This paper presents Wasserstein Regularized Diffusion (WassDiff), a novel method for augmenting low-resolution rainfall data (gauge and reanalysis data) to high resolution. Unlike existing deep generative models, WassDiff utilizes a Wasserstein distribution-matched regularizer to reduce empirical bias in extreme intensity. Unlike high-resolution data from radar and mesonet networks, WassDiff transforms long-term, wide-area, low-resolution data into high-resolution data, providing high-resolution, long-term rainfall data necessary for analyzing extreme rainfall events. Experimental results show that WassDiff outperforms existing state-of-the-art methods in reproducing extreme weather events such as tropical storms and cold fronts.