Fig. 1: Overview of the diffusion model and optimal transport framework for generating TSs.

a, Learning the joint distribution of structures in elementary reactions (reactant in red, TS in yellow and product in blue). A forward diffusion process brings the joint distribution at t = T to independent normal distribution at t = 0. Backwards, an object-aware SE(3) GNN is trained with denoising objective to recover the normal distribution to the original joint distribution. b, Stochastic inference with inpainting in OA-ReactDiff. Starting with samples drawn from normal distribution, the trained GNN is applied to denoise the reactant, TS and product. A diffusion process on reactant and product is combined with the denoising process to ensure the end-point reactant and product at t = T are the same as the true reactant and product. c, Deterministic inference with React-OT. Both the reactant and product are unchanged throughout the entire process from t = 0 to t = T. The linear interpolation of reactant and product is provided as the initial guess structure at t = 0, followed by optimal (that is, linear) transport to the final TS. Atoms are coloured as follows: C, grey; N, blue; O, red; H, white.