We discuss a connection between a generative model, called the diffusion model, and nonequilibrium thermodynamics for the Fokker-Planck equation, called stochastic thermodynamics. Based on the techniques of stochastic thermodynamics, we derive the speed-accuracy relations for the diffusion models, which are inequalities that relate the accuracy of data generation to the entropy production rate, which can be interpreted as the speed of the diffusion dynamics in the absence of the non-conservative force. From a stochastic thermodynamic perspective, our results provide a quantitative insight into how best to generate data in diffusion models. The optimal learning protocol is introduced by the geodesic of space of the 2-Wasserstein distance in optimal transport theory. We numerically illustrate the validity of the speed-accuracy relations for the diffusion models with different noise schedules and the different data. We numerically discuss our results for the optimal and suboptimal learning protocols. We also show the inaccurate data generation due to the non-conservative force, and the applicability of our results to data generation from the real-world image datasets.

翻译：本文探讨了生成模型（即扩散模型）与描述福克-普朗克方程的非平衡热力学（即随机热力学）之间的理论联系。基于随机热力学的技术方法，我们推导出扩散模型的速度-精度关系——该不等式将数据生成的精度与熵产生率相关联，其中熵产生率可解释为无非保守力条件下扩散动力学的速度指标。从随机热力学视角看，我们的研究结果为扩散模型中数据生成的最优策略提供了量化依据。通过最优传输理论中2-瓦瑟斯坦距离空间的测地线，我们构建了最优学习协议。我们通过数值实验验证了不同噪声调度方案及不同数据类型下扩散模型速度-精度关系的有效性，并对最优与次优学习协议的结果进行了数值分析。同时，我们展示了非保守力导致的数据生成失真现象，并论证了该理论在真实世界图像数据集生成任务中的适用性。