# Diff-PIC: Revolutionizing Particle-In-Cell Nuclear Fusion Simulation with Diffusion Models

arXiv: https://arxiv.org/abs/2408.02693 · HTML: https://mlsanity.com/paper/2408.02693/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 22 of its 64 references that are in the map.
- First posted on arXiv 3 Aug 2024.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 22 of 22)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Analyzing and Improving the Image Quality of StyleGAN](https://mlsanity.com/paper/1912.04958/) (2019)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [Cascaded Diffusion Models for High Fidelity Image Generation](https://mlsanity.com/paper/2106.15282/) (2021)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [InstaFlow: One Step is Enough for High-Quality Diffusion-Based Text-to-Image Generation](https://mlsanity.com/paper/2309.06380/) (2023)
- [Diffusion Normalizing Flow](https://mlsanity.com/paper/2110.07579/) (2021)
- [Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics](https://mlsanity.com/paper/2302.00600/) (2023)
- [Accurate transition state generation with an object-aware equivariant elementary reaction diffusion model](https://mlsanity.com/paper/2304.06174/) (2023)
- [Realistic galaxy image simulation via score-based generative models](https://mlsanity.com/paper/2111.01713/) (2021)
- [DiffMD: A Geometric Diffusion Model for Molecular Dynamics Simulations](https://mlsanity.com/paper/2204.08672/) (2022)
- [Deep generative model super-resolves spatially correlated multiregional climate data](https://mlsanity.com/paper/2209.12433/) (2022)
- [Optimising PICCANTE - an Open Source Particle-in-Cell Code for Advanced Simulations on Tier-0 Systems](https://mlsanity.com/paper/1503.02464/) (2015)

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

- [Diffusion for Fusion: Designing Stellarators with Generative AI](https://mlsanity.com/paper/2511.20445/) (2025)
- [Decomposition-Guided Diffusion Language Models for Inertial Confinement Fusion Prediction](https://mlsanity.com/paper/2609.07756/) (2026)

## Abstract (arXiv)

The rapid development of AI highlights the pressing need for sustainable energy, a critical global challenge for decades. Nuclear fusion, generally seen as an ultimate solution, has been the focus of intensive research for nearly a century, with investments reaching hundreds of billions of dollars. Recent advancements in Inertial Confinement Fusion have drawn significant attention to fusion research, in which Laser-Plasma Interaction (LPI) is critical for ensuring fusion stability and efficiency. However, the complexity of LPI upon fusion ignition makes analytical approaches impractical, leaving researchers depending on extremely computation-demanding Particle-in-Cell (PIC) simulations to generate data, presenting a significant bottleneck to advancing fusion research. In response, this work introduces Diff-PIC, a novel framework that leverages conditional diffusion models as a computationally efficient alternative to PIC simulations for generating high-fidelity scientific LPI data. In this work, physical patterns captured by PIC simulations are distilled into diffusion models associated with two tailored enhancements: (1) To effectively capture the complex relationships between physical parameters and corresponding outcomes, the parameters are encoded in a physically-informed manner. (2) To further enhance efficiency while maintaining high fidelity and physical validity, the rectified flow technique is employed to transform our model into a one-step conditional diffusion model. Experimental results show that Diff-PIC achieves 16,200× speedup compared to traditional PIC on a 100 picosecond simulation, with an average reduction in MAE / RMSE / FID of 59.21% / 57.15% / 39.46% with respect to two other SOTA data generation approaches.