Document understanding is a key business process in the data-driven economy, since documents are central to knowledge discovery and business insights. Converting documents into a machine-processable format is a particular challenge here due to their huge variability in formats and complex structure. Accordingly, many algorithms and machine-learning methods emerged to solve particular tasks such as OCR, layout analysis, table-structure recovery, figure understanding and more. We observe adoption of such methods in document understanding solutions offered by all major cloud providers. Yet, publications outlining how such services are designed and optimised to scale in the cloud are scarce. In this paper, we focus on the case of document conversion to illustrate the particular challenges of scaling a complex data processing pipeline with strong reliance on machine-learning methods on cloud infrastructure. Our key objective is to achieve high scalability and responsiveness for different workload profiles in a well-defined resource budget. We outline the requirements, design and implementation choices of our document conversion system and reflect on the challenges we faced. Evidence for the scaling behaviour and resource efficiency is provided for two alternative workload distribution strategies and deployment configurations. Our best-performing method achieves sustained throughput of over one million PDF pages per hour on 3072 CPU cores across 192 nodes.