For object detection, it is possible to view the prediction of bounding boxes as a reverse diffusion process, where the random bounding boxes are iteratively refined as a denoising step, conditioned on the image using a diffusion model. We propose a stochastic accumulator function that starts each run with random bounding boxes and combines the slightly different predictions. We empirically verify that this improves detection performance. The improved detections are leveraged on unlabelled images, as weighted pseudo-labels for semi-supervised learning. We evaluate the method on a challenging out-of-domain test set. Our method brings significant improvements and is on par with human-selected pseudo-labels, while not requiring any human involvement.