  This paper proposes a new 3D molecule generation framework, called GOAT, for
fast and effective 3D molecule generation based on the flow-matching optimal
transport objective. Specifically, we formulate a geometric transport formula
for measuring the cost of mapping multi-modal features (e.g., continuous atom
coordinates and categorical atom types) between a base distribution and a
target data distribution. Our formula is solved within a unified, equivalent,
and smooth representation space. This is achieved by transforming the
multi-modal features into a continuous latent space with equivalent networks.
In addition, we find that identifying optimal distributional coupling is
necessary for fast and effective transport between any two distributions. We
further propose a flow refinement and purification mechanism for optimal
coupling identification. By doing so, GOAT can turn arbitrary distribution
couplings into new deterministic couplings, leading to a unified optimal
transport path for fast 3D molecule generation. The purification filters the
subpar molecules to ensure the ultimate generation performance. We
theoretically prove the proposed method indeed reduced the transport cost.
Finally, extensive experiments show that GOAT enjoys the efficiency of solving
geometric optimal transport, leading to a double speedup compared to the
sub-optimal method while achieving the best generation quality regarding
validity, uniqueness, and novelty.
