揭示扩散模型与热力学熵率的深层联系，给出性能下限。
Thermodynamic Performance Limits for Score-Based Diffusion Models
- 从熵率出发推导数据负对数似然的理论下界。
- 在合成数据上验证该下界，并分析其紧致性。
- 为生成模型提供热力学视角，适合研究物理机制者。
我们通过推导基于熵率的性能极限，建立了得分型扩散模型与非平衡热力学之间的基本联系。核心理论贡献是给出了数据负对数似然的下界，该下界将模型性能与扩散过程的熵率相关联。我们在合成数据集上数值验证了这一下界，并研究其紧致性。通过连接系统熵、内在熵和交换熵等熵率概念，我们为这类模型的热力学运作提供了新见解，类比麦克斯韦妖，并对热力学计算硬件具有启示意义。该框架通过随机热力学将生成建模性能与基本物理原理相联系。
原文摘要 · Abstract (English)
We establish a fundamental connection between score-based diffusion models and non-equilibrium thermodynamics by deriving performance limits based on entropy rates. Our main theoretical contribution is a lower bound on the negative log-likelihood of the data that relates model performance to entropy rates of diffusion processes. We numerically validate this bound on a synthetic dataset and investigate its tightness. By building a bridge to entropy rates - system, intrinsic, and exchange entropy - we provide new insights into the thermodynamic operation of these models, drawing parallels to Maxwell's demon and implications for thermodynamic computing hardware. Our framework connects generative modeling performance to fundamental physical principles through stochastic thermodynamics.
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