Expanding Generable Sets with One-Step Generators

Generative scientific discovery aims to produce valid designs beyond the support of a static pretrained model. The goal is to expand its generable set over the valid design space using only black-box verifier feedback. Existing methods steer multi-step samplers toward unexplored regions, but their sampler implicitly determines how far queries travel and how strongly they remain near the initial model scope. We introduce Expanse, which grows the generable set with a 1-step generator by searching directly in design space with explicit control over exploration and travel. Rejected designs push the generator away from invalid regions, while inference settings trade coverage against validity. We also derive a reachability bound giving a necessary condition for a disconnected valid region to be found, in terms of generator support and query travel. With the same verifier budget and one function evaluation (NFE) per sample, Expanse covers $90.7\%$ of the connected valid region compared to $78.8\%$ for the multi-step baseline, while achieving higher coverage and validity overall.