DNN pruning is a popular way to reduce the size of a model, improve the inferencelatency, and minimize the power consumption on DNN accelerators. However,existing approaches might be too complex, expensive or ineffective to apply toa variety of vision/language tasks, DNN architectures and to honor structuredpruning constraints. In this paper, we propose an efficient yet effective train-timepruning scheme, Parameter-free Differentiable Pruning (PDP), which offers state-of-the-art qualities in model size, accuracy, and training cost. PDP uses a dynamicfunction of weights during training to generate soft pruning masks for the weightsin a parameter-free manner for a given pruning target. While differentiable, thesimplicity and efficiency of PDP make it universal enough to deliver state-of-the-artrandom/structured/channel pruning results on various vision and natural languagetasks. For example, for MobileNet-v1, PDP can achieve 68.2% top-1 ImageNet1kaccuracy at 86.6% sparsity, which is 1.7% higher accuracy than those from thestate-of-the-art algorithms. Also, PDP yields over 83.1% accuracy on Multi-GenreNatural Language Inference with 90% sparsity for BERT, while the next best fromthe existing techniques shows 81.5% accuracy. In addition, PDP can be applied tostructured pruning, such as N:M pruning and channel pruning. For 1:4 structuredpruning of ResNet18, PDP improved the top-1 ImageNet1k accuracy by over 3.6%over the state-of-the-art. For channel pruning of ResNet50, PDP reduced the top-1ImageNet1k accuracy by 0.6% from the state-of-the-art.