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.

翻译：长期以来，研究者们一直致力于建立生成扩散模型与数学物理之间的深层联系。尽管已有诸多努力，但进展仍局限于对单一特定方法的追求。为提升扩散模型的可解释性并探索新的研究方向，有必要建立一种统一的常微分方程（ODE）风格生成扩散模型。此类模型应借鉴物理模型的思想，并具有清晰的几何意义。本文旨在从数学角度精确识别适用于构建ODE风格生成扩散模型的各种物理模型，并将其总结为统一方法。此外，我们通过案例研究，利用该方法识别的理论模型开发了一系列新型扩散模型方法并进行了实验。在CIFAR-10数据集上的实验结果验证了我们方法的有效性。我们构建的计算框架在图像生成速度方面取得了高度优化的结果，同时另一附加模型在Inception分数和FID分数上均表现出卓越性能。这些结果凸显了我们的方法在推动扩散模型领域发展方面的重要意义。