# Relational Abstractions for Spatial Reasoning with Diffusion Models

arXiv: https://arxiv.org/abs/2610.09780 · HTML: https://mlsanity.com/paper/2610.09780/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 6 of its 50 references that are in the map.
- First posted on arXiv 7 Oct 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)
- Diffusion models / [3D, point cloud and scene generation](https://mlsanity.com/diffusion/3d-point-cloud-and-scene-generation/)

## Builds on (most cited first, 6 of 6)

- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [On the Measure of Intelligence](https://mlsanity.com/paper/1911.01547/) (2019)
- [ARC Prize 2024: Technical Report](https://mlsanity.com/paper/2412.04604/) (2024)
- [On Neural Architecture Inductive Biases for Relational Tasks](https://mlsanity.com/paper/2206.05056/) (2022)
- [TangramSR: Can Vision-Language Models Reason in Continuous Geometric Space?](https://mlsanity.com/paper/2602.05570/) (2026)
- [Shedding some light on Light Up with Artificial Intelligence](https://mlsanity.com/paper/2107.10429/) (2021)

## Abstract (arXiv)

Diffusion models excel at image synthesis, but they remain limited in their ability to reliably satisfy structured spatial reasoning constraints. In conditional data distribution modeling tasks with implicit logical structure, such as puzzles defined by visible clues paired with consistent solutions, state-of-the-art generative models tend to approximate pixel-space distributions without learning the underlying logical rules required for inference. To address this limitation, we present a novel framework for spatial reasoning with diffusion models that leverages unsupervised object discovery and abstractions of object relations. We show that the relational knowledge derived from object-centric representations enriches diffusion models with structural primitives, allowing them to effectively guide the generative representation space during both training and inference, and enabling conditional image generation that satisfies reasoning constraints. Additionally, we introduce a large-scale generative spatial reasoning benchmark with four datasets inspired by human-solvable puzzles. Our results show that relational abstractions significantly improve reasoning capabilities of diffusion models on a variety of complex reasoning tasks, while enabling robust generalization in out-of-distribution settings.