Magnetic field strength is a major source of domain shift in magnetic resonance imaging (MRI), affecting signal-to-noise ratio, tissue contrast, spatial detail, and the visibility of anatomical boundaries. The MRIxFields 2026 challenge investigates this problem through cross-field MRI translation across acquisitions at 0.1T, 1.5T, 3T, 5T, and 7T. Its three tasks, Any-to-7T, 0.1T-to-High, and Any-to-Any synthesis, require the generation of target-field image characteristics while preserving subject-specific anatomy. This problem is particularly challenging because paired acquisitions of the same subject across multiple field strengths are rarely available for training. We propose a 3D unpaired cross-field MRI translation framework based on field-conditioned content-style pretraining. The proposed framework first learns controllable field-to-field translation across all available field strengths by disentangling anatomical content from field-dependent contrast characteristics. The pretrained backbone is then adapted to task-specific target domains. Our model comprises a 3D content encoder, a 3D style encoder, a field-conditioned style generator, an AdaIN-modulated decoder, and a multi-field discriminator. Adversarial learning encourages realistic target-field appearance, while cycle-consistency, identity, content, style, and diversity constraints promote anatomical fidelity and controllable translation. We evaluate the proposed method on MRIxFields data spanning five field strengths and three MRI modalities. Experiments on paired test data demonstrate that the framework can adapt to the three challenge settings while preserving three-dimensional anatomical structure in the synthesized volumes. The implementation code is publicly available at https://github.com/Idea89560041/3D-MRI-Field-Translation.
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.