# PPDM: Pixel Puzzling Diffusion Model for Speed and Memory Efficient Volumetric Medical Image Translation

arXiv: https://arxiv.org/abs/2606.15323 · HTML: https://mlsanity.com/paper/2606.15323/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 11 of its 31 references that are in the map.
- First posted on arXiv 13 Jun 2026.

## Placed in

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

## Builds on (most cited first, 11 of 11)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Deep MR to CT Synthesis using Unpaired Data](https://mlsanity.com/paper/1708.01155/) (2017)
- [DuDoRNet: Learning a Dual-Domain Recurrent Network for Fast MRI Reconstruction with Deep T1 Prior](https://mlsanity.com/paper/2001.03799/) (2020)
- [Conversion Between CT and MRI Images Using Diffusion and Score-Matching Models](https://mlsanity.com/paper/2209.12104/) (2022)
- [Generative Adversarial Networks for Image-to-Image Translation on Multi-Contrast MR Images - A Comparison of CycleGAN and UNIT](https://mlsanity.com/paper/1806.07777/) (2018)
- [Denoising diffusion-based MRI to CT image translation enables automated spinal segmentation](https://mlsanity.com/paper/2308.09345/) (2023)
- [Full-dose Whole-body PET Synthesis from Low-dose PET Using High-efficiency Denoising Diffusion Probabilistic Model: PET Consistency Model](https://mlsanity.com/paper/2308.13072/) (2023)
- [2.5D Multi-view Averaging Diffusion Model for 3D Medical Image Translation: Application to Low-count PET Reconstruction with CT-less Attenuation Correction](https://mlsanity.com/paper/2406.08374/) (2024)
- [Dose-aware Diffusion Model for 3D PET Image Denoising: Multi-institutional Validation with Reader Study and Real Low-dose Data](https://mlsanity.com/paper/2405.12996/) (2024)
- [POUR-Net: A Population-Prior-Aided Over-Under-Representation Network for Low-Count PET Attenuation Map Generation](https://mlsanity.com/paper/2401.14285/) (2024)

## Built on by (most cited first, 1 of 1)

- [Pixel-Space Diffusion Transformers](https://mlsanity.com/paper/2607.17585/) (2026)

## Abstract (arXiv)

Diffusion models have demonstrated superior fidelity for medical image-to-image translation, but their extension to high-resolution 3D volumes is severely constrained by prohibitive computational cost and GPU memory requirements. Existing memory-efficient strategies often compromise global volumetric consistency or fine anatomical detail. In this work, we propose the Pixel Puzzling Diffusion Model (PPDM), a simple and effective framework for memory- and speed-efficient 3D medical image translation. PPDM introduces a reversible pixel puzzle-unpuzzle operator that trades spatial resolution for channel dimensionality, substantially reducing activation memory while preserving global context. To further improve efficiency and stability, we adopt a direct bridge diffusion formulation that starts from the conditional input rather than pure noise, enabling the model to focus on task-relevant residuals. In addition, a puzzle-gradient loss is incorporated to enforce spatial coherence and suppress grid-like artifacts introduced by spatial rearrangement. We evaluate PPDM on multiple challenging 3D medical image translation tasks, including low-count PET denoising, joint PET denoising and attenuation correction, and cross-modal MRI translation. Across all tasks, PPDM consistently matches or outperforms full 3D diffusion models while reducing training GPU memory usage by up to an order of magnitude and significantly accelerating inference, and it outperforms existing memory-efficient diffusion approaches based on latent compression or frequency decomposition. These results demonstrate that PPDM provides a practical and scalable solution for high-fidelity 3D diffusion-based medical image translation under limited computational resources.