  We propose a novel machine learning method for sampling from the
high-dimensional probability distributions of Lattice Field Theories, which is
based on a single neural ODE layer and incorporates the full symmetries of the
problem. We test our model on the $\phi^4$ theory, showing that it
systematically outperforms previously proposed flow-based methods in sampling
efficiency, and the improvement is especially pronounced for larger lattices.
Furthermore, we demonstrate that our model can learn a continuous family of
theories at once, and the results of learning can be transferred to larger
lattices. Such generalizations further accentuate the advantages of machine
learning methods.
