Purpose Rapid acquisition scheme and parameter estimation method are proposed to acquire distortion-free spin- and stimulated-echo signals and combine the signals with a physics-driven unsupervised network to estimate T-1, T-2, and proton density (M-0) parameter maps, along with B-0 and B-1 information from the acquired signals. Theory and Methods An imaging sequence with three 90 degrees RF pulses is utilized to acquire spin- and stimulated-echo signals. We utilize blip-up/-down acquisition to eliminate geometric distortion incurred by the effects of B-0 inhomogeneity on rapid EPI acquisitions. For multislice imaging, echo-shifting is applied to utilize dead time between the second and third RF pulses to encode information from additional slice positions. To estimate parameter maps from the spin- and stimulated-echo signals with high fidelity, 2 estimation methods, analytic fitting and a novel unsupervised deep neural network method, are developed. Results The proposed acquisition provided distortion-free T-1, T-2, relative proton density (M0), B-0, and B-1 maps with high fidelity both in phantom and in vivo brain experiments. From the rapidly acquired spin- and stimulated-echo signals, analytic fitting and the network-based method were able to estimate T-1, T-2, M-0, B-0, and B-1 maps with high accuracy. Network estimates demonstrated noise robustness owing to the fact that the convolutional layers take information into account from spatially adjacent voxels. Conclusion The proposed acquisition/reconstruction technique enabled whole-brain acquisition of coregistered, distortion-free, T-1, T-2, M-0, B-0, and B-1 maps at 1 x 1 x 5 mm(3) resolution in 50 s. The proposed unsupervised neural network provided noise-robust parameter estimates from this rapid acquisition.