Diffusion-based super-resolution reconstruction of three-dimensional isotropic turbulence with physical constraints

In this study, we present a physics-guided diffusion framework for three-dimensional (3D) super-resolution reconstruction of turbulent flows, validated on both forced isotropic turbulence and turbulent channel flow at a friction Reynolds number of Reτ=180. The model conditions a 3D U-Net with sinusoidal time step embeddings on a concatenation of a nearest-neighbor upsampled low-resolution (LR) field and an enhanced super-resolution generative adversarial network (ESRGAN) baseline. The 3D U-Net predicts a residual R* that is added back to the baseline to recover the high-resolution field. Training follows an improved cosine noise schedule and a V-prediction objective, and inference uses deterministic denoising diffusion implicit models with closed-form updates. To promote physical fidelity, we augment the diffusion loss with lightweight physics regularization, using divergence and momentum-equation residuals over predicted sequences. For isotropic turbulence, qualitative results show that the diffusion model reconstructs small-scale flow structures beyond the LR input (83) and the ESRGAN baseline while preserving large-scale vortex organization; probability density functions and energy spectra exhibit improved agreement with direct numerical simulation (DNS). To assess generalization to wall-bounded flows, we apply the framework to channel flow at Reτ=180. The model successfully recovers anisotropic near-wall structures, including high- and low-speed streaks and quasi-streamwise vortices. Statistical diagnostics demonstrate that the reconstructed mean velocity profiles and Reynolds stresses closely match DNS data, significantly outperforming baselines in the buffer and logarithmic layers. Overall, these results demonstrate that diffusion-based reconstruction with physical constraints improves spectral fidelity and incompressibility across different flow regimes while remaining practical at inference.