# Spatial Reasoning with Denoising Models

arXiv: https://arxiv.org/abs/2502.21075 · HTML: https://mlsanity.com/paper/2502.21075/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 2 of its 27 references that are in the map.
- First posted on arXiv 28 Feb 2025.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 2 of 2)

- [Cosmos World Foundation Model Platform for Physical AI](https://mlsanity.com/paper/2501.03575/) (2025)
- [Multi-Step Reasoning with Large Language Models, a Survey](https://mlsanity.com/paper/2407.11511/) (2024)

## Built on by (most cited first, 16 of 16)

- [DiffThinker: Towards Generative Multimodal Reasoning with Diffusion Models](https://mlsanity.com/paper/2512.24165/) (2025)
- [SceneTok: A Compressed, Diffusable Token Space for 3D Scenes](https://mlsanity.com/paper/2602.18882/) (2026)
- [Next Visual Granularity Generation](https://mlsanity.com/paper/2508.12811/) (2025)
- [Denoising, Fast and Slow: Difficulty-Aware Adaptive Sampling for Image Generation](https://mlsanity.com/paper/2604.19141/) (2026)
- [Spatial Reasoners for Continuous Variables in Any Domain](https://mlsanity.com/paper/2507.10768/) (2025)
- [Perfect diffusion is mathsfTC0 -- Bad diffusion is Turing-complete](https://mlsanity.com/paper/2507.12469/) (2025)
- [Teaching Transformers to Solve Combinatorial Problems through Efficient Trial & Error](https://mlsanity.com/paper/2509.22023/) (2025)
- [Visual Diffusion Models are Geometric Solvers](https://mlsanity.com/paper/2510.21697/) (2025)
- [Inference-Time Scaling in Diffusion Models through Iterative Partial Refinement](https://mlsanity.com/paper/2605.19317/) (2026)
- [SpatialFly: Implicit 3D Prior-Guided Visual Reparameterization for Continuous UAV Vision-and-Language Navigation](https://mlsanity.com/paper/2603.21046/) (2026)
- [When Do Diffusion Models learn to Generate Multiple Objects?](https://mlsanity.com/paper/2605.00273/) (2026)
- [From Interface to Inference: Eliciting Any-Order Inference from Any-Order Models](https://mlsanity.com/paper/2607.26504/) (2026)
- [SemanticNVS: Improving Semantic Scene Understanding in Generative Novel View Synthesis](https://mlsanity.com/paper/2602.20079/) (2026)
- [AsyncPatch Diffusion: spatially-flexible image generation](https://mlsanity.com/paper/2606.07079/) (2026)
- [Let It Go or Learn to Self-Correct: Continuous Diffusion for Constrained Discrete Tasks](https://mlsanity.com/paper/2609.09009/) (2026)
- [ForcingBooster: Adaptive Patch-wise Denoising for Fast Autoregressive Video Diffusion](https://mlsanity.com/paper/2610.12625/) (2026)

## Abstract (arXiv)

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: https://geometric-rl.mpi-inf.mpg.de/srm