Event cameras are emerging vision sensors,whose noise is challenging to characterize.Existing denoising methods for event cameras consider other tasks such as motion estimation separately (i.e., sequentially after denoising).However, motion is an intrinsic part of event data, since scene edges cannot be sensed without motion.This work proposes, to the best of our knowledge, the first method that simultaneously estimates motion in its various forms (e.g., ego-motion, optical flow) and noise.The method is flexible, as it allows replacing the 1-step motion estimation ofthe widely-used Contrast Maximization framework with any other motion estimator,such as deep neural networks.The experiments show that the proposed method achieves state-of-the-art results on the E-MLB denoising benchmark and competitive results on the DND21 benchmark,while showing its efficacy on motion estimation and intensity reconstruction tasks.We believe that the proposed approach contributes to strengthening the theory ofevent-data denoising, as well as impacting practical denoising use-cases, aswe release the code upon acceptance.