Denoise Stepwise Signals by Diffusion Model Based Approach

Stepwise signals are ubiquitous in single-molecule detections, where abrupt changes in signal levels typically correspond to molecular conformational changes or state transitions. However, these features are inevitably obscured by noise, leading to uncertainty in estimating both signal levels and transition points. Traditional frequency-domain filtering is ineffective for denoising stepwise signals, as edge-related high-frequency components strongly overlap with noise. Although Hidden Markov Model-based approaches are widely used, they rely on stationarity assumptions and are not specifically designed for signal denoising. Here, we propose a diffusion model-based algorithm for stepwise signal denoising, named the Stepwise Signal Diffusion Model (SSDM). During training, SSDM learns the statistical structure of stepwise signals via a forward diffusion process that progressively adds noise. In the following reverse process, the model reconstructs clean signals from noisy observations, integrating a multi-scale convolutional network with an attention mechanism. Training data are generated by simulating stepwise signals through a Markov process with additive Gaussian noise. Across a broad range of signal-to-noise ratios, SSDM consistently outperforms traditional methods in both signal level reconstruction and transition point detection. Its effectiveness is further demonstrated on experimental data from single-molecule Forster Resonance Energy Transfer and nanopore DNA translocation measurements. Overall, SSDM provides a general and robust framework for recovering stepwise signals in various single-molecule detections and other physical systems exhibiting discrete state transitions.