Network parameters of continuous normalizing flows trained for the \(\varphi^4\) theory. Corresponding article: Learning Lattice Quantum Field Theories with Equivariant Continuous Flows [2207.00283] Abstract: 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 \(\varphi^4\) 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.