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

arXiv:2610.09052 · cs.LG, eess.SP · Submitted 2026-10-06 · Read on arXiv

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Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: Today's paper: "BeatFlow-ECG: Rectified Flow for ECG Reconstruction from Indirect Wearable Signals".

Jane: The gist: BeatFlow-ECG introduces a conditional rectified-flow model for reconstructing single-channel ECG from synchronized PPG and inertial measurements,

Tom: First, who's behind it and why it matters.

Paper summary: Jane: So we’re wrapping up this look at BeatFlow-ECG, titled "BeatFlow-ECG: Rectified Flow for ECG Reconstruction from Indirect Wearable Signals," and the authors are Kamel, Selim, Medhat, and Nadeem. What does this actually mean for us listening right now?

Tom: It means that if you want to put cardiac monitoring on a wearable device that people can actually use every day without constant clinical supervision, this approach is showing strong performance. It’s about using the motion data not just as extra noise, but as active guidance for the AI model to get a clearer signal.

Lu: The implication here is that conditional rectification, combined with explicit flow-time conditioning and motion awareness in training can effectively handle the inherent uncertainty of indirect measurements like PPG <ref:2610.09052#pg3>.

Meng: For deployment at scale, I’m curious about what this means for running it on a phone or some small embedded device. What is the computational cost of running this specific model compared to something like Conditional DDPM-1D <ref:2610.09052#pg1>?

Tom: The paper does touch on efficiency, and they say their iterative approach requires twelve explicit Euler steps for inference, which is four hundred twenty-five milliseconds on an NVIDIA H100 GPU <ref:2610.09052#pg1>.

Jane: So that’s a tangible number. That’s what matters when you’re thinking about real-world application. It moves the conversation from just "it's accurate" to "it's fast enough to be useful."

Lalam: I think it shows that when you get the modeling right, especially with those motion features and loss weighting, you can bridge that gap between high performance research and practical deployment <ref:2610.09052#pg1>.

Tom: Yeah. And they confirmed their components matter in the ablation study; removing both motion weighting and STFT loss caused the largest degradation, increasing L1 from zero point six two to zero point eight four <ref:2610.09052#pg1>.

Lu: So they are proving that these specific mechanisms—the motion conditioning and the training curriculum—are genuinely contributing to the final performance gain on PPG-DaLiA and WESAD <ref:2610.09052#pg2>.

Jane: It’s a promising direction for making these continuous cardiac monitoring tools more reliable and useful for people in their daily lives. We should keep an eye on how this approach scales across different devices and populations <ref:2610.09052#pg1>.

Conclusion: Tom: So, to wrap up this look at BeatFlow-ECG, titled "BeatFlow-ECG: Rectified Flow for ECG Reconstruction from Indirect Wearable Signals," the authors are Kamel, Selim, Medhat, and Nadeem. What does this actually mean for us listening right now?

Jane: It means they’ve put together a way to use noisy smartwatch data to get a clear heart signal without needing that expensive clinic setup. It’s about turning movement into helpful guidance for the AI model instead of just treating it like junk noise.

Lu: The main thing is their conditional rectified flow model, which treats the reconstruction as continuous transport from noise to the ECG itself, which is key for avoiding those weird problems with discrete sampling we often see >--- Page three --- <ref:2610.09052#pg3>.

Meng: So they’re using that continuous flow idea, but they’ve layered in motion information through IMU derived features and a specific training schedule to handle the noise better than just standard diffusion models >--- Page two --- <ref:2610.09052#pg1>.

Tom: Yeah. They showed it beats deterministic and adversarial methods across the board, hitting Pearson correlations of zero point nine eight three and zero point nine eight six on their test sets >--- Page two --- <ref:2610.09052#pg1>.

Jane: That means for someone who just uses a fitness tracker or a simple health wearable, the accuracy is actually very high when they are moving around >--- Page one --- <ref:2610.09052#pg1>.

Lalam: And they’ve shown that when you look at the waveform regions with fixed R-peaks, the correlation is higher and the errors are lower across all motion levels >--- Page two --- <ref:2610.09052#pg1>.

Tom: Exactly. It really shows that this rectified flow approach, specifically conditioned by motion, is more effective than what was seen with diffusion-based methods for these kinds of wearable inputs >--- Page two --- <ref <ref:2610.09052#pg1>.

Jane: So it’s a promising path for making continuous cardiac monitoring tools actually reliable and useful for people in their daily lives, not just academic papers >--- Page two --- <ref <ref:2610.09052#pg1>.

Mohamed Kamel, Sahar Selim, Walaa Medhat, Tamer Nadeem

Virginia Commonwealth University · Nile University

cs.LG, eess.SP

Submitted: 2026-10-06

Updated: 2026-10-06

Comments: 27 pages. Preprint. Under review

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 89/100

The gist: The gist: BeatFlow-ECG introduces a conditional rectified-flow model for reconstructing single-channel ECG from synchronized PPG and inertial measurements, achieving state-of-the-art results across

Key concepts

Conditional Rectified Flow Model: This is a mathematical framework that treats ECG reconstruction as a continuous transport process from random noise to the actual ECG signal. The model learns a 'velocity field' that guides the noisy input sample toward the correct target ECG, while simultaneously being conditioned on external wearable data like PPG and motion.
Motion-Aware Conditioning: Since PPG signals are sensitive to movement, this technique uses data from an Inertial Measurement Unit (IMU) to quantify motion intensity. This motion information is used to adjust the model's training weights and curriculum, ensuring the system learns robust reconstructions even when the user is moving.
Easy-to-Hard Training Curriculum: To handle motion artifacts effectively, the training process starts by emphasizing low-motion data and gradually introduces higher-motion scenarios. This structured approach helps the model build a strong foundation in stable signals before tackling more challenging, noisy conditions.

Terminology

Rectified Flow — 1× in this paper · explained in 3 episodes

Summary

The gist: BeatFlow-ECG introduces a conditional rectified-flow model for reconstructing single-channel ECG from synchronized PPG and inertial measurements, achieving state-of-the-art results across multiple metrics under leave-one-subject-out protocols

How it works

BeatFlow-ECG models the reconstruction as conditional transport from noise to ECG using a convolutional encoder-decoder with a transformer bottleneck and explicit flowtime conditioning. The formulation treats ECG reconstruction as continuous transport from noise to ECG using an ODE trajectory. Specifically, for each paired training example (x, c) and noise sample z ∼ N (0, I), the intermediate state is defined by the linear interpolation xt = (1 − t)z + tx <ref:2610.09052#pg5>. The network learns to predict a conditional velocity field vθ(xt, t, c) that transports the sample toward the target ECG while remaining conditioned on wearable observations c <ref:2610.09052#pg5>.

Motion-Aware Conditioning and Training

To address motion artifacts in wearable PPG signals, BeatFlow-ECG incorporates motion information through several mechanisms <ref:2610.09052#pg5>. These include IMU-derived descriptors, acceleration magnitude macc[n] = p ax[n]2 + ay[n]2 + az[n]2 as a compact measure of instantaneous motion intensity <ref:2610.09052#pg6>. Furthermore, the training is adapted using motion-aware loss weighting where the sample weight is set to w = 1 + αs˜motion, and higher-motion windows therefore receive larger training weights <ref:2610.09052#pg5>. Additionally, an easy-to-hard training curriculum is employed where lowermotion windows are emphasized earlier in training and higher-motion windows are gradually introduced <ref:2610.09052#pg5>.

Model Architecture

The model parameterizes the velocity field vθ(xt, t, c) with a hybrid architecture that combines temporal convolutions with global sequence modeling <ref:2610.09052#pg6>. The input state xt is fused with the conditioning signal c through an early fusion step h0 = Convin([xt; c]) <ref:2610.09052#pg6>. This fused representation is then processed by a temporal encoder that extracts local features, followed by a transformer bottleneck to model longer-range dependencies across beats <ref:2610.09052#pg6>. The time-conditioning is handled via an embedding et = MLP(Fourier(t)) <ref:2610.09052#pg7>, which is injected through adaptive RMS normalization (AdaRMSNorm) throughout the blocks <ref:2610.09052#pg6>.

Evaluation and Performance

BeatFlow-ECG was evaluated on PPG-DaLiA and WESAD using leave-one-subject-out (LOSO) protocols <ref:2610.09052#pg3>. The model achieved the best results among the evaluated deterministic, adversarial, and diffusion-based baselines across all reported waveform and beat-timing metrics <ref:2610.09052#pg6>. Specifically, on PPGDaLiA, it reduced L1 error from 0.085 to 0.062 compared to Conditional DDPM-1D <ref:2610.09052#pg8>, increased Pearson correlation from 0.962 to 0.983, and improved R-peak F1 from 0.946 to 0.946 <ref:2610.09052#pg8>. The model also demonstrated robustness across motion levels, as reconstruction error increases with motion for all models, while BeatFlow-ECG remains lowest across all three motion levels <ref:2610.09052#pg9>.

Ablation and Efficiency

The ablation study confirmed the contribution of key components; removing both motion weighting and the STFT loss resulted in the largest degradation, increasing L1 from 0.062 to 0.084 <ref:2610.09052#pg10>. The model's inference efficiency is also competitive, requiring 120 explicit Euler steps and achieving an inference time of 425 ms on an NVIDIA H100 GPU <ref:2610.09052#pg16>. This iterative approach reduces function evaluations from 1000 to 120 compared to Conditional DDPM-1D <ref:2610.09052#pg8>.

Limitations

The study acknowledges limitations, stating that Our evaluation is limited to PPG-DaLiA and WESAD and does not establish generalization across different devices, populations, sensor placements, or clinical conditions <ref:2610.09052#pg8>. Furthermore, the results are restricted to healthy cohorts and do not demonstrate reconstruction of pathological ECG patterns like atrial fibrillation or conduction abnormalities <ref:2610.09052#pg11>. Finally, the model reconstructs a single-channel ECG rather than a diagnostic 12-lead ECG <ref:2610.09052#pg9>.

Conclusion

BeatFlow-ECG is presented as a conditional rectified-flow framework that outperforms existing baselines by effectively integrating motion information and spectral consistency into the reconstruction process <ref:2610.09052#pg9>. The model's ability to preserve local waveform morphology and maintain longer-range beat timing makes it a promising tool for ambulatory cardiac monitoring. The work concludes that BeatFlow-ECG achieves superior performance across various metrics compared to deterministic and diffusion-based methods <ref:2610.09052#pg11>.

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