GFlowNets build feasible designs for directed evolution campaigns

In a directed evolution campaign the budget, not the size of the search space, is the binding constraint: a few hundred assays, a plate of variants a round, to improve an enzyme or a binder. When a hard feasibility constraint applies, the pipelines used today — a genetic algorithm, machine-learning-guided design (MLDE), CMA-ES over a continuous relaxation — cannot represent which sequences are buildable; they draw candidates and subsequently reject the illegal ones, which wastes budget on unmakeable variants and, when feasible designs are scarce, leaves the method unable to run at all. Building each design move by move under a mask that permits only legal continuations removes the bottleneck entirely, since every proposal is then feasible by construction. We present EvoGFN, a GFlowNet that constructs designs over the construction graph rooted at a campaign's parent, enforcing feasibility by masking each move, and test it at wet-lab budgets against those pipelines. Its mean fitness is the highest on every task in our synthetic suite, decisively where few sequences are feasible, though a CMA-ES baseline reaches the same ceiling on the task where both saturate; on the two empirical landscapes it leads narrowly. Throughout it proposes only feasible designs, where the pipelines it is compared against spend much of their budget on designs that cannot be built. The same advantage holds on a real, structure-derived constraint, a folding-stability predicate on the GB1 landscape thresholded on predicted ΔΔG, where a proximal baseline matches it on fitness only at the tightest threshold. Controls separate mask from policy and trace the dependence on predictor quality: porting the mask to a plain genetic algorithm gives it full feasibility and a fitness gain, untraining our own policy costs it little except where the feasible set is small, and injecting noise into the fitness predictor that ranks candidates before any assay is spent erodes the lead only where that predictor was informative. The advantage narrows where the feasibility predicate is simple enough to admit an exact projection — a dynamic program that recovers the best design under an additive decoding score, though not under the true fitness — against which the learned sampler keeps a small edge on some tasks and ties on others. A masked sampler gains most where the constraint is strict, and where an exact decoder can be built it closes much of that gain. Where the constraint couples every position, a local mask reaches almost none of the legal designs, and we leave that regime as an open frontier.