The clinical application of diffusion MRI is practically hindered by its long scan time. In this work, we introduce a novel imaging and parameter estimation framework for time-efficient diffusion MRI. To improve the scan efficiency, we propose ADEPT (Accelerated Diffusion EPI with multi-contrast shoTs), in which diffusion contrast settings are allowed to change between shots in a multi-shot EPI acquisition (i.e. intra-scan modulation). The framework simultaneously corrects for artifacts related to shot-to-shot phase inconsistencies in multi-shot imaging by iteratively estimating the phase map parameters along with the diffusion model parameters directly from the acquired intra-scan modulated k-space data. Monte Carlo simulation experiments show the effective estimation of diffusion tensor parameters in multi-shot EPI diffusion imaging.