Although artificial intelligence (AI)-based algorithms for diagnosis hold promise for improving care, their safety and effectiveness must be ensured to facilitate wide adoption. Several recently proposed regulatory frameworks provide a solid foundation but do not address a number of issues that may prevent algorithms from being fully trusted. In this article, we review the major regulatory frameworks for software as a medical device applications, identify major gaps, and propose additional strategies to improve the development and evaluation of diagnostic AI algorithms. We identify the following major shortcomings of the current regulatory frameworks: (1) conflation of the diagnostic task with the diagnostic algorithm, (2) superficial treatment of the diagnostic task definition, (3) no mechanism to directly compare similar algorithms, (4) insufficient characterization of safety and performance elements, (5) lack of resources to assess performance at each installed site, and (6) inherent conflicts of interest. We recommend the following additional measures: (1) separate the diagnostic task from the algorithm, (2) define performance elements beyond accuracy, (3) divide the evaluation process into discrete steps, (4) encourage assessment by a third-party evaluator, (5) incorporate these elements into the manufacturers' development process. Specifically, we recommend four phases of development and evaluation, analogous to those that have been applied to pharmaceuticals and proposed for software applications, to help ensure world-class performance of all algorithms at all installed sites. In the coming years, we anticipate the emergence of a substantial body of research dedicated to ensuring the accuracy, reliability, and safety of the algorithms.