Designing efficient quantum circuits is a central bottleneck to exploring the potential of quantum computing, particularly for noisy intermediate-scale quantum (NISQ) devices, where circuit efficiency and resilience to errors are paramount. The search space of gate sequences grows combinatorially, and handcrafted templates often waste scarce qubit and depth budgets. We introduce \textsc{FlowQ-Net} (Flow-based Quantum design Network), a generative framework for automated quantum circuit synthesis based on Generative Flow Networks (GFlowNets). This framework learns a stochastic policy to construct circuits sequentially, sampling them in proportion to a flexible, user-defined reward function that can encode multiple design objectives such as performance, depth, and gate count. This approach uniquely enables the generation of a diverse ensemble of high-quality circuits, moving beyond single-solution optimization. We demonstrate the efficacy of \textsc{FlowQ-Net} through an extensive set of simulations. We apply our method to Variational Quantum Algorithm (VQA) ansatz design for molecular ground state estimation, Max-Cut, and image classification, key challenges in near-term quantum computing. Circuits designed by \textsc{FlowQ-Net} achieve significant improvements, yielding circuits that are 10$\times$-30$\times$ more compact in terms of parameters, gates, and depth compared to commonly used unitary baselines, without compromising accuracy. This trend holds even when subjected to error profiles from real-world quantum devices. Our results underline the potential of generative models as a general-purpose methodology for automated quantum circuit design, offering a promising path towards more efficient quantum algorithms and accelerating scientific discovery in the quantum domain.

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