Generative modelling under epistemic uncertainty

The deployment of Deep Learning in safety-critical domains is hindered by pathological overconfidence and an inability to distinguish between aleatoric uncertainty (data ambiguity) and epistemic uncertainty (lack of knowledge). This thesis addresses these limitations by establishing a rigorous framework for Random-Set Deep Learning, shifting from point-estimate probabilities to belief functions over the power set of outcomes. Enabled by a novel Budgeting strategy that ensures scalability, this framework allows models to explicitly represent ignorance. While we validate these principles through Random-Set Neural Networks (RS-NN) for classification and a Unified Evaluation Framework, the primary contribution of this work lies in re-imagining Generative AI under epistemic uncertainty. We introduce Random-Set Large Language Models (RS-LLMs), which predict belief functions over token sets to quantify second-order uncertainty, thereby providing a robust mechanism for hallucination detection. Furthermore, we propose Epistemic Generative Adversarial Networks (GANs) and Epistemic Diffusion Models. By modeling the uncertainty of the generation process itself via second-order distributions, these architectures significantly mitigate mode collapse and enhance sample diversity compared to standard baselines. Finally, we demonstrate the practical utility of these generative capabilities in Autonomous Driving. We introduce the ROAD-INTENT dataset and utilize Random-Set Vision Language Models (RS-VLMs) to automate the annotation of actor intent with calibrated uncertainty scores, paving the way for safer, self-aware AI systems.