Generative diffusion model for surface structure discovery

We present a generative diffusion model specifically tailored to the discovery of surface structures. The generative model takes into account substrate registry and periodicity by including masked atoms and $z$-directional confinement. Using a rotational equivariant neural network architecture, we design a method that trains a denoiser-network for diffusion alongside a force-field for guided sampling of low-energy surface phases. An effective data-augmentation scheme for training the denoiser-network is proposed to scale generation far beyond training data sizes. We showcase the generative model by investigating silver-oxide phases on Ag$(111)$ where we are able to rediscover the ``$\mathrm{Ag}_6$ model'' of $p(4\times4)\mathrm{O/Ag}(111)$ that took scientist years to uncover by means of human intuition.