ICML 2025

Spatial Reasoning with Denoising Models
Christopher Wewer 1 Bart Pogodzinski 1 Bernt Schiele 1 Jan Eric Lenssen 1
SRMs (Ours)
Standard DDPM
Playing MNIST Sudoku with Image Generators….
Figure 1: We introduce Spatial Reasoning Models (SRMs), a framework to systematically investigate diffusion/flow-based
generative models with respect to their reasoning capabilities over multiple variables. We introduce benchmarks that allow
quantification of higher-level reasoning capabilities and show that manual and automatic schemes for sequentialization can
heavily reduce hallucination. Here, we show the solving process of one of the benchmarks, a Sudoku game consisting of
MNIST images, which is solved correctly by our SRMs, while standard diffusion models fail.
Abstract
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 observa-
tions on observed variables. Current generative
models on spatial domains, such as diffusion and
flow matching models, often collapse to hallucina-
tion 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 strate-
gies 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.
1Max Planck Institute for Informatics, Saarland Informat-
ics Campus, Germany. Correspondence to: Christopher Wewer
<cwewer@mpi-inf.mpg.de>, Bart Pogodzinski <bpogodzi@mpi-
inf.m...