Denoising Subordinated Probabilistic Models: Diffusion with a Tempered-Stable Volatility Clock, and What the Noise Mechanism Actually Controls

What the math gives to ML

The paper provides a constructive stochastic-volatility clock for diffusion models: a positive AR(1) variance process whose innovations are tempered-stable rather than independent or globally shared. Its transferable asset is the exact separation between cross-coordinate noise structure and denoiser conditioning: a blind denoiser can transmit volatility clustering, whereas conditioning on the latent variance makes the mixing distribution largely removable in the exact-denoiser limit. The moment identities give a practical way to calibrate persistence and tail-heaviness from observed kurtosis and squared-noise autocorrelation, including a falsifiable feasibility bound. The most promising neural-network use is a sequence or trajectory diffusion model trained with correlated variance mixtures, with the variance clock sampled per example and shared across the sequence axis.