Generative inverse estimation of 3D atomic coordination from near-edge spectra via equivariant diffusion models

Extracting 3D atomic coordinates from spectroscopic data is a longstanding inverse problem. We present an equivariant diffusion model that generates the distribution of site-specific 3D structures directly from near-edge spectra (ELNES/XANES). Trained on Si–O crystals, the model achieves radial accuracy comparable to Extended X-ray Absorption Fine Structure (EXAFS) (bond-distance MAE ~ 0.04 Å) but with superior coordination number precision (errors < 2.0% vs. EXAFS ~ 20%). Crucially, it reconstructs full 3D geometries including bond angles, overcoming the limitations of 1D radial distribution analysis. The model shows encouraging, composition-dependent transferability to amorphous systems despite being trained exclusively on crystalline lattices. Application to experimental O K -edge spectra from α -quartz, cristobalite and stishovite demonstrates feasibility for experimental spectra. This generative approach goes beyond conventional template matching, which retrieves structures from predefined references, by enabling the exploration of candidate 3D structures within a learned structural space and providing a step toward automated, quantitative, 3D local-structure inference from spectroscopic data.