To train ZeoDiff, zeolite structures with sufficient methane accessibility were selected from the IZA and the PCOD database. The methane Henry coefficient served as the metric for evaluating methane accessibility, and a total of 99,362 structures with a Henry coefficient greater than 10 -6 mol kg -1 Pa -1 were selected. Among these selected structures, 63,426 structures (102 from IZA and 63,324 from PCOD) with orthogonal cell angles were further refined and utilized. The structures were randomly divided into two sets (31,713 each), with one set allocated for training and the other set for validation purposes in generating new zeolites. To impose invariances to the model, various data augmentation methods (i.e. translation and rotation) were employed as described in Supplementary section 1.