Diffusion Models Basic Principles

Abstract

The field of generative modeling has experienced exponential growth in recent years, with new algorithms andmethods emerging at an unprecedented rate. This rapid advancement has led to remarkable breakthroughs in areas such as image synthesis, natural language processing, and audio generation. However, with this flurry of innovation, there is a noticeable gap in foundational research aimed at understanding the underlying mechanisms and theoretical underpinnings of these methods. This lack of deep theoretical insight poses a significant challenge to the field, potentially hindering long-term progress and the development of more efficient and effective algorithms. Our research focuses on a particular class of generative models known as diffusion models. These models have gained considerable attention due to their ability to generate high-quality samples and their unique approach to learning data distributions. Diffusion models operate by gradually adding noise to data and then learning to reverse this process, allowing for the generation of new samples. While their empirical success is evident, the theoretical foundations underlying their performance remain largely unexplored. The primary objective of our work is to bridge this gap between practical application and theoretical under- standing in the domain of diffusion models. We aim to develop a comprehensive framework for analyzing these models, drawing insights from diverse fields of study. This interdisciplinary approach not only deepens our understanding of existing methods but also paves the way for the development of novel, theoretically grounded algorithms.