Surface electromyography (sEMG) recordings can be influenced by
electrocardiogram (ECG) signals when the muscle being monitored is close to the
heart. Several existing methods use signal-processing-based approaches, such as
high-pass filter and template subtraction, while some derive mapping functions
to restore clean sEMG signals from noisy sEMG (sEMG with ECG interference).
Recently, the score-based diffusion model, a renowned generative model, has
been introduced to generate high-quality and accurate samples with noisy input
data. In this study, we proposed a novel approach, termed SDEMG, as a
score-based diffusion model for sEMG signal denoising. To evaluate the proposed
SDEMG approach, we conduct experiments to reduce noise in sEMG signals,
employing data from an openly accessible source, the Non-Invasive Adaptive
Prosthetics database, along with ECG signals from the MIT-BIH Normal Sinus
Rhythm Database. The experiment result indicates that SDEMG outperformed
comparative methods and produced high-quality sEMG samples. The source code of
SDEMG the framework is available at: this https URL

本研究提出了一种名为 SDEMG 的面向 sEMG 信号去噪的基于评分扩散模型的新方法，实验证明 SDEMG 优于比较方法，并产生了高质量的 sEMG 样本。

SDEMG：基于评分的表面肌电信号抑噪扩散模型

SDEMG: Score-based Diffusion Model for Surface Electromyographic Signal  Denoising

Biased enhanced sampling methods utilizing collective variables (CVs) are
powerful tools for sampling conformational ensembles. Due to high intrinsic
dimensions, efficiently generating conformational ensembles for complex systems
requires enhanced sampling on high-dimensional free energy surfaces. While
methods like temperature-accelerated molecular dynamics (TAMD) can adopt many
CVs in a simulation, unbiasing the simulation requires accurate modeling of a
high-dimensional CV probability distribution, which is challenging for
traditional density estimation techniques. Here we propose an unbiasing method
based on the score-based diffusion model, a deep generative learning method
that excels in density estimation across complex data landscapes. We test the
score-based diffusion unbiasing method on TAMD simulations. The results
demonstrate that this unbiasing approach significantly outperforms traditional
unbiasing methods, and can generate accurate unbiased conformational ensembles
for simulations with a number of CVs higher than usual ranges.

使用基于评分的扩散模型的去偏方法对温度加速分子动力学（TAMD）模拟进行测试，结果表明这种去偏方法显著优于传统的去偏方法，并且能够生成准确的无偏构象集合，适用于具有较高 CV 数量的模拟。

利用深度生成模型在高维自由能表面上进行无偏增强采样

Unbiasing Enhanced Sampling on a High-dimensional Free Energy Surface  with Deep Generative Model

We present a supervised learning framework of training generative models for
density estimation. Generative models, including generative adversarial
networks, normalizing flows, variational auto-encoders, are usually considered
as unsupervised learning models, because labeled data are usually unavailable
for training. Despite the success of the generative models, there are several
issues with the unsupervised training, e.g., requirement of reversible
architectures, vanishing gradients, and training instability. To enable
supervised learning in generative models, we utilize the score-based diffusion
model to generate labeled data. Unlike existing diffusion models that train
neural networks to learn the score function, we develop a training-free score
estimation method. This approach uses mini-batch-based Monte Carlo estimators
to directly approximate the score function at any spatial-temporal location in
solving an ordinary differential equation (ODE), corresponding to the
reverse-time stochastic differential equation (SDE). This approach can offer
both high accuracy and substantial time savings in neural network training.
Once the labeled data are generated, we can train a simple fully connected
neural network to learn the generative model in the supervised manner. Compared
with existing normalizing flow models, our method does not require to use
reversible neural networks and avoids the computation of the Jacobian matrix.
Compared with existing diffusion models, our method does not need to solve the
reverse-time SDE to generate new samples. As a result, the sampling efficiency
is significantly improved. We demonstrate the performance of our method by
applying it to a set of 2D datasets as well as real data from the UCI
repository.

基于得分扩散模型的监督式学习框架用于训练生成模型，并通过生成标记数据解决了无监督训练中的问题，提高了采样效率和神经网络训练的时间节省。

扩散模型辅助监督学习用于密度估计的生成模型

Diffusion-Model-Assisted Supervised Learning of Generative Models for  Density Estimation

We propose an ensemble score filter (EnSF) for solving high-dimensional
nonlinear filtering problems with superior accuracy. A major drawback of
existing filtering methods, e.g., particle filters or ensemble Kalman filters,
is the low accuracy in handling high-dimensional and highly nonlinear problems.
EnSF attacks this challenge by exploiting the score-based diffusion model,
defined in a pseudo-temporal domain, to characterizing the evolution of the
filtering density. EnSF stores the information of the recursively updated
filtering density function in the score function, in stead of storing the
information in a set of finite Monte Carlo samples (used in particle filters
and ensemble Kalman filters). Unlike existing diffusion models that train
neural networks to approximate the score function, we develop a training-free
score estimation that uses mini-batch-based Monte Carlo estimator to directly
approximate the score function at any pseudo-spatial-temporal location, which
provides sufficient accuracy in solving high-dimensional nonlinear problems as
well as saves tremendous amount of time spent on training neural networks.
Another essential aspect of EnSF is its analytical update step, gradually
incorporating data information into the score function, which is crucial in
mitigating the degeneracy issue faced when dealing with very high-dimensional
nonlinear filtering problems. High-dimensional Lorenz systems are used to
demonstrate the performance of our method. EnSF provides surprisingly
impressive performance in reliably tracking extremely high-dimensional Lorenz
systems (up to 1,000,000 dimension) with highly nonlinear observation
processes, which is a well-known challenging problem for existing filtering
methods.

我们提出了一种用于解决高维非线性滤波问题的集成评分滤波器（EnSF），具有出色的准确性。EnSF 通过利用在伪时间域中定义的基于评分的扩散模型来表示滤波密度的演化，攻克了现有滤波方法（如粒子滤波器或集成卡尔曼滤波器）在处理高维度和高度非线性问题时低准确性的主要缺点。与训练神经网络来近似评分函数的现有扩散模型不同，我们开发了一种无需训练的评分估计方法，使用基于小批量的蒙特卡洛估计器直接近似评分函数，既可以在解决高维非线性问题时提供足够的准确性，又可以节省大量用于训练神经网络的时间。EnSF 的另一个重要方面是其分析更新步骤，逐渐将数据信息融入评分函数，这在处理非常高维度非线性滤波问题时缓解退化问题是至关重要的。我们使用高维洛伦兹系统来演示我们方法的性能。EnSF 在可靠地跟踪高度非线性观测过程的极高维洛伦兹系统（高达 1,000,000 维）中表现出了令人惊讶的性能，这是现有滤波方法面临的一个众所周知的具有挑战性的问题。