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.

翻译：本文探讨了扩散模型这一生成模型与针对福克-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中数据生成速度与精度之间的权衡关系。研究结果表明，前向过程中的熵产生率会影响数据生成误差。从随机热力学视角出发，我们的研究为扩散模型中如何最优生成数据提供了定量化的理论见解。最优学习协议可通过随机热力学中的保守力与最优传输理论中2-Wasserstein距离空间的测地线来构建。我们通过数值实验验证了具有不同噪声调度方案（包括余弦调度、条件最优传输及最优传输）的扩散模型中速度-精度权衡关系的有效性。