Inverse design of valley photonic crystals via a dual-stage physics-guided diffusion transformer

Inverse design has become a powerful tool for the study of topological photonic devices, yet existing generative frameworks face fundamental limitations when applied to valley photonic crystals (VPCs). Convolutional backbones struggle to capture long-range spatial correlations that underpin the topological invariants and bandgap formations, while latent diffusion models suffer from boundary distortions due to lossy compression. Here, we propose a dual-stage physics-guided diffusion framework for the inverse design of VPCs, supplying high-fidelity geometric features for accurate bandgap and topological invariant predictions. By employing a Diffusion Transformer (DiT) backbone in the initial stage, the model is enabled to learn global structural coherence, which is critical for representing the nonlocal symmetry conditions that define topological phases. To address the diverse and computationally demanding landscapes of design constraints, we introduce a fine-tuning stage with the adoption of a low-rank adapter (LoRA), allowing the pretrained DiT to be efficiently adapted to the target conditions with minimal retraining cost and high generative fidelity. Trained on a dataset of 20000 VPC samples, our framework achieves a low relative error (< 10%) across a moderate bandgap range (5%∼20%) in closed-loop simulations without variational autoencoders, whereas the near-gap-closing regime (< 5%) remains challenging. For a gap-ratio condition of 0.076, we demonstrate low errors of 3.68% ± 0.34% (gap-ratio) and 3.93% ± 0.51% (gap) across five random seeds, showing high robustness of the proposed workflow. We further verify the practical utility of the generated VPCs by constructing topological waveguides, exhibiting high optical transmissions (> 0.8) even with the defects or sharp bends. Our work shows that the principled combination of DiT and LoRA can be physically motivated to address the key challenges in inverse design of topological photonics, offering a scalable and balanced paradigm beyond incremental gains over conventional models.