Quantum generative models constitute an important class of quantum machine learning approaches for preparing complex quantum states and probability distributions, and most existing studies rely on variational quantum circuits with universal logic gates. However, in discrete-variable linear-optical quantum systems, the implementation of universal logic gates typically requires measurement-induced nonlinearities, which are accompanied by substantial ancillary-photon overheads and rapidly decreasing postselection success probabilities. These constraints severely limit the scalability of gate-based generative models on linear-optical platforms. In this work, we develop an interferometer-based quantum optical generative model framework together with a dedicated training methodology for discrete-variable linear-optical systems under postselection constraints. The framework directly optimizes the interferometer matrix while balancing generation fidelity and postselection success probability, enabling the generation of target quantum states and probability distributions with significantly higher success probabilities than gate-based schemes. Furthermore, we introduce an adaptive optimization strategy and a sampling-based training scheme, showing that the proposed framework exhibits good convergence behavior and broad applicability under limited sampling resources. Thus, our work provides a physically feasible pathway toward scalable quantum generative models and in situ training on linear-optical platforms.

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• Quantum algorithms & computation
• Quantum optics