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

Nikolaj Rønne, Tejs Vegge, Arghya Bhowmik

TL;DR

GO-Diff presents a data-free diffusion framework for global structure optimization on atomic potential energy surfaces by training with a Boltzmann-weighted score-matching loss and a self-sampling loop. It avoids explicit relaxation and force labels, instead using energy evaluations and annealing (temperature $T$) together with force-field guidance to efficiently concentrate samples in thermodynamically favorable regions. The method enables amortized optimization through transfer of pretrained models across related systems and demonstrates superior sample efficiency versus random structure search in Pt surface tasks. These features position diffusion-based generative models as practical engines for atomistic design, with potential extensions to multi-objective and compositional optimization.

Abstract

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.

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

TL;DR

GO-Diff presents a data-free diffusion framework for global structure optimization on atomic potential energy surfaces by training with a Boltzmann-weighted score-matching loss and a self-sampling loop. It avoids explicit relaxation and force labels, instead using energy evaluations and annealing (temperature ) together with force-field guidance to efficiently concentrate samples in thermodynamically favorable regions. The method enables amortized optimization through transfer of pretrained models across related systems and demonstrates superior sample efficiency versus random structure search in Pt surface tasks. These features position diffusion-based generative models as practical engines for atomistic design, with potential extensions to multi-objective and compositional optimization.

Abstract

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.
Paper Structure (30 sections, 8 equations, 2 figures, 5 tables, 1 algorithm)

This paper contains 30 sections, 8 equations, 2 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methods
  3. Training loop.
  4. Boltzmann-weighted score matching.
  5. Annealing strategy.
  6. Force-field guidance.
  7. Diffusion process.
  8. Results
  9. Pt-addatom on stepped Pt surface.
  10. Pt-heptamer on Pt(111).
  11. Discussion
  12. Extending to multi-objective or compositional design.
  13. Limitations
  14. Samples, temperature profile and training steps.
  15. Scalability.
  16. ...and 15 more sections

Figures (2)

  • Figure 1: Addatom optimization on a stepped Pt surface. (a) Projected 2D energy surface for different addatom placements. Colored dots indicate buffer samples, with color denoting annealing temperature (red = high, blue = low). (b) Evolution of buffer structure energies during annealing. Sampling gradually concentrates in low-energy basins.
  • Figure 2: Benchmarking GO-Diff on Pt-heptamer discovery. Mean best energy over eight independent experiments with faint lines showing the moving average evaluate energy of each run (Only plotted for GO-Diff and GO-Diff + Transfer). Crosses indicate discovery of the Pt-heptamer. GO-Diff rapidly improves, while RSS stagnates. Transfer learning further accelerates convergence.