Spatial Reasoning with Denoising Models

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%.