The diffusion model operates with forward and backward processes. The forward process involves gradually adding random noise (typically Gaussian noise) to the individual representations of crystal structures over a series of steps, transitioning the crystal structure (C0) into a completely random state (CT). The denoising model, which is based on an equivariant GNN ensuring E(3) symmetry, predicts the noise that was added at each step in the forward process and iteratively removes it, thereby reconstructing the original data from pure noise. The details of the diffusion model implementation are provided in the Method section.