We introduce Spatial Reasoning Models (SRMs), a framework to perform reasoning over sets of continuous variables via denoising generative models. SRMs infer continuous representations on a set of unobserved variables, given observations on observed variables. Current generative models on spatial domains, such as diffusion and flow matching models, often collapse to hallucination in case of complex distributions. To measure this, we introduce a set of benchmark tasks that test the quality of complex reasoning in generative models and can quantify hallucination. The SRM framework allows to report key findings about importance of sequentialization in generation, the associated order, as well as the sampling strategies during training. It demonstrates, for the first time, that order of generation can successfully be predicted by the denoising network itself. Using these findings, we can increase the accuracy of specific reasoning tasks from $<$1% to $>$50%. Our project website provides additional videos, code, and the benchmark datasets.

Insufficient spatial resolution remains a serious obstacle for many potential applications of Sentinel-2 images. Therefore, a number of super-resolution techniques have been proposed, including single-image and multi-image approaches. While the former may hallucinate (rather than reconstruct) the image details, the latter are underpinned with information fusion that helps address these issues. However, given the five-days-long revisit time, a multi-temporal series of Sentinel-2 images contains temporal changes that affect the performance of multi-image super-resolution. In this paper, we propose a solution that allows for selecting a single image in the series to specify the point in time, at which the scene should be reconstructed. We report the results of our extensive experiments which confirm that our approach leads to improving the reconstruction quality, while preserving the temporal consistency. Importantly, the proposed solutions are potentially applicable to a variety of existing super-resolution techniques and they are not limited to Sentinel-2 images.