Biomolecular networks underpin emerging technologies in synthetic biology-from robust biomanufacturing and metabolic engineering to smart therapeutics and cell-based diagnostics-and also provide a mechanistic language for understanding complex dynamics in natural and ecological systems. Yet designing chemical reaction networks (CRNs) that implement a desired dynamical function remains largely manual: while a proposed network can be checked by simulation, the reverse problem of discovering a network from a behavioral specification is difficult, requiring substantial human insight to navigate a vast space of topologies and kinetic parameters with nonlinear and possibly stochastic dynamics. Here we introduce GenAI-Net, a generative AI framework that automates CRN design by coupling an agent that proposes reactions to simulation-based evaluation defined by a user-specified objective. GenAI-Net efficiently produces novel, topologically diverse solutions across multiple design tasks, including dose responses, complex logic gates, classifiers, oscillators, and robust perfect adaptation in deterministic and stochastic settings (including noise reduction). By turning specifications into families of circuit candidates and reusable motifs, GenAI-Net provides a general route to programmable biomolecular circuit design and accelerates the translation from desired function to implementable mechanisms.