  Feynman path integrals provide an elegant, classically inspired
representation for the quantum propagator and the quantum dynamics, through
summing over a huge manifold of all possible paths. From computational and
simulational perspectives, the ergodic tracking of the whole path manifold is a
hard problem. Machine learning can help, in an efficient manner, to identify
the relevant subspace and the intrinsic structure residing at a small fraction
of the vast path manifold. In this work, we propose the Feynman path generator
for quantum mechanical systems, which efficiently generates Feynman paths with
fixed endpoints, from a (low-dimensional) latent space and by targeting a
desired density of paths in the Euclidean space-time. With such path
generators, the Euclidean propagator as well as the ground-state wave function
can be estimated efficiently for a generic potential energy. Our work provides
an alternative approach for calculating the quantum propagator and the
ground-state wave function, paves the way toward generative modeling of quantum
mechanical Feynman paths, and offers a different perspective to understand the
quantum-classical correspondence through deep learning.
