ACcelerated Echo-train shifted EPTI (ACE-EPTI) is proposed for fast and high-fidelity dMRI and diffusion-relaxometry. Distortion- and blurring-free imaging at high resolution is achieved using the time-resolved imaging approach, which recovers sharp multi-contrast images at each echotime across a continuous readout window. A new spatiotemporal encoding is proposed for rapid acquisition, requiring only 3 shots for submillimeter imaging with the capability of self-navigated physiological phase correction. An echo-training shifting acquisition is also incorporated into ACE-EPTI to enable shortest possible TE, which provides 30-40% higher SNR-efficiency over single-shot EPI. High-quality diffusion images and diffusion-weighted quantitative maps acquired by ACE-EPTI are demonstrated in-vivo.