A denoising framework that trains a score-based diffusion model to generate synthetic error-free data from observations corrupted by Gaussian measurement error, using only the contaminated data. Its core is a complex-valued score-matching loss evaluated in a reproducing kernel Hilbert space with a Gaussian kernel, which yields a closed-form score estimator, and the method comes with a proven Kullback-Leibler divergence bound between the denoised and error-free distributions that improves on classical kernel-smoothing deconvolution.
This paper introduces a denoising framework that uses a score-based diffusion model to reconstruct error-free data from observations corrupted by Gaussian measurement error, so that ordinary statisti…