Fig. 3: Assessment of symmetry-awareness of molecular generative artificial intelligence.

a Illustration of the adversarial purification experiments used to assess the symmetry awareness of the models. A molecule with rich symmetries is initially attacked by a model-specific forward diffusion process, during which its symmetries are gradually lost due to blurring with white noise, and then restored by the backward diffusion process learned by the model. A model trained on a dataset which contains high-symmetry molecules is expected to restore as many symmetry elements as possible after the backward diffusion process. The upper panel corresponds to the asynchronous multimodal diffusion schedule (as in MolEdit), and the lower panel corresponds to the synchronous diffusion schedule (as in the baseline E(3) equivariant diffusion model, EDM²⁴). b The loss of symmetries (the decreased number of symmetry elements after adversarial purification experiments, normalized with respect to the original molecules) varies across different forward attack diffusion time steps of MolEdit and EDM model. For each noise scale, we sampled 1024 forward and backward diffusion processes. Data are shown as median, with error bars representing the first and third quartiles (Q1 and Q3). c MolEdit produces physically valid molecules with high symmetry in alignment with the dataset distribution. Source data are provided as a Source Data file.