An Overview of Diffusion Models: Applications, Guided Generation, Statistical Rates and Optimization (2404.07771v1)

Abstract: Diffusion models, a powerful and universal generative AI technology, have achieved tremendous success in computer vision, audio, reinforcement learning, and computational biology. In these applications, diffusion models provide flexible high-dimensional data modeling, and act as a sampler for generating new samples under active guidance towards task-desired properties. Despite the significant empirical success, theory of diffusion models is very limited, potentially slowing down principled methodological innovations for further harnessing and improving diffusion models. In this paper, we review emerging applications of diffusion models, understanding their sample generation under various controls. Next, we overview the existing theories of diffusion models, covering their statistical properties and sampling capabilities. We adopt a progressive routine, beginning with unconditional diffusion models and connecting to conditional counterparts. Further, we review a new avenue in high-dimensional structured optimization through conditional diffusion models, where searching for solutions is reformulated as a conditional sampling problem and solved by diffusion models. Lastly, we discuss future directions about diffusion models. The purpose of this paper is to provide a well-rounded theoretical exposure for stimulating forward-looking theories and methods of diffusion models.

Theoretical Advances and Future Directions in Diffusion Models

Introduction to Diffusion Models

Diffusion models have emerged as a significant area of paper within the field of artificial intelligence, particularly within generative modeling. These models, initially inspired by thermodynamics, exemplify an approach to high-dimensional data generation through a process of adding and then removing noise. Compared to traditional generative models like Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs), diffusion models have displayed remarkable success across a spectrum of applications, including image and audio generation, sequential data modeling, and reinforcement learning, among others.

Core Mechanisms of Diffusion Models

The fundamental operation of diffusion models can be conceptualized through two primary processes: the forward and the backward process. The forward process systematically corrupts data by introducing Gaussian noise, transforming a data distribution eventually into a Gaussian distribution. In contrast, the backward process aims to denoise, or reverse this corruption, ideally generating new data samples from the Gaussian noise. This procedure is formalized within a continuous-time framework using stochastic differential equations (SDEs), offering a clean, systematic approach that closely aligns with practical implementations.

Conditional Diffusion Models

Diffusion models have been extended to conditioned environments where the goal is to generate data samples based on specific conditions. These conditional diffusion models are particularly notable for their application in controlled generation tasks, where they've proven capable of generating high-fidelity samples across varied domains. The training of such models involves learning a conditional score function, which reflects the gradient of the log probability density conditioned on certain properties or attributes. Methods like classifier guidance and classifier-free guidance have been pivotal in optimizing these models for practical applications.

Theoretical Foundations and Insights

Despite their empirical success, theoretical examinations of diffusion models have lagged behind. Recent efforts have aimed to bridge this gap, focusing on questions of efficiency, accuracy in data distribution learning, and the implications of structured optimization through these models. These studies have led to a deeper understanding of score function approximation, estimation, and how guiding diffusion models can refine the generation process towards desired characteristics.

Applications and Innovations

Diffusion models have been deployed across various applications, demonstrating their versatility and effectiveness. From creating photorealistic images in computer vision to designing proteins in computational biology, these models have set new standards for generative models. Moreover, their utilization in reinforcement learning and control tasks signifies a growing recognition of their potential to solve complex, high-dimensional optimization problems.

Future Directions

Looking ahead, the integration of diffusion models with stochastic control theories presents a promising avenue for enhancing model performance and developing new methodological innovations. This perspective could yield more principled approaches to designing and tuning models across different tasks. Additionally, exploring diffusion models in the context of adversarial robustness, distributionally robust optimization, and discrete data generation represents exciting frontiers that could further broaden the applicability and impact of these models in artificial intelligence.

Conclusion

Diffusion models stand at a fascinating juncture of theoretical and practical advancements within artificial intelligence. As the field continues to develop, the balance between empirical successes and foundational theory will be crucial for unlocking the full potential of these models. With continued exploration and understanding, diffusion models are poised to contribute significantly to the landscape of generative modeling and beyond.