Generative diffusion models apply the concept of Langevin dynamics in physics
to machine leaning, attracting a lot of interest from industrial application,
but a complete picture about inherent mechanisms is still lacking. In this
paper, we provide a transparent physics analysis of the diffusion models,
deriving the fluctuation theorem, entropy production, Franz-Parisi potential to
understand the intrinsic phase transitions discovered recently. Our analysis is
rooted in non-equlibrium physics and concepts from equilibrium physics, i.e.,
treating both forward and backward dynamics as a Langevin dynamics, and
treating the reverse diffusion generative process as a statistical inference,
where the time-dependent state variables serve as quenched disorder studied in
spin glass theory. This unified principle is expected to guide machine learning
practitioners to design better algorithms and theoretical physicists to link
the machine learning to non-equilibrium thermodynamics.

透明物理分析推导了扩散模型中的涨落定理、熵产生、Franz-Parisi 势函数，从非平衡物理的角度理解了最近发现的内在相变现象，该统一原理预计将引导机器学习从业者设计更好的算法，也将把机器学习与非平衡热力学联系起来。

生成型扩散模型的非平衡物理学

Nonequilbrium physics of generative diffusion models

We describe a strategy to improve the efficiency of free energy estimates by
reducing dissipation in nonequilibrium Monte Carlo simulations. This strategy
generalizes the targeted free energy perturbation approach [Phys. Rev. E. 65,
046122, 2002] to nonequilibrium switching simulations, and involves generating
artificial, "escorted" trajectories by coupling the evolution of the system to
updates in external work parameter. Our central results are: (1) a generalized
fluctuation theorem for the escorted trajectories, and (2) estimators for the
free energy difference Delta F in terms of these trajectories. We illustrate
the method and its effectiveness on model systems.

本文提出了一种新策略来通过在非平衡 Monte Carlo 模拟中减少耗散来提高自由能估计的效率，其包括通过耦合系统的演化到外部工作参数更新以生成人工的 “护送” 轨迹，得到被 “护送” 轨迹的广义波动定理和自由能差估计器。

护送自由能模拟

Escorted free energy simulations

There are only a very few known relations in statistical dynamics that are
valid for systems driven arbitrarily far-from-equilibrium. One of these is the
fluctuation theorem, which places conditions on the entropy production
probability distribution of nonequilibrium systems. Another recently discovered
far-from-equilibrium expression relates nonequilibrium measurements of the work
done on a system to equilibrium free energy differences. In this paper, we
derive a generalized version of the fluctuation theorem for stochastic,
microscopically reversible dynamics. Invoking this generalized theorem provides
a succinct proof of the nonequilibrium work relation.

本文推导了关于随机宏观可逆动力学的波动定理的广义版本，应用该波动定理证明了非平衡条件下测量系统所做的功和平衡自由能差的关系。