# Spectrally Regularized Latent Flow Matching for Turbulence Generation Source: [Spectrally Regularized Latent Flow Matching for Turbulence Generation]() Collection index: [llms.txt]() Data updated: 2026-06-12T05:00:05.419Z Authors: Khalid Rafiq, Aditya G. Nair Published: 2026-06-10T06:09:51.000Z ## Abstract 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Unconditional Generation on 2D Turbulence (test)](): Unconditional Generation; 2D Turbulence (test); IR Bias: -0.03. ## Original sources and implementation [Original paper]() [PDF]()