Dynamic Wyckoff symmetry constraints for fractional-coordinate diffusion

Establish dynamically varying symmetry constraints on fractional coordinates in asymmetric units as the associated Wyckoff positions and space groups change at each diffusion step, enabling jointly evolving fractional coordinates and Wyckoff positions to satisfy the appropriate Wyckoff symmetry constraints during training and sampling.

Background

SbCD jointly evolves fractional coordinates and Wyckoff positions rather than relying on fixed Wyckoff positions throughout training and inference. Existing approaches such as DiffCSP++, SGFM, and SGEquiDiff impose space-group constraints on fractional coordinates using fixed or previously sampled Wyckoff positions, whereas SbCD must accommodate Wyckoff symmetry constraints that change dynamically as the diffusion process evolves between space groups.

The authors explicitly identify the enforcement of these dynamically changing constraints as non-trivial and leave it for future investigation. The problem is therefore to develop a principled mechanism that maintains valid Wyckoff symmetry for fractional coordinates throughout the joint diffusion of coordinates and Wyckoff positions.