Cylindrical Geodesic Flow Matching for Quasiperiodic Physiological Signal Transformation

2026-10-06

AI Summary

This study addresses the limitation of conventional methods for cross-location physiological signal mapping in wearable devices, which neglect the geometric structures of phase circularity and amplitude positivity. To this end, this work proposes a cylindrical geodesic flow matching method that incorporates a phase-amplitude cylinder as an inductive bias. By constructing closed-form geodesic paths to replace standard affine trajectories, it explicitly learns phase transport between paired signals for the first time. Integrated with deep neural networks, this approach enables geometry-consistent waveform translation, effectively eliminating amplitude and instantaneous frequency distortion artifacts during interpolation. Experimental results demonstrate that on zero-shot PPG and limited-support SCG benchmarks, the proposed method reduces Hilbert transform, L2, and DTW distances by approximately 15% compared to the strongest baselines, surpassing the performance of directly supervised prediction.

Abstract

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 cylinder eliminates these artifacts and converts each training pair into dense, geometry-consistent velocity supervision. On zero-shot photoplethysmography and limited-support seismocardiography adaptation benchmarks, our method consistently outperforms interpolation baselines and matches or exceeds direct supervised prediction, reducing Hilbert Transform, $L_2$, and Dynamic Time Warping distance by up to ${\sim}15\%$ over the strongest competing baseline. These results suggest that bridge geometry is a critical inductive bias for flow matching on oscillatory signal translation.

Problem

• Quasiperiodic Signal Transformation
• Flow Matching
• Physiological Waveform Translation
• Phase-Amplitude Structure

Innovation

• Cylindrical Geodesic Flow Matching
• Quasiperiodic Signal Translation
• Phase-Amplitude Cylinder
• Flow Matching
• Physiological Waveform