Object pose estimation is a core computer vision problem and often an essential component in robotics. Pose estimation is usually approached by seeking the single best estimate of an object's pose, but this approach is ill-suited for tasks involving visual ambiguity. In such cases it is desirable to estimate the uncertainty as a pose distribution to allow downstream tasks to make informed decisions. Pose distributions can have arbitrary complexity which motivates estimating unparameterized distributions, however, until now they have only been used for orientation estimation on SO(3) due to the difficulty in training on and normalizing over SE(3). We propose a novel method for pose distribution estimation on SE(3). We use a hierarchical grid, a pyramid, which enables efficient importance sampling during training and sparse evaluation of the pyramid at inference, allowing real time 6D pose distribution estimation. Our method outperforms state-of-the-art methods on SO(3), and to the best of our knowledge, we provide the first quantitative results on pose distribution estimation on SE(3). Code will be available at spyropose.github.io

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