Evolutionary One-Step Generators: Fast and Diverse Sampling for Discrete Design

Several discrete design tasks, such as molecular discovery, require diverse collections of useful candidates at low computational cost. High validity alone does not guarantee a useful candidate library: repeatedly generating the same valid structures leaves few distinct alternatives. Training for both feasibility and diversity is challenging because many relevant criteria can only be evaluated after hard decoding. To address this challenge, we propose EGO (Evolutionary Generators with One-step inference), a framework for training compact generators directly on discrete outputs. The method combines distribution matching with structural constraints and optional diversity or history-dependent rewards, using antithetic low-rank evolution strategies without requiring criterion-specific differentiable surrogates. Once trained, the generator produces the entire graph in a single neural-network evaluation. On molecular generation benchmarks, our compact generator achieves over $50\times$ the valid-and-unique yield per estimated dense operation compared to recent one-step flow-map baselines while retaining high chemical validity. In scaffold completion, EGO achieves an observed $44.3\times$ speedup over MoLeR in generation to SMILES and produces approximately $10\times$ as many filter-passing proposals within matched time budgets for generation and screening Beyond chemistry, EGO produces $1.54\times$ as many distinct held-out elite architectures as relaxed gradient training on NAS-Bench-101. The low generation cost may enable real-time candidate generation across discrete design tasks, supporting interactive exploration of constrained design spaces and rapid construction of candidate sets for downstream evaluation.