🤖 AI Summary
This work addresses the absence of a thermodynamic interpretation for existing stochastic differential equation (SDE)-based generative models—such as diffusion models and Schrödinger bridges—within the framework of nonequilibrium statistical mechanics. By extending the classical Jarzynski equality to scenarios involving time-varying temperature and non-conservative driving forces, the study introduces, for the first time, trajectory-level definitions of work, heat, and entropy production. It derives a generalized Jarzynski equality and a second-law-like inequality, thereby embedding SDE generative models into the formalism of stochastic thermodynamics. Leveraging tools from stochastic calculus, path integrals, and nonequilibrium statistical mechanics, this work establishes a comprehensive thermodynamic formulation for SDE-based generative modeling, offering deeper insight into their physical underpinnings and opening new avenues for the design and analysis of such models.
📝 Abstract
SDE-based generative models, including diffusion models and the Schrödinger bridge, have found broad applications in signal processing tasks such as speech enhancement, image restoration, and time-series generation. This note presents a modeling framework for such models within the context of stochastic thermodynamics. The main results of this note are trajectory-level definitions of work, heat, and entropy production, along with a generalized Jarzynski identity and a second-law-like inequality. The proposed framework extends the original Jarzynski setup to accommodate time-dependent bath temperature and nonconservative driving forces. This thermodynamic perspective may deepen our understanding of diffusion models and the Schrödinger bridge from a nonequilibrium statistical mechanics viewpoint.