BeatFlow-ECG: Rectified Flow for ECG Reconstruction from Indirect Wearable Signals

1 INTRODUCTION

• Most prior work does not address subject-independent ECG reconstruction from multimodal wearable signals under substantial motion.PPG is easier to acquire continuously than ECG, but is indirect and sensitive to motion; reconstruction must preserve local morphology and longer-range beat timing.Source: §1 · p. 1
• The paper formulates reconstruction from synchronized wearable PPG and inertial measurements as conditional transport from noise to ECG.The target is a single-channel ECG waveform.Source: §1 · pp. 1–2
• Motion information enters through IMU-derived conditioning features, motion-weighted velocity matching, and a curriculum that gradually introduces higher-motion windows.The paper evaluates these components through ablations.Source: §1 · p. 2
• BeatFlow-ECG achieves the best overall waveform and beat-timing results among evaluated deterministic, capacity-matched, adversarial, and diffusion-based baselines under LOSO on PPG-DaLiA and WESAD.Additional analyses examine regional waveform agreement, motion robustness, and inference efficiency.Source: §1 · p. 2

2.1 ECG RECONSTRUCTION FROM INDIRECT WEARABLE SIGNALS

• Most indirect ECG reconstruction methods use PPG alone, while reported results vary across datasets and protocols, limiting direct numerical comparison.BeatFlow-ECG instead uses wrist PPG with IMU-derived motion information and evaluates CardioGAN under the same LOSO protocol on both datasets.Source: §2.1 · p. 2

2.2 ECG RESTORATION, MORPHOLOGY RECONSTRUCTION, AND LEAD RECONSTRUCTION

• ECG restoration methods begin with ECG observations and restore missing or corrupted content, whereas BeatFlow-ECG reconstructs ECG from peripheral PPG and IMU measurements.Prior directions include denoising, imputation, lead reconstruction, and beat-morphology reconstruction from indirect ECG observations.Source: §2.2 · p. 2

2.3 GENERATIVE MODELING FOUNDATIONS FOR PHYSIOLOGICAL TIME SERIES

• Diffusion methods have been applied to physiological-signal generation but typically rely on iterative sampling, which can increase inference cost; rectified flow offers a continuous-time alternative.BeatFlow-ECG applies rectified flow to wearable ECG reconstruction with PPG/IMU conditioning and motion-aware training.Source: §2.3 · pp. 2–3

3.1 PROBLEM FORMULATION

• The method maps synchronized wearable conditioning signals to a one-channel ECG target, modeling reconstruction as continuous-time conditional transport rather than one-shot deterministic regression.The learned velocity field transports noise toward the target ECG while conditioned on wearable observations.Source: §3.1 · p. 3

3.2 CONDITIONAL RECTIFIED-FLOW FORMULATION

• Rectified flow trains a conditional velocity field along a path from noise to ECG, then reconstructs the signal by integrating that field over an ODE trajectory.The model uses L1 velocity matching, with an Euler discretization for reconstruction.Source: §3.2 · pp. 3–4

3.3 BEATFLOW-ECG ARCHITECTURE

• The model concatenates the intermediate state and wearable conditioning, then uses a convolutional encoder, transformer bottleneck, and decoder to predict the conditional velocity.Skip connections preserve finer temporal features, the transformer models longer-range dependencies including beat relationships, and learned flow-time embeddings condition activations.Source: §3.3 · pp. 4–5, Figure 1 · p. 4

3.4 MOTION-AWARE CONDITIONING AND TRAINING

• Motion-aware training adds IMU-derived motion descriptors, upweights higher-motion windows in the flow-matching objective, and gradually introduces harder windows through an easy-to-hard curriculum.An auxiliary STFT magnitude loss encourages frequency-domain consistency in reconstructed ECG.Source: §3.4 · pp. 5–6

3.5 SIGNAL PREPROCESSING AND FEATURE CONSTRUCTION

• Preprocessing filters PPG at 0.4–8 Hz and ECG at 0.5–40 Hz, then resamples all modalities to 125 Hz and z-score normalizes each 10-second window.Aligned modalities are extracted as overlapping 10-second windows with a 5-second stride; conditioning includes PPG-cycle phase and IMU motion features.Source: §3.5 · p. 6

4.1 DATASETS AND EVALUATION PROTOCOL

• PPG-DaLiA provides wrist PPG and inertial data with chest ECG from 15 subjects during motion-rich daily activities; WESAD supplies synchronized wearable, motion, and ECG signals under a different acquisition protocol.Each dataset is evaluated separately.Source: §4.1 · p. 6
• Each leave-one-subject-out fold tests on a subject excluded from model fitting and checkpoint selection, measuring generalization to an unseen subject.The protocol is run separately for each dataset.Source: §4.1 · pp. 6–7

4.2 BASELINES AND METRICS

• Comparisons include direct-regression, capacity-matched, diffusion, and adversarial baselines; reported metrics cover waveform fidelity and beat timing.Metrics include L1 error, RMSE, Pearson correlation, R-peak F1 with a 100-ms tolerance, and absolute heart-rate error.Source: §4.2 · p. 7

4.3 IMPLEMENTATION DETAILS

• Models use 125-Hz, 1250-sample windows; validation windows may share raw samples with training windows, but the held-out test subject remains isolated.BeatFlow-ECG uses 120 explicit Euler steps at inference.Source: §4.3 · p. 7

5 RESULTS

• 0.062 vs 0.085 L1 error and 0.983 vs 0.962 Pearson correlation on PPG-DaLiA; on WESAD, L1 error is 0.055 vs 0.074 and R-peak F1 is 0.955 vs 0.918, for BeatFlow-ECG versus Conditional DDPM-1D.BeatFlow-ECG achieves the best results across all reported metrics; Table 1 reports mean values with 95% confidence intervals across held-out subject folds.Source: Table 1 · p. 7, §5 · p. 7
• Across 15 held-out PPG-DaLiA subjects, BeatFlow-ECG has lower L1 and heart-rate error than Conditional DDPM-1D and UNet1D (p < 0.01 for each comparison).The comparisons use paired Wilcoxon signed-rank tests.Source: §5 · p. 7

5.1 MORPHOLOGY-SENSITIVE ANALYSIS

• BeatFlow-ECG has the highest correlation in the P-wave, QRS, and T-wave regions, including the lower-amplitude P- and T-wave regions.These morphology results are limited to the study’s healthy cohorts and do not establish generalization to pathological ECG morphology.Source: Table 2 · p. 8, §5.1 · p. 8

5.2 SUBJECT-WISE ANALYSIS

• S6 and S10 are among the more difficult PPG-DaLiA folds; S6 is retained despite a reported recording-hardware issue that reduced valid recording duration.The dataset authors report the hardware issue for S6.Source: §5.2 · p. 8

5.3 QUALITATIVE RECONSTRUCTION ANALYSIS

• Qualitative examples show BeatFlow-ECG preserving dominant beat structure, timing, and local waveform morphology across windows with varying reconstruction error.Figure 3 panels show wearable PPG, reconstructed ECG, reference ECG, and motion signals.Source: §5.3 · p. 8, Figure 3 · p. 8

5.4 MOTION ROBUSTNESS ANALYSIS

• Reconstruction error increases with motion for all models, while BeatFlow-ECG has the lowest error across low-, medium-, and high-motion groups.Groups use the 33rd and 67th percentiles of the motion-score distribution; the score measures motion exposure, not ECG SNR.Source: §5.4 · pp. 8–9, Table 3 · p. 9

5.5 ABLATION STUDY

• All evaluated ablations degrade performance; removing both motion weighting and STFT loss increases L1 from 0.062 to 0.084 and heart-rate error from 4.89 to 5.85 bpm.Motion conditioning, the curriculum, and the STFT objective each also improve performance.Source: Table 4 · p. 9, §5.5 · p. 9

6 DISCUSSION

• BeatFlow-ECG is slower than single-pass deterministic models but requires substantially fewer function evaluations than the evaluated DDPM configuration.Capacity-matched variants remain weaker, while regional correlations and motion-stratified errors also favor BeatFlow-ECG on PPG-DaLiA.Source: §6 · p. 9

7 LIMITATIONS

• Evaluation on PPG-DaLiA and WESAD does not establish generalization across devices, populations, sensor placements, or clinical conditions.Both datasets mainly contain healthy subjects, and the model reconstructs single-channel rather than diagnostic 12-lead ECG.Source: §7 · p. 9

• BeatFlow-ECG achieves the best overall waveform and beat-timing results among evaluated baselines under leave-one-subject-out evaluation on PPG-DaLiA and WESAD.Source: §8 · p. 10
• On PPG-DaLiA, BeatFlow-ECG shows higher regional waveform correlations and lower reconstruction error across motion levels.Source: §8 · p. 10
• BeatFlow-ECG is a conditional rectified-flow framework for reconstructing ECG from indirect wearable signals.Source: §8 · p. 10

• BeatFlow-ECG reconstructs ECG rather than directly measuring it.Source: ETHICS STATEMENT · p. 10
• Reconstruction errors could lead to false reassurance or false alarms if the system is used clinically.Source: ETHICS STATEMENT · p. 10
• The study does not establish diagnostic validity; prospective clinical validation is required before clinical use.Source: ETHICS STATEMENT · p. 10

• The main paper describes the model formulation, preprocessing pipeline, leave-one-subject-out evaluation protocol, baselines, and evaluation metrics.Source: REPRODUCIBILITY STATEMENT · p. 10
• The appendix provides architecture and training details, preprocessing equations, baseline configurations, confidence intervals, subject-wise results, and efficiency analyses.Source: REPRODUCIBILITY STATEMENT · p. 10
• All experiments use the publicly available PPG-DaLiA and WESAD datasets.Source: REPRODUCIBILITY STATEMENT · p. 10

A.2 TRAINING OBJECTIVE AND OPTIMIZATION DETAILS

• The model combines motion-weighted L1 velocity matching with an STFT magnitude loss and reconstructs ECG from Gaussian noise using 120 explicit-Euler integration steps.The STFT loss uses λSTFT = 0.10 and nfft = 256; the ablation removes motion weighting and the STFT term.Source: §A.2 · pp. 14–15

A.3 MOTION-AWARE TRAINING DETAILS

• Motion-aware training weights windows by mini-batch-normalized motion scores, uses α = 1.0, and gradually expands training from lower-motion windows to all windows.Higher-motion windows receive larger weights; mini-batch normalization avoids dataset-level calibration.Source: §A.3 · p. 15

B.1 DATASET PREPROCESSING DETAILS

• Preprocessing filters PPG at 0.4–8 Hz and ECG at 0.5–40 Hz, resamples modalities to 125 Hz, and extracts overlapping 10-second windows with 5-second stride.Conditioning also includes a PPG-derived phase feature and acceleration magnitude as a motion descriptor.Source: §B.1 · pp. 16–17

B.2 EVALUATION METRICS

• Evaluation reports waveform errors, Pearson correlation, R-peak F1 with a 100 ms matching tolerance, and heart-rate error; the AI-use statement limits LLM use to editing.The authors state that all scientific content was developed and verified by them.Source: AI USE STATEMENT · p. 10, §B.2 · pp. 17–18

C.1–C.3 ADDITIONAL RECONSTRUCTION, PEAK-ALIGNMENT, AND TRAJECTORY EXAMPLES

• Additional examples show preserved dominant beat structure and local waveform shape, close predicted-to-reference R-peak alignment, and gradual ECG-structure emergence along the reconstruction trajectory.The trajectory visualizations illustrate iterative reconstruction from initial Gaussian noise to the final ECG.Source: §C.1 · p. 18, §C.2 · p. 19, Figure 6 · p. 19

D.1 INFERENCE EFFICIENCY

• 120 function evaluations and 425 ms inference time give BeatFlow-ECG an approximately 8.3× speedup over Conditional DDPM-1D on the evaluated H100 setup.The comparison concerns reconstructing a 10-second window and excludes signal acquisition, preprocessing, and data transfer.Source: Table 5 · p. 21, §D.1 · p. 21

D.2 MOTION ROBUSTNESS VISUALIZATIONS

• Reconstruction error generally rises with acceleration-derived motion, although windows at similar motion levels vary; most windows fall in lower-RMSE and higher-correlation regions.The continuous analysis complements the motion-stratified results in Table 3.Source: §D.2 · p. 21, Figure 10 · p. 21

D.3 PER-SUBJECT TABLES

• On PPG-DaLiA, BeatFlow-ECG has lower reconstruction error than Conditional DDPM-1D and UNet1D-Large on difficult folds S6 and S10, amid variability across subjects and metrics.The subject-wise tables cover 15 held-out subjects on PPG-DaLiA and WESAD.Source: §D.3 · p. 22, Table 6 · p. 22, Table 7 · p. 22
• Table 11 reports WESAD LOSO performance for UNet1D-Large across 15 subjects.Source: Table 11 · p. 24

D.4 BASELINE QUALITATIVE COMPARISONS

• Baseline examples show close ECG reconstructions in some windows but local morphology, amplitude, or temporal-alignment errors in others.These qualitative examples complement aggregate and subject-wise results.Source: §D.4 · p. 24, Figure 11 · p. 24

D.5 MORPHOLOGY-SENSITIVE REGION ANALYSIS

• Morphology-sensitive evaluation computes Pearson correlation separately in fixed R-peak-centered P-wave, QRS, and T-wave regions shared across models.The regions are −200 to −60 ms, −60 to +60 ms, and +60 to +400 ms, respectively, within a 600-ms interval around each reference R-peak.Source: §D.5 · p. 24

E.1 BASELINE MODEL DETAILS

• Baseline parameter counts were UNet1D 4.2M, UNet1D-Large 13.2M, AttnSeq 8.5M, AttnSeq-Large 12.3M, and Conditional DDPM-1D 12.6M.UNet and AttnSeq each include standard and capacity-matched variants; Conditional DDPM-1D shares BeatFlow-ECG’s hybrid backbone and conditioning inputs and uses 1000-step training and reverse-diffusion schedules.Source: §E.1 · p. 25
• CardioGAN was evaluated as a PPG-only baseline under the study’s dataset-specific LOSO protocol, not as a reproduction of its original experimental setting.Released weights were excluded because their pooled training data included PPG-DaLiA and WESAD, potentially exposing held-out subjects.Source: §E.1 · p. 25

E.2 LEARNING-RATE SELECTION FOR UNET1D-LARGE

• UNet1D-Large’s PPG-DaLiA learning rate was selected using non-test-subject validation L1 on development folds, then fixed at 3 × 10−4 for all 15 LOSO folds.The sweep trained for 80 epochs at 3 × 10−4, 1 × 10−4, and 3 × 10−5; held-out subjects in development folds were excluded from selection.Source: §E.2 · p. 26, Table 12 · p. 26
• UNet1D-Large achieved L1 0.138, RMSE 0.210, Pearson r 0.925, R-peak F1 0.875, and HR error 6.95 bpm on PPG-DaLiA; it did not improve over UNet1D.The model was retuned at 3 × 10−4 and evaluated across all 15 LOSO folds; it is retained as a capacity-matched control.Source: §E.2 · p. 26

E.3 BEATFLOW-ECG HYPERPARAMETERS

• Table 13 summarizes BeatFlow-ECG’s main hyperparameters and the shared experimental windowing settings.Baseline training settings are provided in Appendix E.1.Source: §E.3 · p. 26, Table 13 · p. 26

E.4 ABLATION DETAILS

• Without motion conditioning, L1 error increased from 0.062 to 0.078 and R-peak F1 decreased from 0.946 to 0.920.The variant removes explicit IMU-derived motion descriptors while leaving the other architecture and training choices unchanged.Source: §E.4 · p. 27
• Without the easy-to-hard curriculum, L1 error increased to 0.071 and HR error to 5.35 bpm.This variant used all training windows throughout training.Source: §E.4 · p. 27
• Removing the STFT loss increased L1 error from 0.062 to 0.069 and decreased R-peak F1 from 0.946 to 0.926.The motion-weighted flow-matching objective was retained.Source: §E.4 · p. 27
• Removing motion weighting and STFT loss produced the largest degradation: L1 error rose to 0.084 and HR error to 5.85 bpm.Both components were removed in this variant.Source: §E.4 · p. 27

E.5 EXPERIMENTAL WORKFLOW

• Each fold trains and selects a checkpoint using 14 subjects, then evaluates it on the held-out subject.The workflow preprocesses paired wearable/ECG windows, creates subject-level manifests and splits, and saves aggregate metrics and per-window predictions.Source: §E.5 · p. 27