  Sampling from known probability distributions is a ubiquitous task in
computational science, underlying calculations in domains from linguistics to
biology and physics. Generative machine-learning (ML) models have emerged as a
promising tool in this space, building on the success of this approach in
applications such as image, text, and audio generation. Often, however,
generative tasks in scientific domains have unique structures and features --
such as complex symmetries and the requirement of exactness guarantees -- that
present both challenges and opportunities for ML. This Perspective outlines the
advances in ML-based sampling motivated by lattice quantum field theory, in
particular for the theory of quantum chromodynamics. Enabling calculations of
the structure and interactions of matter from our most fundamental
understanding of particle physics, lattice quantum chromodynamics is one of the
main consumers of open-science supercomputing worldwide. The design of ML
algorithms for this application faces profound challenges, including the
necessity of scaling custom ML architectures to the largest supercomputers, but
also promises immense benefits, and is spurring a wave of development in
ML-based sampling more broadly. In lattice field theory, if this approach can
realize its early promise it will be a transformative step towards
first-principles physics calculations in particle, nuclear and condensed matter
physics that are intractable with traditional approaches.
