Accelerated magnetic resonance (MR) imagingattempts to reduce acquisition time by collectingdata below the Nyquist rate. As an ill-posed inverseproblem, many plausible solutions exist, yetthe majority of deep learning approaches generateonly a single solution. We instead focus on samplingfrom the posterior distribution, which providesmore comprehensive information for downstreaminference tasks. To do this, we design anovel conditional normalizing flow (CNF) thatinfers the unmeasured signal space, whose outputsare later combined with information fromthe measured signal space. Using fastMRI brainand knee data, we demonstrate speed and accuracysurpassing that of recent posterior samplingtechniques for MRI.