Match the Geometry, Skip the Surrogate: Extreme Low-Budget Optimization in High Dimensions

Low-budget molecular optimization is often framed as Bayesian optimization in a learned latent space, but standard benchmarks typically allow hundreds or thousands of evaluations, whereas a realistic wet-lab round may allow only a few dozen. We revisit this regime using a SELFIES molecular variational autoencoder and GuacaMol objectives at $N=30$ oracle calls. The main finding is not a new surrogate model, but a geometric mismatch in candidate generation. The training latents of the VAE concentrate near a narrow spherical shell, while many high-dimensional optimizers propose candidates from boxes or box-shaped trust regions. Such candidates can leave the decoder's training distribution even when their coordinates look individually plausible. We study a simple geometric constraint, the on-sphere scaffold, that restricts candidate generation to the empirical shell occupied by the VAE training latents. Uniform random search on this shell already outperforms most of the classical box-supported Bayesian optimization baselines. We then introduce two minimal optimizers to probe what remains useful once the support is fixed. GeoWalk performs geodesic local search on the empirical sphere and outperforms every published Bayesian optimization baseline tested. GeoCMA keeps the scaffold but adds covariance learning in a random subspace, becoming preferable when the search representation contains learnable directional or semantic structure, as in LassoBench, NAS-Bench-101 graph-VAE optimization, and GSM8K text-latent prompt optimization. A controlled ablation of three recent Gaussian-process recipes, changing only whether candidates are proposed on the empirical sphere or on the published box-supported domain, shows that the scaffold rather than the surrogate is the load-bearing component. The practical lesson is simple: first match the empirical search support; add a surrogate or covariance learner only when the remaining search space contains directional structure that can be learned from the available budget.