arXiv:2608.26748cs.LG2026-08

让扩散模型生成更符合物理规律的动态图像,不依赖每步求解方程。

Self-Augmented Diffusion Guidance for Physics-Informed Generation

论文配图:Self-Augmented Diffusion Guidance for Physics-Informed Generation
图 1 · 摘自论文原文
  • 用自生成数据增强引导扩散过程,学习偏离物理规律的程度。
  • 生成样本的物理偏差显著降低,优于标准扩散模型。
  • 无需每步求解方程,适合复杂物理模拟,生成更快。

扩散模型可用于生成流体动力学等物理现象的时空信号,如时间序列图像。然而,标准扩散模型缺乏对底层物理定律的约束,导致生成结果虽视觉合理,但与真实动态偏差较大。本文提出一种基于自生成数据增强的扩散引导方法,通过学习在不同物理偏差程度下的数据分布,并在生成时将偏差设为零,从而生成符合物理规律的样本。该方法将物理方程验证与扩散模型训练及采样解耦,避免在去噪每一步都求解控制方程,因此适用于需昂贵数值模拟的问题,且生成速度更快。实验表明,该方法相比标准扩散模型显著减少偏差,结合现有物理约束方法后进一步提升效果。

原文摘要 · Abstract (English)

Diffusion models can be used to generate spatiotemporal signals of physical phenomena, such as time-series images of fluid dynamics. However, a major limitation of standard diffusion models is that they do not incorporate constraints derived from the underlying physical laws. Consequently, generated samples may appear visually plausible while deviating substantially from the true dynamics. In this study, we propose a simple yet effective physics-informed approach based on diffusion guidance with self-generated data augmentation. The proposed method learns the data distribution conditioned on the degree of deviation from the physically correct dynamics and generates samples by explicitly setting the deviation condition to be zero. The method decouples the evaluation of the governing equations from the diffusion model training and sampling processes, avoiding the need to solve the governing equations at every iteration of the denoising process. This design makes the method applicable to problems requiring computationally expensive numerical simulations and enables faster sample generation. Experimental results demonstrate that the proposed model not only significantly reduces the deviations compared with standard diffusion models but also achieves further reductions when combined with existing physics-constrained diffusion methods.

扩散模型物理信息生成建模

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