Multi-Domain Discrete Graph Generation

Current graph generative models are overwhelmingly trained on a single input distribution and then sampled to reproduce it. In this work, we propose extending graph generation into multiple structural domains. Under our proposed multi-domain setting, existing single-domain models, even when given a domain label, sample every domain from a single shared internal distribution. In preliminary benchmarking, we demonstrate the existing model paradigm fails, even when state-of-the-art models are trained with multi-domain awareness. To address this, we propose Discrete-interpolative Graph Generation or DiG${}^2$, a graph diffusion model specially-designed to internalize domain-conditioning along a bridged discrete path. Benchmarking demonstrates that DiG${}^2$ achieves at least $85\%$ sampling accuracy across all tested domains, while current domain-conditioned models suffer mode-collapse. Additionally, DiG${}^2$ has the unique capacity for interpolating between domains and extrapolating to unseen structures. This interpolation mechanism uncovers targeted molecule generation for achieving comparable performance relative to a $38$-times larger models.