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:在相当长的一段时间里,研究人员一直侧重于开发一种方法,在基因扩散模型和数学物理学之间建立深层联系。尽管以前作了努力,但进展仅限于追求一种单一的专门方法。为了提高传播模型的可解释性并探索新的研究方向,必须建立一个统一的ODE型基因扩散模型。这种模型应当从物理模型中汲取灵感并具有明确的几何意义。本文件旨在从数学角度确定各种适合于准确构建ODE型基因扩散模型的物理模型。然后我们将这些模型归纳成一种统一的方法。此外,我们进行了一项案例研究,我们利用我们方法确定的理论模型来开发一系列新的传播模型方法并进行实验。我们在CIFAR-10上进行的实验证明了我们的方法的有效性。我们建立了一个计算框架,在图像生成速度方面取得了非常精准的结果,同时还建立了另一个模型,显示在接受分和FID分两方面的出色表现。这些结果突出表明了我们方法在推进传播模型领域方面的重要性。</s>