Lazy Diffusion: Mitigating spectral collapse in generative diffusion-based stable autoregressive emulation of turbulent flows

• URL: http://arxiv.org/abs/2512.09572v1
• Date: Wed, 10 Dec 2025 12:05:32 GMT
• Title: Lazy Diffusion: Mitigating spectral collapse in generative diffusion-based stable autoregressive emulation of turbulent flows
• Authors: Anish Sambamurthy, Ashesh Chattopadhyay,
• Abstract summary: We show that standard DDPMs induce a fundamental emphspectral collapse.<n>We introduce power-law schedules that preserve fine-scale structure deeper into diffusion time.<n>These methods are applied to high-Reynolds-number 2D Kolmogorov turbulence and $1/12circ$ Gulf of Mexico ocean reanalysis.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Turbulent flows posses broadband, power-law spectra in which multiscale interactions couple high-wavenumber fluctuations to large-scale dynamics. Although diffusion-based generative models offer a principled probabilistic forecasting framework, we show that standard DDPMs induce a fundamental \emph{spectral collapse}: a Fourier-space analysis of the forward SDE reveals a closed-form, mode-wise signal-to-noise ratio (SNR) that decays monotonically in wavenumber, $|k|$ for spectra $S(k)\!\propto\!|k|^{-λ}$, rendering high-wavenumber modes indistinguishable from noise and producing an intrinsic spectral bias. We reinterpret the noise schedule as a spectral regularizer and introduce power-law schedules $β(τ)\!\propto\!τ^γ$ that preserve fine-scale structure deeper into diffusion time, along with \emph{Lazy Diffusion}, a one-step distillation method that leverages the learned score geometry to bypass long reverse-time trajectories and prevent high-$k$ degradation. Applied to high-Reynolds-number 2D Kolmogorov turbulence and $1/12^\circ$ Gulf of Mexico ocean reanalysis, these methods resolve spectral collapse, stabilize long-horizon autoregression, and restore physically realistic inertial-range scaling. Together, they show that naïve Gaussian scheduling is structurally incompatible with power-law physics and that physics-aware diffusion processes can yield accurate, efficient, and fully probabilistic surrogates for multiscale dynamical systems.

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