Curse of Dimensionality is an unavoidable challenge in statistical probability models, yet diffusion models seem to overcome this limitation, achieving impressive results in high-dimensional data generation. Diffusion models assume that they can learn the statistical properties of the underlying probability distribution, enabling sampling from this distribution to generate realistic samples. But is this really how they work? To address this question, this paper conducts a detailed analysis of the objective function and inference methods of diffusion models, leading to several important conclusions that help answer the above question: 1) In high-dimensional sparse scenarios, the target of the objective function fitting degrades from a weighted sum of multiple samples to a single sample. 2) The mainstream inference methods can all be represented within a simple unified framework, without requiring statistical concepts such as Markov chains and SDEs. 3) Guided by this simple framework, more efficient inference methods can be discovered.

本研究探讨了高维数据生成中扩散模型面临的维度诅咒问题。通过对扩散模型目标函数和推断方法的详细分析，研究揭示了这些模型在高维稀疏场合下的适应机制，并提出了一种统一的框架，从而发现了更高效的推断方法。这项工作对理解和优化扩散模型具有重要影响。

重新思考高维中的扩散模型