Reliable in-situ monitoring of Laser Powder Bed Fusion (LPBF) remains challenging because acoustic emission (AE) signals exhibit data drift under changes in material composition, scan parameters, and sensor conditions. We propose an explainable Learnable Wavelet Scattering (LWS) framework that learns physics-consistent time–frequency representations and enables cross-domain generalization via zero-shot transfer learning. A trainable Morlet wavelet bank adaptively refines its center frequencies and bandwidths to capture process-specific spectral patterns. Multi-scale scattering coefficients are projected into a compact latent space and classified into melt-pool regimes: lack of fusion (LoF), conduction, and keyhole. Bayesian optimization selects an effective parameter configuration, achieving ∼97% validation accuracy with stable convergence. Model-level causal influence quantifies band-wise contributions, showing that keyhole dynamics are dominated by low-frequency bands, whereas conduction and LoF rely on mid-to-higher frequencies. The learned filters converge toward physically meaningful bands most responsive to melt-pool transitions, providing actionable guidance for sensor bandwidth selection and tuning. Zero-shot transfer to an unseen dataset maintains high performance without retraining, indicating domain-invariant embeddings. Overall, LWS delivers an interpretable and robust AE-based monitoring approach for LPBF under realistic process drift. The framework is lightweight, requires only AE waveforms, and can be integrated into digital-twin workflows for scalable transferable process-state recognition.