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 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) (RMSD ~0.06 {\AA}) but with superior coordination number precision (errors < 4.3% vs. EXAFS ~20%). Crucially, it reconstructs full 3D geometries including bond angles, overcoming the limitations of 1D radial distribution analysis. The model demonstrates robust out-of-distribution generalization, accurately predicting local structures in amorphous systems despite being trained exclusively on crystalline lattices. Application to experimental O K-edge spectra from {\alpha}-quartz validates practical applicability. This generative approach outperforms template matching and establishes automated, quantitative 3D structure determination from spectroscopic data.