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Cylindrical Geodesic Flow Matching for Quasiperiodic Physiological Signal Transformation

NeurIPS 2026 · Probabilistic and scientific modeling › Molecules and proteins · approach: Flow matching generative modeling

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Proposes cylindrical geodesic flow matching, which learns paired PPG and SCG waveform translation on the phase-amplitude cylinder using a closed-form geodesic bridge instead of the affine path.

Problem

Paired translation between quasiperiodic physiological waveforms (e.g., sternum-to-finger PPG, clavicle-to-sternum SCG) where phase is circular, amplitude is positive, and beat alignment drifts; standard affine flow-matching paths distort amplitude and instantaneous frequency.

Approach

Embed each analytic-signal sample as (cos phi, sin phi, a) on the phase-amplitude cylinder and use the closed-form shortest-arc geodesic as the conditional flow matching bridge, with an oracle velocity of constant norm and an intrinsic tangent parameterization with per-substep projection.

Key results

• On PPG under HT, cylindrical geodesic path gives HT Dist 0.8294, L2 0.5944, DTW 4.7902, best on all metrics versus time-series affine (0.9073, 0.6951, 5.6048).
• On SCG under HT, cylindrical geodesic path achieves HT Dist 0.8936, L2 0.6181, DTW 4.2618, best on all three metrics versus direct supervised (1.0419, 0.7103, 4.9158).
• Reductions of roughly 9-15% over the strongest competing baseline in the best cells; under EHT on PPG, direct supervision is marginally better on HT Dist (0.9777 vs 1.0110).

Surprising findings

• The Hilbert naive path trained in the same (phi, a) coordinates without cylindrical embedding is worse than the source reference on SCG, indicating naive phase-amplitude training fails.
• Under EHT on PPG, direct supervised prediction is best on HT Dist, so the geodesic advantage is not uniform across metrics and transforms.

Limitations

• Uses flat product metric d phi^2 + da^2; log-amplitude or Fisher-Rao metrics not explored.
• Analytic-signal representation is ill-defined near low-amplitude segments, where EHT only partially mitigates.
• Evaluated only on two cardiovascular translation tasks from a single institution; no cross-site or sensor heterogeneity tests.

Experimental setup

Datasets: in-house PPG cohort (20 subjects) in-house SCG cohort (13 subjects, 24 sessions)

Benchmarks: in-house PPG zero-shot translation in-house SCG limited-support adaptation

Metrics: HT Dist L2 error DTW distance

Baselines: Hilbert naive path time series affine path direct supervised predictor

Builds on: conditional flow matching Riemannian flow matching Hilbert transform extended Hilbert transform

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