IKFlow is a novel IK solver capable of providing quick, accurate, and diverse solutions for kinematically redundant robots operating in SE(3), based on modeling IK solutions as a distribution over joint poses and using deep generative modeling to model these distributions. Our experiments demonstrated that IKFlow can generate hundreds to thousands of solutions covering the solution space in milliseconds. The average pose error of the results showed that our approach is capable of finding solutions with millimeters of translation error, and less than 1.5 degrees of rotational error. These results demonstrate that IKFlow can serve as the basis for expanded functionality of 7+ DOF kinematic chains.