Research on rock permeability plays a crucial role in understanding fluid flow in geological formations, which contributes significantly to addressing challenges in sustainable energy production and CO₂ sequestration. Currently, numerous advanced techniques are used for predicting permeability in porous media, including experimental methods, numerical simulations, and deep learning approaches. However, existing methods often face difficulties in accurately predicting properties across multiple scales. In this study, we propose an integrated workflow that combines deep learning and physical constraints to achieve accurate and multiscale permeability prediction. The workflow begins with a 3D pore-segmentation stage, where a novel architecture is developed, achieving a segmentation accuracy exceeding 0.99. We then introduce a progressive transfer learning approach to directly predict permeability at varying scales. This method achieves R² scores of 0.94, 0.83, and 0.84 for subvolumes of 150³ voxels, 300³ voxels, and 600³ voxels (2.25 µm/voxel), respectively. To address reduced accuracy for larger volumes, we further develop a physics-constrained upscaling method. This approach enhances predictive performance, achieving R² scores of 0.98 for transitions from subvolumes of 150³ voxels to 300³ voxels and 0.99 for transitions from 300³ voxels to 600³ voxels. This research underscores the potential of integrating advanced deep learning with physics-informed constraints, providing a robust framework for accurate and scalable permeability prediction in digital rock physics and paving the way for core-scale applications and future studies.