Spectrally Regularized Latent Flow Matching for Turbulence Generation

Latent diffusion and flow matching have emerged as leading approaches for synthetic turbulence generation, yet they systematically under-represent dissipation-range amplitudes. We introduce a latent flow matching framework with a spectrally regularized compression stage that directly targets this failure mode. On a $256^2$ DNS dataset at $Re_f \approx 2250$, replacing an MSE-trained VAE with a zone-weighted log-spectral objective raises deep-dissipation retained spectral power from 25\% to 94\% in reconstruction and from 20\% to 79\% in unconditional generation. The improved latent representation also yields a substantially better sampling cost-fidelity tradeoff: the MSE-trained latent space imposes a fundamental quality ceiling near DD bias $-0.70$ that no integrator or step-count can overcome, while the spectrally regularized latent space reaches DD bias $-0.117$ at just $20$ function evaluations. Mechanistically, encoder-decoder swap experiments show that the improvement is driven primarily by encoder-induced latent reorganization rather than decoder capacity, while a support-amplitude decomposition reveals that MSE-trained models behave as conservative suppression models, minimizing pointwise error by attenuating intermittent high-wavenumber structure. Both pipelines recover the second-order structure function and the correct sign of $S_3$, indicating the correct cascade direction without explicit supervision. A small residual gap in the magnitude of $S_3$ suggests that phase-coherent triadic organization remains a complementary axis to amplitude fidelity for future generative turbulence models.