GO-Diff: Data-free and amortized global structure optimization

We introduce GO-Diff, a diffusion-based method for global structure optimization that learns to directly sample low-energy atomic configurations without requiring prior data or explicit relaxation. GO-Diff is trained from scratch using a Boltzmann-weighted score-matching loss, leveraging only the known energy function to guide generation toward thermodynamically favorable regions. The method operates in a two-stage loop of self-sampling and model refinement, progressively improving its ability to target low-energy structures. Compared to traditional optimization pipelines, GO-Diff achieves competitive results with significantly fewer energy evaluations. Moreover, by reusing pretrained models across related systems, GO-Diff supports amortized optimization - enabling faster convergence on new tasks without retraining from scratch.