Introducing time-correlated "active" noise sources into the forward diffusion process of score-based generative models can improve their ability to learn complex data distributions and generate higher-quality samples.
This paper introduces Generative Fractional Diffusion Models (GFDM), a novel approach to image generation that leverages the correlated increments and long-term memory of fractional Brownian motion (fBM) to enhance image quality, diversity, and distribution coverage compared to traditional diffusion models reliant on Brownian motion.
Generative diffusion models have shown high success in various fields with a powerful theoretical foundation. This study provides an overview of the theoretical developments in this domain, categorizing the research into training-based and sampling-based approaches.
Generative diffusion models exhibit phase transitions and critical instability, revealing a deep connection to equilibrium statistical mechanics.