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For a considerable time, researchers have focused on developing a method thatestablishes a deep connection between the generative diffusion model andmathematical physics. Despite previous efforts, progress has been limited tothe pursuit of a single specialized method. In order to advance theinterpretability of diffusion models and explore new research directions, it isessential to establish a unified ODE-style generative diffusion model. Such amodel should draw inspiration from physical models and possess a cleargeometric meaning. This paper aims to identify various physical models that aresuitable for constructing ODE-style generative diffusion models accurately froma mathematical perspective. We then summarize these models into a unifiedmethod. Additionally, we perform a case study where we use the theoreticalmodel identified by our method to develop a range of new diffusion modelmethods, and conduct experiments. Our experiments on CIFAR-10 demonstrate theeffectiveness of our approach. We have constructed a computational frameworkthat attains highly proficient results with regards to image generation speed,alongside an additional model that demonstrates exceptional performance in bothInception score and FID score. These results underscore the significance of ourmethod in advancing the field of diffusion models.

Interpretable ODE-style Generative Diffusion Model via Force Field Construction