A denoising diffusion model is employed for generating crystal structures which are represented as 𝐶 = (𝐴, 𝑋, 𝐿), where 𝐴 ∈ ℤ @ represent the atom types, 𝑋 ∈ ℤ @×A denote the fractional coordinates of the atoms within the unit cell, and L ∈ ℤ A×A is the lattice matrix defining the unit cell dimensions and angles.