Factorized Initial Noise Optimization with Diffusion and Flow Priors for Multi-Objective Scientific Inverse Design

Scientific inverse design seeks structures in a vast design space that achieve a target property while satisfying domain-specific constraints. Generative models provide expressive priors over such design spaces, but existing inference-time methods steer generation toward either the target property or the constraints. We propose factorized initial noise optimization (FINO), which casts constrained inverse design as optimization over the initial noise of a pretrained generative model, and treats the reward and constraints as separate objectives. At each iteration, FINO first verifies whether the current iterate lies within the feasible set: if falls outside, then takes a constraint-restoration step; otherwise take a reward step toward the target property. This factorization confines reward optimization to the feasible region and requires no retraining, no modification of the sampling trajectory, and no constraint weights as trade-off. On topological photonic inverse design and molecule generation, FINO achieves low target-property error without sacrificing constraint satisfaction, and even robustly remains effective for target property values beyond the training distribution that of greatest scientific interest.