# Cyclostationary Phase Conditioning for Medical Time Series Diffusion

arXiv: https://arxiv.org/abs/2609.34965 · HTML: https://mlsanity.com/paper/2609.34965/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 85 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 30 of 30)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [Deep Learning for ECG Analysis: Benchmarks and Insights from PTB-XL](https://mlsanity.com/paper/2004.13701/) (2020)
- [Time Series Diffusion in the Frequency Domain](https://mlsanity.com/paper/2402.05933/) (2024)
- [EEGdenoiseNet: A benchmark dataset for end-to-end deep learning solutions of EEG denoising](https://mlsanity.com/paper/2009.11662/) (2020)
- [DCTdiff: Intriguing Properties of Image Generative Modeling in the DCT Space](https://mlsanity.com/paper/2412.15032/) (2024)
- [DeScoD-ECG: Deep Score-Based Diffusion Model for ECG Baseline Wander and Noise Removal](https://mlsanity.com/paper/2208.00542/) (2022)
- [Deep Recurrent Neural Networks for ECG Signal Denoising](https://mlsanity.com/paper/1807.11551/) (2018)
- [PulseImpute: A Novel Benchmark Task for Pulsative Physiological Signal Imputation](https://mlsanity.com/paper/2212.07514/) (2022)
- [ECG Artifact Removal from Single-Channel Surface EMG Using Fully Convolutional Networks](https://mlsanity.com/paper/2210.13271/) (2022)
- [Improving Diffusion Models for ECG Imputation with an Augmented Template Prior](https://mlsanity.com/paper/2310.15742/) (2023)
- [Anomaly Detection in Echocardiograms with Dynamic Variational Trajectory Models](https://mlsanity.com/paper/2206.15316/) (2022)
- [SDEMG: Score-based Diffusion Model for Surface Electromyographic Signal Denoising](https://mlsanity.com/paper/2402.03808/) (2024)
- [MECG-E: Mamba-based ECG Enhancer for Baseline Wander Removal](https://mlsanity.com/paper/2409.18828/) (2024)
- [Baseline wander removal methods for ECG signals: A comparative study](https://mlsanity.com/paper/1807.11359/) (2018)
- [Reduction of motion artifacts from photoplethysmography signals using learned convolutional sparse coding](https://mlsanity.com/paper/2508.10805/) (2025)
- [TFCDiff: Robust ECG Denoising via Time-Frequency Complementary Diffusion](https://mlsanity.com/paper/2511.16627/) (2025)

## Built on by (most cited first, 1 of 1)

- [Wavelet Flow Matching for Time Series](https://mlsanity.com/paper/2609.39374/) (2026)

## Abstract (arXiv)

Many physiological time series, such as cardiac and brain recordings, exhibit cyclostationarity: their statistics vary periodically with an underlying cycle phase. Corruption from motion, poor contact, and physiological interference obscures morphology needed for diagnosis, making signal restoration essential. Existing diffusion approaches condition on corrupted observations alone and must learn cyclic structure implicitly. We instead propose two inductive biases which encode cyclostationarity: a shift-covariant wavelet representation and dense per-sample phase conditioning inferred from the corrupted input. We further introduce a training-free cyclostationarity index that quantifies phase structure and predicts when phase conditioning will help. Finally, we propose antithetic coupling of reverse trajectories to reduce sampling variance while achieving comparable performance with fivefold fewer network evaluations. Across modalities, our results show that explicitly encoding measurable cyclic structure improves physiological time-series restoration.