Recent advances in neural interfacing have enabled significant improvements in human-computer interaction, rehabilitation, and neuromuscular diagnostics. Motor unit (MU) decomposition from surface electromyography (sEMG) is a key technique for extracting neural drive information, but traditional blind source separation (BSS) methods fail to incorporate biophysical constraints, limiting their accuracy and interpretability. In this work, we introduce a novel Biophysical-Model-Informed Source Separation (BMISS) framework, which integrates anatomically accurate forward EMG models into the decomposition process. By leveraging MRI-based anatomical reconstructions and generative modeling, our approach enables direct inversion of a biophysically accurate forward model to estimate both neural drive and motor neuron properties in an unsupervised manner. Empirical validation in a controlled simulated setting demonstrates that BMISS achieves higher fidelity motor unit estimation while significantly reducing computational cost compared to traditional methods. This framework paves the way for non-invasive, personalized neuromuscular assessments, with potential applications in clinical diagnostics, prosthetic control, and neurorehabilitation.