# Spatial Reasoners for Continuous Variables in Any Domain

arXiv: https://arxiv.org/abs/2507.10768 · HTML: https://mlsanity.com/paper/2507.10768/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 19 of its 20 references that are in the map.
- First posted on arXiv 14 Jul 2025.

## Placed in

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

## Builds on (most cited first, 19 of 19)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [Diffusion Forcing: Next-token Prediction Meets Full-Sequence Diffusion](https://mlsanity.com/paper/2407.01392/) (2024)
- [Autoregressive Image Generation without Vector Quantization](https://mlsanity.com/paper/2406.11838/) (2024)
- [Simple diffusion: End-to-end diffusion for high resolution images](https://mlsanity.com/paper/2301.11093/) (2023)
- [Reconstruction vs. Generation: Taming Optimization Dilemma in Latent Diffusion Models](https://mlsanity.com/paper/2501.01423/) (2025)
- [Deep Compression Autoencoder for Efficient High-Resolution Diffusion Models](https://mlsanity.com/paper/2410.10733/) (2024)
- [One Transformer Fits All Distributions in Multi-Modal Diffusion at Scale](https://mlsanity.com/paper/2303.06555/) (2023)
- [Rolling Diffusion Models](https://mlsanity.com/paper/2402.09470/) (2024)
- [Beyond Next-Token: Next-X Prediction for Autoregressive Visual Generation](https://mlsanity.com/paper/2502.20388/) (2025)
- [FasterDiT: Towards Faster Diffusion Transformers Training without Architecture Modification](https://mlsanity.com/paper/2410.10356/) (2024)
- [Spatial Reasoning with Denoising Models](https://mlsanity.com/paper/2502.21075/) (2025)

## Built on by (most cited first, 3 of 3)

- [DiffThinker: Towards Generative Multimodal Reasoning with Diffusion Models](https://mlsanity.com/paper/2512.24165/) (2025)
- [Teaching Transformers to Solve Combinatorial Problems through Efficient Trial & Error](https://mlsanity.com/paper/2509.22023/) (2025)
- [When Do Diffusion Models learn to Generate Multiple Objects?](https://mlsanity.com/paper/2605.00273/) (2026)

## Abstract (arXiv)

We present Spatial Reasoners, a software framework to perform spatial reasoning over continuous variables with generative denoising models. Denoising generative models have become the de-facto standard for image generation, due to their effectiveness in sampling from complex, high-dimensional distributions. Recently, they have started being explored in the context of reasoning over multiple continuous variables. Providing infrastructure for generative reasoning with such models requires a high effort, due to a wide range of different denoising formulations, samplers, and inference strategies. Our presented framework aims to facilitate research in this area, providing easy-to-use interfaces to control variable mapping from arbitrary data domains, generative model paradigms, and inference strategies. Spatial Reasoners are openly available at https://spatialreasoners.github.io/