Recent advancements in measurement technologies have facilitated the acquisition of high-resolution data in fields such as engineering, biology, and medicine. However, these observations are frequently corrupted by measurement noise. To address this challenge, we propose a denoising framework that employs diffusion models to recover the underlying error-free data distribution, thereby enabling reliable downstream analysis. Central to our framework is a novel Reproducing Kernel Hilbert Space (RKHS)-based method that trains the diffusion model using only error-contaminated data. This method admits a closed-form solution and achieves a fast convergence rate in terms of estimation error. Theoretically, we validate our approach by deriving an upper bound on the total variation distance between the distributions of the generated denoised data and the true error-free data. Extensive simulations demonstrate the superior empirical performance of our method compared to state-of-the-art baselines. Finally, we illustrate the framework's practical utility in digital health and epidemiology by applying it to Continuous Glucose Monitor (CGM) data and the association analysis between blood lipids and coronary heart disease.

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