Latent cycle phase as an inductive bias for conditional diffusion

Inductive biases can encode assumptions about data structure, and their utility should depend on both how well those assumptions hold and how the corresponding information is supplied to the model. We study this question for conditional diffusion restoration of cyclostationary physiological signals by conditioning on the latent cycle phase. In practice, physiological recordings are corrupted by motion, poor contact with the source, and interference, which obscure the fine signal that diagnosis and automated analysis depend on, so restoration is a prerequisite for their use. In the absence of an observation, knowing the signal phase reduces the minimum achievable mean-squared error by the fraction of signal variance explained by phase, which can be estimated from clean data before training. Across four physiological modalities, the benefit of phase conditioning follows the strength of their cycle structure. This benefit also depends on phase estimation: a classical detector applied to the corrupted signal provides no improvement, whereas a learned estimator of the clean-signal phase does. These results characterize when latent cycle phase provides a useful inductive bias in generative modeling for physiological signal restoration.