  Molecules are frequently represented as graphs, but the underlying 3D
molecular geometry (the locations of the atoms) ultimately determines most
molecular properties. However, most molecules are not static and at room
temperature adopt a wide variety of geometries or $\textit{conformations}$. The
resulting distribution on geometries $p(x)$ is known as the Boltzmann
distribution, and many molecular properties are expectations computed under
this distribution. Generating accurate samples from the Boltzmann distribution
is therefore essential for computing these expectations accurately. Traditional
sampling-based methods are computationally expensive, and most recent machine
learning-based methods have focused on identifying $\textit{modes}$ in this
distribution rather than generating true $\textit{samples}$. Generating such
samples requires capturing conformational variability, and it has been widely
recognized that the majority of conformational variability in molecules arises
from rotatable bonds. In this work, we present VonMisesNet, a new graph neural
network that captures conformational variability via a variational
approximation of rotatable bond torsion angles as a mixture of von Mises
distributions. We demonstrate that VonMisesNet can generate conformations for
arbitrary molecules in a way that is both physically accurate with respect to
the Boltzmann distribution and orders of magnitude faster than existing
sampling methods.
