Conditional diffusion machine-learning framework for mapping valence electron distribution from convergent beam electron diffraction

Quantitative convergent beam electron diffraction (QCBED) enables determination of aspherical valence electron (VE) distributions but requires solving a highly nonlinear inverse problem with many parameters, making it time-consuming and difficult to apply to complex systems. Here, the authors introduce a machine-learning framework that replaces traditional refinement. Using a large synthetic CBED dataset generated by Bloch-wave simulations, they train a conditional diffusion model to infer multipole density formalism for VE mapping, from CBED patterns alone. This approach enables practical, high-throughput, and in situ QCBED, opening new opportunities for real-time VE mapping and their correlation with functional responses in quantum materials.