Likelihood-Based One-Class Scoring in CWT Latent Space for Confusion-Limited LISA Gravitational-Wave Detection

We study one-class scoring for resolvable-source detection in confusion-limited LISA time-series data represented as continuous-wavelet-transform (CWT) scalograms. With data generation and preprocessing held fixed, we benchmark geometry-style scoring against likelihood-style latent-density scoring, while also evaluating morphology-augmented and contrastive variants. Geometry-only and geometry+morphology methods provide modest gains over the reconstruction baseline, and contrastive variants do not show stable improvement. Likelihood scoring on AE latents is consistently stronger: across three seeds, latent-only likelihood reaches ROC-AUC $0.8555\pm 0.0181$ and PR-AUC $0.9219 \pm 0.0118$, versus ROC-AUC $0.7663 \pm 0.0450$ and PR-AUC $0.8667 \pm 0.0255$ for AE+manifold. These results indicate that explicit latent density modeling can outperform local off-manifold distance in this confusion-limited regime. We provide seed-based comparisons, unified ROC/PR visual summaries, and reproducible experimental artifacts to support follow-on work in LISA anomaly detection.