SE(3)-Equivariant Diffusion Graph Nets: Synthesizing Flow Fields by Denoising Invariant Latents on Graphs

Abstract

We introduce SE(3)-equivariant diffusion graph nets (SE3-DGNs) for generating physical fields on graphs. SE3-DGNs integrate a SE(3)-equivariant variational graph autoencoder (VGAE) and a diffusion graph net (DGN) to produce high-quality, SE(3)-equivariant flow fields. The S-VGAE learns an invariant latent space that abstracts directional information, and the DGN is trained on this latent space. Equivariant inference requires minimal additional computation, needing only a single evaluation of the edge encoder and node decoder. Demonstrated on laminar vortex-shedding under out-of-distribution Reynolds numbers and fluid domain parameters, SE3-DGNs showed superior sample quality compared to baseline DGNs and latent DGNs. SE3-DGNs can efficiently generate fully-developed flow fields to use as initial conditions for numerical solvers, bypassing the need for simulating transition regimes.