  Inverse molecular design with diffusion models holds great potential for
advancements in material and drug discovery. Despite success in unconditional
molecule generation, integrating multiple properties such as synthetic score
and gas permeability as condition constraints into diffusion models remains
unexplored. We present the Graph Diffusion Transformer (Graph DiT) for
multi-conditional molecular generation. Graph DiT has a condition encoder to
learn the representation of numerical and categorical properties and utilizes a
Transformer-based graph denoiser to achieve molecular graph denoising under
conditions. Unlike previous graph diffusion models that add noise separately on
the atoms and bonds in the forward diffusion process, we propose a
graph-dependent noise model for training Graph DiT, designed to accurately
estimate graph-related noise in molecules. We extensively validate the Graph
DiT for multi-conditional polymer and small molecule generation. Results
demonstrate our superiority across metrics from distribution learning to
condition control for molecular properties. A polymer inverse design task for
gas separation with feedback from domain experts further demonstrates its
practical utility.
