (SMLD): This approach leverages noise to guide the generation of graph structures by iteratively refining noisy data through score-based mechanisms that assess data distribution gradients.
2. Denoising Diffusion Probabilistic Models (DDPM): Utilizing a reverse Markov chain process, DDPMs facilitate the restoration of noise-laden data by building probabilistic models that learn to generate graph structures from Gaussian-distributed noise.
3. Score-based Generative Models (SGM): By employing stochastic differential equations, SGMs present a more continuous approach to the diffusion process, handling both edge and node features simultaneously.

Numerical Results and Key Findings

The survey provides an extensive review of graph diffusion methods with applications in molecule conformation generation and molecular docking, highlighting numerical successes in generating realistic molecular structures that meet specified geometric and chemical properties. Methods like GeoDiff and GDSS demonstrate superior performance in modeling 3D molecular structures, while others like DiGress capitalize on graph transformers for graph-based diffusion, leading to state-of-the-art results in categorical feature generation.

Implications and Future Directions

The implications of these advancements are far-reaching, impacting drug discovery, biochemical research, and social network analysis. The complexity in graph generation, given its inherently discrete and permutation-invariant structure, presents challenges in applying continuous techniques like diffusion models. The paper identifies several key areas for future exploration, including:

• Conditional Generation: This involves enhancing control over the generative process by integrating external auxiliary conditions, which could improve model specificity and applicability in targeted scenarios like drug design.
• Trustworthiness and Fairness: As graph diffusion models are applied to sensitive data, ensuring robustness against adversarial attacks, and fairness and privacy in data handling is imperative. Addressing these aspects would reinforce trust in the deployment of such models in critical applications.
• Evaluation Metrics: Developing robust and reliable evaluation metrics specific to graph generation would enable better benchmarking and validation of generative model performance, essential for advancing this research domain.

Conclusion

Overall, the exploration of generative diffusion models on graphs is paving new pathways in handling graph-structured data. The survey underscores both the progress and challenges in applying diffusion techniques in this domain, providing a roadmap for future research that could vastly improve graph representation and generation across various scientific and technological fields.