Beyond Synthetic Data: Generative Deep Learning from ECG Modeling and Anomaly Detection to Machine Unlearning

Generative modeling matured along seemingly distinct lines: adversarial objectives, energy minimization, and invertible or continuous flows. However, these approaches are actually better seen as distinct views of one single geometric and probabilistic challenge, specifically transporting probability mass from a simple distribution to a complex one. This work develops and advances this unifying perspective both theoretically and empirically. It shows how classic objectives, such as adversarial training, maximum likelihood, score matching, and diffusion, can all be read as optimizing distances within a shared space of probability measures differing mainly in the choice of metric and path parameterization. Building on this view, the thesis solidifies continuous generative flows as a scalable method, articulating principles such as conditional flow matching and other trajectory design techniques. These advancements avoid costly simulation while successfully preserving the approach’s original geometric interpretability. In biomedical signal modeling, we present high-fidelity electrocardiogram generators that preserve clinically salient morphology and variability; a multi-modal, patient-specific mapping between 12-lead ECG and vectorcardiography that improves downstream classification; and a geometric–probabilistic approach to anomaly detection in multivariate time series based on the effort required to transport sequences into learned normal flows, providing both accuracy and interpretability. Finally, the thesis casts machine unlearning as distributional transport: by integrating energy-based reweighting into flow objectives, it achieves targeted removal of content while retaining non-target behavior, offering a practical route toward privacy-aware, auditable generative systems. The contributions herein confirm that a unified framework of geometry and probability serves as a coherent language for all aspects of generative modeling: design, training, and querying. This perspective unifies leading methodologies and furnishes generative systems with enhanced capabilities for deployment in clinical and societal applications.