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 encoding and 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.