Generative Inverse Estimation of 3D Atomic Coordination from Near-Edge Spectra via Equivariant Diffusion Models

TL;DR

This paper introduces an equivariant diffusion model that accurately reconstructs 3D atomic structures from near-edge spectra, surpassing traditional methods in precision and generalization, enabling automated structure determination from spectroscopic data.

Contribution

The paper presents a novel generative equivariant diffusion model capable of directly estimating 3D atomic coordinates from spectroscopic data, including bond angles, with high accuracy and out-of-distribution robustness.

Findings

Achieves radial accuracy comparable to EXAFS (RMSD ~0.06 Å).

Provides superior coordination number precision (<4.3% error).

Successfully predicts structures in amorphous systems and from experimental spectra.

Abstract

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.