  For a considerable time, researchers have focused on developing a method that
establishes a deep connection between the generative diffusion model and
mathematical physics. Despite previous efforts, progress has been limited to
the pursuit of a single specialized method. In order to advance the
interpretability of diffusion models and explore new research directions, it is
essential to establish a unified ODE-style generative diffusion model. Such a
model should draw inspiration from physical models and possess a clear
geometric meaning. This paper aims to identify various physical models that are
suitable for constructing ODE-style generative diffusion models accurately from
a mathematical perspective. We then summarize these models into a unified
method. Additionally, we perform a case study where we use the theoretical
model identified by our method to develop a range of new diffusion model
methods, and conduct experiments. Our experiments on CIFAR-10 demonstrate the
effectiveness of our approach. We have constructed a computational framework
that attains highly proficient results with regards to image generation speed,
alongside an additional model that demonstrates exceptional performance in both
Inception score and FID score. These results underscore the significance of our
method in advancing the field of diffusion models.
