Spatial Reasoning with Denoising Models (2502.21075v2)

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 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

Spatial Reasoning with Denoising Models: An Analytical Overview

The paper introduces Spatial Reasoning Models (SRMs), which are presented as a sophisticated framework designed to handle reasoning over sets of continuous variables via denoising generative models. The core objective of this research is to assess the reasoning capabilities of such models in spatial domains, specifically utilizing constructs like diffusion and flow-based generative models.

Methodological Insights

SRMs are conceptualized to improve reasoning over continuous data by addressing inherent limitations found in traditional generative models. Generative models, particularly diffusion models, tend to hallucinate when exposed to complex distributions, primarily due to their incapability to effectively sequentialize high-dimensional, continuous data. This research establishes benchmark tasks aimed at evaluating and quantifying hallucination levels in these models.

Key to SRMs is the notion of sequentialization—introducing sequential steps in the generative process that mimic the problem-solving pathways akin to human reasoning, as seen in chain-of-thought methodologies for LLMs. This paper displays a notable advancement whereby the order of generation can be anticipated by the denoising network itself, significantly enhancing accuracy in specific tasks. This finding is empirically supported by an increase in accuracy from less than 1% to over 50% in select reasoning tasks.

Numerical Results and Claims

Benchmarks such as the Sudoku game with MNIST images underscore the proposed framework's efficacy. Standard diffusion models struggled with correctly solving such tasks (achieving near 0% accuracy in complex instances), whereas SRMs demonstrated more than 50% accuracy, marking a significant improvement. This performance leap indicates the superior capability of SRMs to manage and process spatial and continuous variables effectively compared to traditional methods.

Implications for AI Research

The implications of this research are manifold. On a practical level, SRMs could greatly enhance applications necessitating spatial reasoning, such as autonomous vehicle navigation, robotics, and computer vision tasks. Theoretically, the findings propose a re-evaluation of how generative processes can be structured to augment reasoning tasks in AI.

Moreover, the potential to combine non-traditional noise schedules with stochastic sampling facilitates more accurate and reliable generative models, bypassing the limitations inherent in previously established approaches like DDPM and DDIM.

Future Directions

This research presents several avenues for future exploration. Among them is the refinement of strategies for automatic prediction of generation order, potentially incorporating machine learning techniques for adaptive ordering. Additionally, there is a suggestion that integrating backtracking strategies could further bolster the efficacy of SRMs, especially in scenarios with complex dependencies or multiple valid outcomes.

In summary, the paper provides a rigorous exploration of spatial reasoning using denoising models and asserts SRMs as a promising direction for advancing AI's reasoning capabilities in continuous and spatial domains. Such advancements can catalyze further developments in AI, transcending current limitations and offering robust solutions to multidimensional spatial reasoning challenges.