Cylindrical Geodesic Flow Matching for Quasiperiodic Physiological Signal Transformation

Onur Selim Kilic, Afra Nawar, Cem Okan Yaldiz, Michael J. Cho, Ahmet Rasim Emirdagi +4

Paired translation between quasiperiodic physiological waveforms (i.e., recovering a target oscillatory signal from the source) is central to the interpretation of cardiovascular signals derived from wearables placed at different body locations. This source-to-target mapping in these problems carries inherent geometric structure: the phase wraps around the cycle and must be treated as a circular variable, the amplitude remains strictly positive, and the beat-to-beat alignment can drift unpredictably across cycles and subjects. While deep neural networks have been used for phase estimation and complex-valued signal modeling, prior work does not explicitly learn phase transport between paired signals. Consequently, neither endpoint-supervised regression nor the standard affine path used in flow matching accounts for this phase--amplitude structure. We introduce \emph{cylindrical geodesic flow matching} for paired cardiovascular waveform translation. We show that the standard affine path used in flow matching distorts intermediate amplitude and instantaneous frequency when interpolating between quasiperiodic signals; replacing it with a closed-form geodesic on the phase--amplitude…