Fig. 2: Structures and properties of generated a-SiO₂ structures are nearly indistinguishable from simulated ones.

a Comparison between the partial pair distribution functions (PDFs) of simulated (solid lines) and generated (dashed lines) shows that generated structures are quite similar to simulated ones. This close agreement is also seen in other structural metrics, including b distributions of Si-O-Si and O-Si-O bond angles and c ring size distributions. In (c), the error bar is the standard deviation of across six simulated or generated samples. d Elastic properties of generated structures are indistinguishable from the simulated ones. The properties computed here include the bulk modulus (K), shear modulus (G), Young’s modulus (E), and Poisson’s ratio (ν). e Generated structures follow the expected distribution of amorphous environments, as quantified by an information-theoretical strategy.²² The overlap between generated (Gen) and simulated (Sim) distributions of environments (black) is nearly equal to the overlap between simulated and simulated (blue) distributions. In (d and e), the thicker line, box, and whiskers depict the median, interquartile range, and range of the distribution, respectively. f Structures generated without a large external noise schedule cannot reproduce the information content of the reference structures, instead leading to structures with a high number of outlier environments (high entropy). On the other hand, a denoising process that includes an external noise schedule is able to generate more realistic structures.