cs.LGAug 27, 2026

Self-Augmented Diffusion Guidance for Physics-Informed Generation

Authors: Akira Osaka, Naoya Takeishi, Takehisa Yairi

Organizations: School of Engineering The University of Tokyo

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Abstract

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.

Figures & tables

MethodConstraint Evaluation during TrainingConstraint Evaluation during SamplingGradient of ConstraintProjection / Correction
PG Diffusion ( Shu et al., 2023 )✓✓✓–
PIDM ( Bastek et al., 2025 )✓–✓–
CoCoGen ( Jacobsen et al., 2025 )–✓✓–
ECI ( Cheng et al., 2025 )–––✓
Proposed––––
Table 1: Comparison of assumptions required by previous physics-informed generative methods and ours.
Figure 1: Overview of the proposed guidance approach.
Figure 2: Comparison of samples and residuals generated by the standard diffusion model and the proposed guidance model in the Darcy flow experiment. The residual represents the PDE residual of the Darcy flow equation.
Figure 3: Distribution of the mean residuals across independent runs under different conditions in the Darcy flow experiment. The red dashed lines show the mean values. The notation 1x and 2x indicate that the proposed method is applied once and twice, respectively.
Figure 4: Residual distributions of 1000 generated samples in 2 different trials in the Darcy flow experiment.
Figure 5: Comparison of samples and residuals generated by the standard diffusion model and the proposed guidance model in the time-series fluid experiment. The residual represents the deviation between generated samples and the corresponding snapshots obtained by numerically integrating the Navier–Stokes equations from the same initial states.
Figure 6: Distribution of the mean residuals across independent runs under different conditions in the time-series fluid experiment. The red dashed lines show the mean values. The notation 1x and 2x indicate that the proposed method is applied once and twice, respectively.
Figure 7: Residual distributions of 1000 generated samples in 2 different trials in the time-series fluid experiment.
Sampling methodMean Sampling Time ±\pm Std. [s]
PG Diffusion265.9±7.4265.9\pm 7.4
CoCoGen135.6±4.4135.6\pm 4.4
Classifier-free guidance-based (proposed)66.8±0.8\mathbf{66.8\pm 0.8}
Table 2: Comparison of the wall-clock time required to generate 1000 samples in the time-series fluid experiment. Results are reported as the mean ±\pm standard deviation across trials.
Experimental conditionMean Residual ±\pm Std.Median Residual (IQR)
Standard Diffusion (baseline)4.97×10−2±2.90×10−24.97\times 10^{-2}\pm 2.90\times 10^{-2}4.02×10−2 (3.98×10−2)4.02\times 10^{-2}\ (3.98\times 10^{-2})
Noise Augmentation (guidance)1.28×10−2±7.92×10−41.28\times 10^{-2}\pm 7.92\times 10^{-4}1.31×10−2 (8.95×10−4)1.31\times 10^{-2}\ (8.95\times 10^{-4})
Diffusion-Based Augmentation (guidance)1.19×10−2±5.96×10−3\mathbf{1.19\times 10^{-2}\pm 5.96\times 10^{-3}}8.64×10−3 (5.84×10−3)\mathbf{8.64\times 10^{-3}\ (5.84\times 10^{-3})}
PIDM + CoCoGen (baseline)6.90×10−3±2.23×10−36.90\times 10^{-3}\pm 2.23\times 10^{-3}6.45×10−3 (2.42×10−3)6.45\times 10^{-3}\ (2.42\times 10^{-3})
Noise Augmentation (guidance)1.07×10−3±9.89×10−51.07\times 10^{-3}\pm 9.89\times 10^{-5}1.08×10−3 (1.64×10−4)1.08\times 10^{-3}\ (1.64\times 10^{-4})
Diffusion-Based Augmentation (guidance)8.43×10−4±4.64×10−4\mathbf{8.43\times 10^{-4}\pm 4.64\times 10^{-4}}7.11×10−4 (7.15×10−4)\mathbf{7.11\times 10^{-4}\ (7.15\times 10^{-4})}
Table 3: Comparison of mean residuals between models augmented with Gaussian noise and with diffusion-generated samples. Results across trials are reported as the mean ±\pm standard deviation and the median with the interquartile range shown in parentheses.
Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 8: Examples from the Darcy flow dataset.
ParameterSetting
Model
ArchitectureU-Net
Base channels64
Channel multipliers(1,2,4,8)(1,2,4,8)
Residual blocks2 per resolution
Attention16×1616\times 16 resolution
Appendix
Table 4: Experimental settings for the Darcy flow experiments.
Figure 9: Residual distributions over 1000 generated samples for 6 independent trials in the Darcy flow experiment. Each histogram corresponds to a different random seed.
Figure 10: Comparison of samples and residuals generated under different conditions in the Darcy flow experiment.
Figure 11: Samples generated using PIDM + CoCoGen with the proposed guidance and their three nearest neighbors in the training dataset for the Darcy flow experiment.
Figure 12: Examples of time-series 2D fluid data.
ParameterSetting
Model
ArchitectureU-Net
Base channels64
Channel multipliers(1,2,2,4)(1,2,2,4)
Residual blocks2 per resolution
Attention16×1616\times 16 resolution
Appendix
Table 5: Experimental settings for the time-series 2D fluid experiments.
Figure 13: Residual distributions over 1000 generated samples for 6 independent trials in the time-series 2D fluid experiment. Each histogram corresponds to a different random seed.
Figure 14: Comparison of samples and residuals generated by the standard diffusion baseline and the proposed guidance models in the time-series 2D fluid experiment.
Figure 15: Comparison of samples and residuals generated by the physics-informed diffusion baselines and their combination with the proposed guidance in the time-series 2D fluid experiment.
Figure 16: Samples generated using PIDM + CoCoGen with the proposed guidance and their three nearest neighbors in the training dataset for the time-series 2D fluid experiment.
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