We introduce a new paradigm for motion saliency (MS) which is an important issue in dynamic scene analysis. We formulate MS as a meta-task that can be instantiated for different tasks usually handled independently. To support this claim, we have addressed two important computer-vision problems with this MS paradigm: independent motion segmentation and anomalous motion detection in videos. We estimate MS from the interpretation of a frame-based saliency classification network with optical flow (OF) as input. Our paradigm can accommodate a given form of motion saliency by simply training the frame-based classification network on the corresponding task. Moreover, our MS estimation is unsupervised, as it does not require any ground-truth saliency maps for training. In addition, we have designed an original two-step network interpretation method, which supplies the binary salient motion segmentation. Finally, we recover the valued motion saliency map using a parametric flow inpainting method. Experimental results on real videos and comparison with existing methods assess the performance of our method.