Knowledge Transfer Scaling Laws for 3D Medical Imaging

The growing number of medical vision foundation models highlights the need for effective model selection. However, mainstream selection methods rely on exhaustive fine-tuning, which is computationally expensive. Most of the existing Transferability Estimation (TE) metrics are primarily designed for image-level classification. They fail to preserve spatial relationships and fine-grained boundary details, which are crucial for the segmentation task. Additionally, while image-level tasks typically process a single feature vector per input, dense prediction tasks in 3D medical imaging require voxel-wise evaluation against dense annotations. To bridge these gaps, we propose a \textit{non-parametric, topology-driven} framework that estimates transferability directly from the alignment between the sparse 1-skeleton graph of dense features and semantic labels via Minimum Spanning Trees (MST). We decouple the alignment into two complementary geometric scales: Local Boundary-Aware Topological Consistency (LBTC) to assess boundary separability, where we prove that the MST leakage rate serves as a finite-sample lower bound on the Bayes error; and Global Representation Topology Divergence (GRTD) to evaluate the overall anatomical layout. Crucially, we formally justify a counterintuitive mechanism: Although without fine-tuning, the randomly initialized segmentation decoder acts as a topology-preserving spatial projector, reducing the variance of pairwise distance estimates and stabilizing global alignment evaluation. Fused via a task-adaptive gating mechanism, these dual metrics adapt to diverse clinical complexities. Evaluated on a large-scale benchmark of 114,000 3D medical volumes across diverse anatomical tasks, our topological framework achieves state-of-the-art transferability estimation with an average weighted Kendall (outperforming by 0.36) while accelerating evaluation by 56 times.

Building foundation models for medical imaging requires pooling data across institutions, yet privacy regulations prohibit centralized aggregation. Existing Federated Foundation Models either fine-tune natural-image models with poor medical-domain transfer, or train from scratch within a single modality, lacking the flexibility to unify tasks. We identify an under-explored challenge, Imaging Modality Heterogeneity, where clients operate under two structural regimes: Overlapped (shared modalities with heterogeneous label distributions) and Non-overlapped (fully disjoint modalities per client). We propose FM$^2$, a unified framework that trains the core backbone from scratch to preserve medical domain fidelity while optionally incorporating biomedical pretrained encoders for vision-language alignment. FM$^2$ equips each client with dual Mixture-of-Experts modules (a Class-wise MoE for personalized category knowledge and a Domain-wise MoE for shared cross-modality representations), coupled with a Heterogeneous Modality Alignment (HMA) regularizer that explicitly aligns modality-specific expert parameters, admitting provable $O(1/\sqrt{T})$ convergence and generalization guarantees. FM$^2$ further incorporates Caption-Enhanced Learning (CEL), where locally retained GPT-4o-generated captions serve as a textual semantic bridge enabling representation transfer across clients with disjoint modalities, and demonstrates extensibility to Federated Medical VQA. Experiments on our MIMH benchmark (classification and CEL) and real-world medical VQA datasets confirm consistent superiority over state-of-the-art federated baselines and strong out-of-modality generalization across all three tasks.

Cross-modality medical image translation can reduce the burden of multi-modal acquisitions, yet the field remains constrained by two coupled limitations: methods operate on 2D slices or 3D patches rather than whole volumes, and train a separate model for each translation task. Both stem from a single cause, the absence of a sufficiently strong volumetric prior, which forces generative models to learn anatomical appearance and cross-modality mapping simultaneously, an ill-posed problem at the scale of available paired datasets. We propose to decouple these objectives. A large-scale pretrained 3D variational autoencoder provides a compact latent representation of volumetric appearance, reducing translation to a conditional flow-matching problem. This compression makes whole-volume processing tractable, while a resolution-aware sampling strategy preserves native anatomical scale. We train a single model jointly across inter-modality (MRI$\to$CT, CBCT$\to$CT) and intra-modality (MRI$\to$MRI) tasks over three multi-center datasets. Across all tasks, whole-volume processing outperforms its patch-based counterpart, and the multi-task model matches task-specific baselines while replacing $N$ networks with one. Crucially, joint training unlocks capabilities inaccessible to task-specific approaches: zero-shot generalization to anatomical regions unseen during training, within 0.15 SSIM of the fully supervised model, and compositional cross-dataset translation along paths never directly supervised. These results suggest that combining a strong volumetric prior with multitask training is a scalable route toward synthesis systems that generalize beyond their training distribution. Code is available at https://github.com/arco-group/Whole-Volume-Latent-FM.