Structure as context: learned cycle phase in probabilistic diffusion for time-series restoration

Non-stationarity can limit time-series model generalization. Yet signals often exhibit intrinsic structure; for instance, their statistics may vary with latent cycle phase. We study whether encoding this cyclostationary structure as an inductive bias improves restoration using physiological signals with different degrees of cyclic organization. A conditional diffusion model is conditioned on a dense estimate of cycle phase together with the corrupted observation. In the absence of an observation, the reduction in mean-squared error from knowing phase equals the fraction of signal variance explained by phase, which can be estimated before training. Across four modalities, the benefit of phase conditioning follows the strength of cycle structure and depends on phase estimation: a classical detector applied to the corrupted signal provides no improvement, whereas a learned estimator of clean-signal phase does. The representation also generalizes to unseen datasets without retraining, while antithetic sampling reduces inference cost. These results characterize when cycle structure provides a useful inductive bias for time-series restoration.