Large Language Models (LLMs) are increasingly utilised in software engineering, yet their ability to generate structured artefacts such as UML diagrams remains underexplored. In this work we present NOMAD, a cognitively inspired, modular multi-agent framework that decomposes UML generation into a series of role-specialised subtasks. Each agent handles a distinct modelling activity, such as entity extraction, relationship classification, and diagram synthesis, mirroring the goal-directed reasoning processes of an engineer. This decomposition improves interpretability and allows for targeted verification strategies. We evaluate NOMAD through a mixed design: a large case study (Northwind) for in-depth probing and error analysis, and human-authored UML exercises for breadth and realism. NOMAD outperforms all selected baselines, while revealing persistent challenges in fine-grained attribute extraction. Building on these observations, we introduce the first systematic taxonomy of errors in LLM-generated UML diagrams, categorising structural, relationship, and semantic/logical. Finally, we examine verification as a design probe, showing its mixed effects and outlining adaptive strategies as promising directions. Together, these contributions position NOMAD as both an effective framework for UML class diagram generation and a lens onto the broader research challenges of reliable language-to-model workflows.