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 trade-off for the diffusion models, which is a trade-off relationship between the speed and accuracy of data generation in diffusion models. Our result implies that the entropy production rate in the forward process affects the errors in data generation. From a stochastic thermodynamic perspective, our results provide quantitative insight into how best to generate data in diffusion models. The optimal learning protocol is introduced by the conservative force in stochastic thermodynamics and the geodesic of space by the 2-Wasserstein distance in optimal transport theory. We numerically illustrate the validity of the speed-accuracy trade-off for the diffusion models with different noise schedules such as the cosine schedule, the conditional optimal transport, and the optimal transport.

基于随机热力学技术，我们讨论了扩散模型与非平衡态热力学之间的关系，并推导出了扩散模型中速度与准确性的权衡关系，该结果说明正向过程的熵产生速率会影响数据生成中的错误。从随机热力学的视角来看，我们的结果为如何在扩散模型中最佳生成数据提供了定量洞察。最优学习协议是通过随机热力学中的保守力和最优输运理论中的2-Wasserstein距离空间的测地线引入的。我们通过采用不同噪声计划（如余弦计划、条件最优输运和最优输运）的扩散模型对速度与准确性的权衡进行了数值验证。

扩散模型的速度-准确性权衡：非平衡热力学和最优输运的智慧