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Synthetic biology aims to achieve predictable, programmable control over living systems by designing and engineering biological components and functions. Over the past 25 years, the field has advanced from foundational molecular tools to increasingly complex systems-level architectures. A new inflection point has emerged with the integration of generative artificial intelligence (AI), catalyzing a fundamental shift in how biological design is conceived and executed. Generative AI now enables the data-driven creation of novel designs with predictable functionality and context-aware precision. Here, we examine the convergence of synthetic biology and generative AI, highlighting key innovations at this emerging frontier of deep generative design across biological parts and systems. We discuss how design frameworks have evolved and outline the opportunities and challenges that lie ahead, spanning biomolecular elements, genetic circuits, and genomes. Finally, we propose a roadmap for how generative AI can unlock a new era of predictable, programmable synthetic biological systems.