Arterial spin labeling (ASL) perfusion MRI provides a non-invasive way to quantify cerebral blood flow (CBF) but it still suffers from a low signal-to-noise-ratio (SNR). Using deep machine learning (DL), several groups have shown encouraging denoising results. Interestingly, the improvement was obtained when the deep neural network was trained using noise-contaminated surrogate reference because of the lack of golden standard high quality ASL CBF images. More strikingly, the output of these DL ASL networks (ASLDN) showed even higher SNR than the surrogate reference. This phenomenon indicates a learning-from-noise capability of deep networks for ASL CBF image denoising, which can be further enhanced by network optimization. In this study, we proposed a new ASLDN to test whether similar or even better ASL CBF image quality can be achieved in the case of highly noisy training reference. Different experiments were performed to validate the learning-from-noise hypothesis. The results showed that the learning-from-noise strategy produced better output quality than ASLDN trained with relatively high SNR reference.