  Spin-glasses are universal models that can capture complex behavior of
many-body systems at the interface of statistical physics and computer science
including discrete optimization, inference in graphical models, and automated
reasoning. Computing the underlying structure and dynamics of such complex
systems is extremely difficult due to the combinatorial explosion of their
state space. Here, we develop deep generative continuous spin-glass
distributions with normalizing flows to model correlations in generic discrete
problems. We use a self-supervised learning paradigm by automatically
generating the data from the spin-glass itself. We demonstrate that key
physical and computational properties of the spin-glass phase can be
successfully learned, including multi-modal steady-state distributions and
topological structures among metastable states. Remarkably, we observe that the
learning itself corresponds to a spin-glass phase transition within the layers
of the trained normalizing flows. The inverse normalizing flows learns to
perform reversible multi-scale coarse-graining operations which are very
different from the typical irreversible renormalization group techniques.
