  Generative diffusion models have achieved spectacular performance in many
areas of machine learning and generative modeling. While the fundamental ideas
behind these models come from non-equilibrium physics, variational inference
and stochastic calculus, in this paper we show that many aspects of these
models can be understood using the tools of equilibrium statistical mechanics.
Using this reformulation, we show that generative diffusion models undergo
second-order phase transitions corresponding to symmetry breaking phenomena. We
show that these phase-transitions are always in a mean-field universality
class, as they are the result of a self-consistency condition in the generative
dynamics. We argue that the critical instability that arises from the phase
transitions lies at the heart of their generative capabilities, which are
characterized by a set of mean-field critical exponents. Finally, we show that
the dynamic equation of the generative process can be interpreted as a
stochastic adiabatic transformation that minimizes the free energy while
keeping the system in thermal equilibrium.
