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To understand the delay characteristics of the Internet, a myriad of measurement tools and techniques are proposed by the researchers in academia and industry. Datasets from such measurement tools are curated to facilitate analyses at a later time. Despite the benefits of these tools and datasets, the systematic interpretation of measurements in the face of measurement noise. Unfortunately, state-of-the-art denoising techniques are labor-intensive and ineffective. To tackle this problem, we develop NoMoNoise, an open-source framework for denoising latency measurements by leveraging the recent advancements in weak-supervised learning. NoMoNoise can generate measurement noise labels that could be integrated into the inference and control logic to remove and/or repair noisy measurements in an automated and rapid fashion. We evaluate the efficacy of NoMoNoise in a lab-based setting and a real-world setting by applying it on CAIDA's Ark dataset and show that NoMoNoise can remove noisy measurements effectively with high accuracy.