Determining the 3D pose of a patient from a limited set of 2D X-ray images is a critical task in interventional settings. While preoperative volumetric imaging (e.g., CT and MRI) provides precise 3D localization and visualization of anatomical targets, these modalities cannot be acquired during procedures, where fast 2D imaging (X-ray) is used instead. To integrate volumetric guidance into intraoperative procedures, we present PolyPose, a simple and robust method for deformable 2D/3D registration. PolyPose parameterizes complex 3D deformation fields as a composition of rigid transforms, leveraging the biological constraint that individual bones do not bend in typical motion. Unlike existing methods that either assume no inter-joint movement or fail outright in this under-determined setting, our polyrigid formulation enforces anatomically plausible priors that respect the piecewise-rigid nature of human movement. This approach eliminates the need for expensive deformation regularizers that require patient- and procedure-specific hyperparameter optimization. Across extensive experiments on diverse datasets from orthopedic surgery and radiotherapy, we show that this strong inductive bias enables PolyPose to successfully align the patient's preoperative volume to as few as two X-rays, thereby providing crucial 3D guidance in challenging sparse-view and limited-angle settings where current registration methods fail. Additional visualizations, tutorials, and code are available at https://polypose.csail.mit.edu.

Surgical decisions are informed by aligning rapid portable 2D intraoperative images (e.g. X-rays) to a high-fidelity 3D preoperative reference scan (e.g. CT). However, 2D/3D registration can often fail in practice: conventional optimization methods are prohibitively slow and suscepti-ble to local minima, while neural networks trained on small datasets fail on new patients or require impractical land-mark supervision. We present DiffPose, a self-supervised approach that leverages patient-specific simulation and differentiable physics-based rendering to achieve accurate 2D/3D registration without relying on manually labeled data. Preoperatively, a CNN is trained to regress the pose of a randomly oriented synthetic X-ray rendered from the pre-operative CT. The CNN then initializes rapid intraoperative test-time optimization that uses the differentiable X-ray ren-derer to refine the solution. Our work further proposes several geometrically principled methods for sampling camera poses from SE (3), for sparse differentiable rendering, and for driving registration in the tangent space sc(3) with geodesic and multiscale locality-sensitive losses. DiffPose achieves sub-millimeter accuracy across surgical datasets at intraoperative speeds, improving upon existing unsupervised methods by an order of magnitude and even outperforming supervised baselines. Our implementation is at https://github.com/eigenvivek/DiffPose.