Difference Transition Matching for Crystal Structure Generation

Generative models of crystal structures are a foundation of the inverse design of materials, but it remains an open problem to develop a model that generates novel and thermodynamically stable structures of high crystallographic symmetry while keeping the generative process unconstrained. We present a generative model built on Difference Transition Matching, which realizes the transition kernel of the sampler as a lightweight inner flow matching model conditioned on the current state. Every update of the atom types, the fractional coordinates, and the lattice is drawn from this kernel, and no degree of freedom of the state is restricted at any step of the generation. Trained on MP-20, the model reaches the crystallographic symmetry of a diffusion-based crystal generator while evaluating its backbone $64$ times per crystal and sampling $15$ times faster than MatterGen, and lowering the noise of the sampler raises that symmetry further at the cost of novelty. Its share of metastable, unique, and novel structures does not yet reach that of the strongest diffusion model baseline, and closing that gap is the task ahead.