  Normalizing flows are exact-likelihood generative neural networks which
approximately transform samples from a simple prior distribution to samples of
the probability distribution of interest. Recent work showed that such
generative models can be utilized in statistical mechanics to sample
equilibrium states of many-body systems in physics and chemistry. To scale and
generalize these results, it is essential that the natural symmetries in the
probability density -- in physics defined by the invariances of the target
potential -- are built into the flow. We provide a theoretical sufficient
criterion showing that the distribution generated by \textit{equivariant}
normalizing flows is invariant with respect to these symmetries by design.
Furthermore, we propose building blocks for flows which preserve symmetries
which are usually found in physical/chemical many-body particle systems. Using
benchmark systems motivated from molecular physics, we demonstrate that those
symmetry preserving flows can provide better generalization capabilities and
sampling efficiency.
