We introduce MxDiffusion, a hybrid physics- and data-driven diffusion-based framework that enables the efficient and highly accurate generation of photonic structures from target optical properties. The improved accuracy is achieved through a two-stage generation strategy, in which the first diffusion model is explicitly trained with Maxwell's equation-based loss to embed physical insight directly into the inverse design process, while the second model maps the physically consistent intermediate representation to the final structural geometry with significantly higher fidelity than solely data-driven approaches. The performance of MxDiffusion is validated on two representative applications: gold pattern optimization for random spectral responses and a tunable bandpass filter design based on a phase change material. In both cases, the proposed framework consistently outperforms a conventional data-driven diffusion model benchmark, particularly for out-of-training distribution design targets and highly constrained resonance conditions. These results demonstrate the efficacy and superiority of MxDiffusion as a general physics-guided inverse design paradigm.
Mondal et al. (Mon,) studied this question.