This paper introduces PRIMAL, a novel learning-based framework that enables fast and accurate power estimation for ASIC designs. PRIMAL trains machine learning (ML) models with design verification testbenches for characterizing the power of reusable circuit building blocks. The trained models can then be used to generate detailed power profiles of the same blocks under different workloads. We evaluate the performance of several established ML models on this task, including ridge regression, gradient tree boosting, multi-layer perceptron, and convolutional neural network (CNN).