  Flows are exact-likelihood generative neural networks that transform samples
from a simple prior distribution to the samples of the probability distribution
of interest. Boltzmann Generators (BG) combine flows and statistical mechanics
to sample equilibrium states of strongly interacting many-body systems such as
proteins with 1000 atoms. In order to scale and generalize these results, it is
essential that the natural symmetries of the probability density - in physics
defined by the invariances of the energy function - are built into the flow.
Here we develop theoretical tools for constructing such equivariant flows and
demonstrate that a BG that is equivariant with respect to rotations and
particle permutations can generalize to sampling nontrivially new
configurations where a nonequivariant BG cannot.
