  Advanced generative model (e.g., diffusion model) derived from simplified
continuity assumptions of data distribution, though showing promising progress,
has been difficult to apply directly to geometry generation applications due to
the multi-modality and noise-sensitive nature of molecule geometry. This work
introduces Geometric Bayesian Flow Networks (GeoBFN), which naturally fits
molecule geometry by modeling diverse modalities in the differentiable
parameter space of distributions. GeoBFN maintains the SE-(3) invariant density
modeling property by incorporating equivariant inter-dependency modeling on
parameters of distributions and unifying the probabilistic modeling of
different modalities. Through optimized training and sampling techniques, we
demonstrate that GeoBFN achieves state-of-the-art performance on multiple 3D
molecule generation benchmarks in terms of generation quality (90.87% molecule
stability in QM9 and 85.6% atom stability in GEOM-DRUG. GeoBFN can also conduct
sampling with any number of steps to reach an optimal trade-off between
efficiency and quality (e.g., 20-times speedup without sacrificing
performance).
