With more well-performing anomaly detection methods proposed, many of the single-view tasks have been solved to a relatively good degree. However, real-world production scenarios often involve complex industrial products, whose properties may not be fully captured by one single image. While normalizing flow based approaches already work well in single-camera scenarios, they currently do not make use of the priors in multi-view data. We aim to bridge this gap by using these flow-based models as a strong foundation and propose Multi-Flow, a novel multi-view anomaly detection method. Multi-Flow makes use of a novel multi-view architecture, whose exact likelihood estimation is enhanced by fusing information across different views. For this, we propose a new cross-view message-passing scheme, letting information flow between neighboring views. We empirically validate it on the real-world multi-view data set Real-IAD and reach a new state-of-the-art, surpassing current baselines in both image-wise and sample-wise anomaly detection tasks.