  Billions of organic molecules are known, but only a tiny fraction of the
functional inorganic materials have been discovered, a particularly relevant
problem to the community searching for new quantum materials. Recent
advancements in machine-learning-based generative models, particularly
diffusion models, show great promise for generating new, stable materials.
However, integrating geometric patterns into materials generation remains a
challenge. Here, we introduce Structural Constraint Integration in the
GENerative model (SCIGEN). Our approach can modify any trained generative
diffusion model by strategic masking of the denoised structure with a diffused
constrained structure prior to each diffusion step to steer the generation
toward constrained outputs. Furthermore, we mathematically prove that SCIGEN
effectively performs conditional sampling from the original distribution, which
is crucial for generating stable constrained materials. We generate eight
million compounds using Archimedean lattices as prototype constraints, with
over 10% surviving a multi-staged stability pre-screening. High-throughput
density functional theory (DFT) on 26,000 survived compounds shows that over
50% passed structural optimization at the DFT level. Since the properties of
quantum materials are closely related to geometric patterns, our results
indicate that SCIGEN provides a general framework for generating quantum
materials candidates.
