# Object-centric Denoising Diffusion Models for Physical Reasoning

arXiv: https://arxiv.org/abs/2507.04920 · HTML: https://mlsanity.com/paper/2507.04920/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Discrete and text diffusion, one of 14 directions in Diffusion models.
- Builds on 16 of its 20 references that are in the map.
- First posted on arXiv 7 Jul 2025.

## Placed in

- Diffusion models / [Discrete and text diffusion](https://mlsanity.com/diffusion/discrete-and-text-diffusion/)

## Builds on (most cited first, 16 of 16)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Planning with Diffusion for Flexible Behavior Synthesis](https://mlsanity.com/paper/2205.09991/) (2022)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [MotionDiffuser: Controllable Multi-Agent Motion Prediction using Diffusion](https://mlsanity.com/paper/2306.03083/) (2023)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [Tutorial on Diffusion Models for Imaging and Vision](https://mlsanity.com/paper/2403.18103/) (2024)
- [Learning Long-term Visual Dynamics with Region Proposal Interaction Networks](https://mlsanity.com/paper/2008.02265/) (2020)
- [DDLP: Unsupervised Object-Centric Video Prediction with Deep Dynamic Latent Particles](https://mlsanity.com/paper/2306.05957/) (2023)
- [Forward Prediction for Physical Reasoning](https://mlsanity.com/paper/2006.10734/) (2020)
- [Diffusion Models for Multi-target Adversarial Tracking](https://mlsanity.com/paper/2307.06244/) (2023)

## Abstract (arXiv)

Reasoning about the trajectories of multiple, interacting objects is integral to physical reasoning tasks in machine learning. This involves conditions imposed on the objects at different time steps, for instance initial states or desired goal states. Existing approaches in physical reasoning generally rely on autoregressive modeling, which can only be conditioned on initial states, but not on later states. In fields such as planning for reinforcement learning, similar challenges are being addressed with denoising diffusion models. In this work, we propose an object-centric denoising diffusion model architecture for physical reasoning that is translation equivariant over time, permutation equivariant over objects, and can be conditioned on arbitrary time steps for arbitrary objects. We demonstrate how this model can solve tasks with multiple conditions and examine its performance when changing object numbers and trajectory lengths during inference.