Current multiple sclerosis (MS) diagnosis relies primarily on focal white matter lesions (WMLs), which are frequently mimicked by other conditions. Normal-appearing white matter (NAWM) harbours complementary pathological information but remains clinically underutilised because NAWM alterations are macroscopically occult on routine scans and require non-routine quantitative imaging to visualise. Here, we show that NAWM-related diagnostic information can be recovered from routine structural MRI using a cross-modal deep-learning model. We developed DeepMS, a model co-trained on diffusion and structural MRI that operates solely on structural MRI at deployment. DeepMS achieved ROC-AUCs of 0.968 internally (n=837) and 0.940-0.974 across two international external cohorts (n=293 and n=1,756). In a multi-reader study, DeepMS outperformed the 2024 McDonald criteria imaging biomarkers. DeepMS retained robust performance after digital lesion removal and exhibited NAWM-dominant activation maps. Combined with established imaging biomarkers, DeepMS improved sensitivity (92.1% vs 74.8%) while maintaining high specificity (95.6% vs 92.3%) compared with corresponding biomarker composite based on the 2024 McDonald criteria. By decoding latent NAWM signals from routine scans and integrating them with WML features, this framework can potentially advance MS diagnosis beyond the current lesion-centric paradigm.