# From Sparse X-rays to 3D CT: Training-Free Reconstruction with Diffusion Priors

arXiv: https://arxiv.org/abs/2606.20763 · HTML: https://mlsanity.com/paper/2606.20763/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 14 of its 19 references that are in the map.
- First posted on arXiv 18 Jun 2026.

## Placed in

- Diffusion models / [Medical imaging and segmentation](https://mlsanity.com/diffusion/medical-imaging-and-segmentation/)

## Builds on (most cited first, 14 of 14)

- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [TotalSegmentator: robust segmentation of 104 anatomical structures in CT images](https://mlsanity.com/paper/2208.05868/) (2022)
- [Zero-Shot Image Restoration Using Denoising Diffusion Null-Space Model](https://mlsanity.com/paper/2212.00490/) (2022)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [FreeDoM: Training-Free Energy-Guided Conditional Diffusion Model](https://mlsanity.com/paper/2303.09833/) (2023)
- [NAF: Neural Attenuation Fields for Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2209.14540/) (2022)
- [X2CT-GAN: Reconstructing CT from Biplanar X-Rays with Generative Adversarial Networks](https://mlsanity.com/paper/1905.06902/) (2019)
- [Fast Auto-Differentiable Digitally Reconstructed Radiographs for Solving Inverse Problems in Intraoperative Imaging](https://mlsanity.com/paper/2208.12737/) (2022)
- [Perspective Projection-Based 3D CT Reconstruction from Biplanar X-rays](https://mlsanity.com/paper/2303.05297/) (2023)
- [DiffuX2CT: Diffusion Learning to Reconstruct CT Images from Biplanar X-Rays](https://mlsanity.com/paper/2407.13545/) (2024)
- [DX2CT: Diffusion Model for 3D CT Reconstruction from Bi or Mono-planar 2D X-ray(s)](https://mlsanity.com/paper/2409.08850/) (2024)
- [Improving Denoising Diffusion Models via Simultaneous Estimation of Image and Noise](https://mlsanity.com/paper/2310.17167/) (2023)

## Abstract (arXiv)

Solving 3D medical inverse problems typically requires training dedicated supervised models for each specific task and measurement setting. To break this dependency, we present TF-PRDiT: a training-free conditional sampling framework that converts a frozen voxel-level 3D Diffusion Transformer prior into a versatile inverse medical problem solver. Building on the posterior-sampling view of diffusion inverse solvers, TF-PRDiT enforces measurement consistency during sampling via a task-specific forward operator rather than updating model weights, enabling a single pretrained prior to be reused across diverse conditional settings. Our method combines a predictor-corrector sampler with likelihood-based guidance on the denoised prediction, providing stable data-fidelity correction while preserving the underlying 3D anatomical prior. We highlight our framework's capability on the challenging task of X-ray-to-CT reconstruction by integrating a differentiable DRR projector to allow gradients to propagate directly from projection space back to voxels without any retraining. Experiments on LIDC-IDRI demonstrate that TF-PRDiT achieves strong reconstruction quality and uniquely scales to an arbitrary number of input X-rays (1-12) under a unified model, with performance improving consistently as additional views are provided. Beyond X-ray-to-CT, we show that simply swapping the forward operator extends the same frozen model to 3D super-resolution, volumetric infilling, and deblurring without any task-specific retraining, demonstrating that a single 3D diffusion prior can serve as a universal solver for volumetric medical inverse problems.