In recent years, research on out-of-distribution (OoD) detection for semantic segmentation has mainly focused on road scenes -- a domain with a constrained amount of semantic diversity. In this work, we challenge this constraint and extend the domain of this task to general natural images. To this end, we introduce: 1. the ADE-OoD benchmark, which is based on the ADE20k dataset and includes images from diverse domains with a high semantic diversity, and 2. a novel approach that uses Diffusion score matching for OoD detection (DOoD) and is robust to the increased semantic diversity. ADE-OoD features indoor and outdoor images, defines 150 semantic categories as in-distribution, and contains a variety of OoD objects. For DOoD, we train a diffusion model with an MLP architecture on semantic in-distribution embeddings and build on the score matching interpretation to compute pixel-wise OoD scores at inference time. On common road scene OoD benchmarks, DOoD performs on par or better than the state of the art, without using outliers for training or making assumptions about the data domain. On ADE-OoD, DOoD outperforms previous approaches, but leaves much room for future improvements.