Deep learning (DL) has emerged as a promising tool for photonic inverse design. Nevertheless, despite the initial success in retrieving spectra of modest complexity with nearly instantaneous readout, DL-assisted design methods often underperform in accuracy compared with advanced optimization techniques and have not proven competitive in handling spectra of practical usefulness. Here, we introduce a tandem optimization model that combines a mixture density network (MDN) and a fully connected (FC) network to inversely design practical thin-film high reflectors. The multimodal nature of the MDN gives access to infinite candidate designs described by probability distributions, which are iteratively sampled and evaluated by the FC network to allow for rapid optimization. We show that the proposed model can retrieve the reflectance spectra of 20-layer thin-film structures. More interestingly, it reproduces with high precision the periodic structures of high reflectors derived from physical principles, even though no such information is included in the training data. Improved designs with extended high-reflectance zones are also demonstrated. Our approach combines the high-efficiency advantage of DL with the optimization-enabled performance improvement, enabling efficient and on-demand inverse design for practical applications.

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