  Generating new molecules is fundamental to advancing critical applications
such as drug discovery and material synthesis. Flows can generate molecules
effectively by inverting the encoding process, however, existing flow models
either require artifactual dequantization or specific node/edge orderings, lack
desiderata such as permutation invariance, or induce discrepancy between the
encoding and the decoding steps that necessitates post hoc validity correction.
We circumvent these issues with novel continuous normalizing E(3)-equivariant
flows, based on a system of node ODEs coupled as a graph PDE, that repeatedly
reconcile locally toward globally aligned densities. Our models can be cast as
message-passing temporal networks, and result in superlative performance on the
tasks of density estimation and molecular generation. In particular, our
generated samples achieve state-of-the-art on both the standard QM9 and
ZINC250K benchmarks.
