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Open-vocabulary segmentation is the task of segmenting anything that can be named in an image. Recently, large-scale vision-language modelling has led to significant advances in open-vocabulary segmentation, but at the cost of gargantuan and increasing training and annotation efforts. Hence, we ask if it is possible to use existing foundation models to synthesise on-demand efficient segmentation algorithms for specific class sets, making them applicable in an open-vocabulary setting without the need to collect further data, annotations or perform training. To that end, we present OVDiff, a novel method that leverages generative text-to-image diffusion models for unsupervised open-vocabulary segmentation. OVDiff synthesises support image sets for arbitrary textual categories, creating for each a set of prototypes representative of both the category and its surrounding context (background). It relies solely on pre-trained components and outputs the synthesised segmenter directly, without training. Our approach shows strong performance on a range of benchmarks, obtaining a lead of more than 5% over prior work on PASCAL VOC.