# Point-wise Diffusion Models for Physical Systems with Shape Variations: Application to Spatio-temporal and Large-scale system

arXiv: https://arxiv.org/abs/2508.01230 · HTML: https://mlsanity.com/paper/2508.01230/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in 3D, point cloud and scene generation, one of 14 directions in Diffusion models.
- Builds on 26 of its 52 references that are in the map.
- First posted on arXiv 2 Aug 2025.

## Placed in

- Diffusion models / [3D, point cloud and scene generation](https://mlsanity.com/diffusion/3d-point-cloud-and-scene-generation/)

## Builds on (most cited first, 26 of 26)

- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [Neural General Circulation Models for Weather and Climate](https://mlsanity.com/paper/2311.07222/) (2023)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [DYffusion: A Dynamics-informed Diffusion Model for Spatiotemporal Forecasting](https://mlsanity.com/paper/2306.01984/) (2023)
- [MultiScale MeshGraphNets](https://mlsanity.com/paper/2210.00612/) (2022)
- [Predicting Physics in Mesh-reduced Space with Temporal Attention](https://mlsanity.com/paper/2201.09113/) (2022)
- [Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation](https://mlsanity.com/paper/2309.01745/) (2023)
- [Skillful joint probabilistic weather forecasting from marginals](https://mlsanity.com/paper/2506.10772/) (2025)
- [Geom-DeepONet: A Point-cloud-based Deep Operator Network for Field Predictions on 3D Parameterized Geometries](https://mlsanity.com/paper/2403.14788/) (2024)
- [AROMA: Preserving Spatial Structure for Latent PDE Modeling with Local Neural Fields](https://mlsanity.com/paper/2406.02176/) (2024)
- [DrivAerML: High-Fidelity Computational Fluid Dynamics Dataset for Road-Car External Aerodynamics](https://mlsanity.com/paper/2408.11969/) (2024)
- [Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads](https://mlsanity.com/paper/2306.03645/) (2023)
- [Text2PDE: Latent Diffusion Models for Accessible Physics Simulation](https://mlsanity.com/paper/2410.01153/) (2024)
- [Erwin: A Tree-based Hierarchical Transformer for Large-scale Physical Systems](https://mlsanity.com/paper/2502.17019/) (2025)
- [Generative Learning of the Solution of Parametric Partial Differential Equations Using Guided Diffusion Models and Virtual Observations](https://mlsanity.com/paper/2408.00157/) (2024)
- [Physics-aware Reduced-order Modeling of Transonic Flow via β-Variational Autoencoder](https://mlsanity.com/paper/2205.00608/) (2022)
- [Surrogate Modeling of Car Drag Coefficient with Depth and Normal Renderings](https://mlsanity.com/paper/2306.06110/) (2023)
- [Inexpensive High Fidelity Melt Pool Models in Additive Manufacturing Using Generative Deep Diffusion](https://mlsanity.com/paper/2311.16168/) (2023)
- [Wheel Impact Test by Deep Learning: Prediction of Location and Magnitude of Maximum Stress](https://mlsanity.com/paper/2210.01126/) (2022)
- [Deep Learning for Melt Pool Depth Contour Prediction From Surface Thermal Images via Vision Transformers](https://mlsanity.com/paper/2404.17699/) (2024)
- [Rigid-Deformation Decomposition AI Framework for 3D Spatio-Temporal Prediction of Vehicle Collision Dynamics](https://mlsanity.com/paper/2503.19712/) (2025)

## Built on by (most cited first, 2 of 2)

- [Flow Matching and Diffusion Models via PointNet for Generating Fluid Fields on Irregular Geometries](https://mlsanity.com/paper/2601.03030/) (2026)
- [Signal-Aware Conditional Diffusion Surrogates for Transonic Wing Pressure Prediction](https://mlsanity.com/paper/2604.11263/) (2026)

## Abstract (arXiv)

This study introduces a novel point-wise diffusion model that processes spatio-temporal points independently to efficiently predict complex physical systems with shape variations. This methodological contribution lies in applying forward and backward diffusion processes at individual spatio-temporal points, coupled with a point-wise diffusion transformer architecture for denoising. Unlike conventional image-based diffusion models that operate on structured data representations, this framework enables direct processing of any data formats including meshes and point clouds while preserving geometric fidelity. We validate our approach across three distinct physical domains with complex geometric configurations: 2D spatio-temporal systems including cylinder fluid flow and OLED drop impact test, and 3D large-scale system for road-car external aerodynamics. To justify the necessity of our point-wise approach for real-time prediction applications, we employ denoising diffusion implicit models (DDIM) for efficient deterministic sampling, requiring only 5-10 steps compared to traditional 1000-step and providing computational speedup of 100 to 200 times during inference without compromising accuracy. In addition, our proposed model achieves superior performance compared to image-based diffusion model: reducing training time by 94.4% and requiring 89.0% fewer parameters while achieving over 28% improvement in prediction accuracy. Comprehensive comparisons against data-flexible surrogate models including DeepONet and Meshgraphnet demonstrate consistent superiority of our approach across all three physical systems. To further refine the proposed model, we investigate two key aspects: 1) comparison of final physical states prediction or incremental change prediction, and 2) computational efficiency evaluation across varying subsampling ratios (10%-100%).