Designing sequences such as nucleic acids and proteins with desired properties is a fundamental challenge in biology. Due to the vast, discrete nature of sequence spaces and the high cost of experimental evaluation, offline computational sequence design plays a crucial role in proposing novel sequences before costly wet-lab validation. In practice, it is also essential that proposed designs are diverse to increase the likelihood of downstream experimental success. This motivates methods that balance performance, novelty, and diversity, whilst mitigating against uncertainty inherent to offline optimization. Quality-Diversity optimization (QD) can discover diverse, high-performing solutions, making it well suited to this problem, but its elitist nature makes reliable exploration under uncertainty challenging. To address this, we introduce Prior-guided Offline MAP-Elites (POME), an uncertainty-aware QD framework explicitly adapted to the offline regime. Our method leverages foundation models as priors to guide search toward biologically plausible regions and enable robust exploration under uncertainty. Across three sequence design tasks, POME consistently improves both performance and diversity over prior offline QD methods, and achieves the most reliable balance compared to offline MBO baselines, obtaining the best performance on two tasks and the second-best on the third, while maintaining high diversity and novelty.

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