Diffusion-based generative models offer a principled framework for probabilistic forecasting, but we show they suffer from a fundamental spectral collapse when applied to turbulent flows. A Fourier-space analysis of the forward SDE reveals that the mode-wise signal-to-noise ratio decays monotonically in wavenumber for power-law spectra, rendering high-wavenumber content indistinguishable from noise. We reinterpret the noise […]