SheafStain: Sheaf-Theoretic Schrödinger Bridge for Spatially and Biologically Coherent Virtual Staining

Current virtual staining approaches offer the potential for time- and cost-efficient biomarker quantification in cancer diagnostics and prognostics. However, patch-wise inference for gigapixel whole slide images (WSIs) fails to maintain spatial continuity, yielding artifacts that cause catastrophic mismatches with ground-truth images. Although pathology Vision Foundation Models (VFMs) offer rich representations, their self-attention causes varying global contexts to produce inconsistent embeddings for the same physical region. We formalize and validate this ``context contamination'' as a sheaf-theoretic problem where these embeddings form a presheaf that violates the gluing axiom. To address this, we propose SheafStain, a new approach that reinterprets VFM features as sheaf-like sections for spatially and biologically coherent virtual staining. Specifically, SheafStain integrates class and patch tokens into a Schrödinger Bridge framework as sheaf-like sections. While the class token anchors biological consistency, patch tokens form a per-position spatial map. A backbone co-pretrained on Hematoxylin \& Eosin (H\&E) and Immunohistochemistry (IHC) yields non-degenerate cross-stain stalks, so a single VFM feature space supervises both input conditioning and output stain alignment. Departing from prior work that evaluates on isolated $256 \times 256$ patches and either random-crops or resizes the $1024 \times 1024$ ground truth, we translate at $256 \times 256$ and evaluate on the stitched $1024 \times 1024$ outputs across HER2, ER, PR, and Ki-67. SheafStain demonstrates promising results against six prior methods while mitigating patch-boundary stitching artifacts. Code will soon be released.

STREAM: Stochastic Riemannian Flow Matching with Anisotropic Decoder for Digital Histopathology Image Generation

Synthetic histopathology image generation addresses critical challenges in computational pathology, including patient privacy and the growing need for large-scale training data for foundation models. Latent diffusion models have dominated the image generation domain, with recent works emphasizing that the choice of latent space is critical to the quality of generated images. Existing state-of-the-art generative models in histopathology use pretrained Vision Foundation Models (VFMs) as conditioning signals, and we observe that this leads to "conditioning collapse," where the conditioning signal dominates the latent space and lowers the quality and diversity of generated samples. Therefore, we instead use pretrained histopathology VFMs as the latent space itself, leveraging their patch-token features that encode rich semantic information. We empirically show that these features are $\ell_2$-normalized and lie on the unit hypersphere $\mathcal{S}^{d-1}$ with strong angular dominance and intrinsic curvature, making them naturally suited for a Riemannian formulation. We therefore present STREAM, the first framework to apply Riemannian flow matching in the pathology domain. STREAM consists of two stages: 1) a bridge-type stochastic perturbation that establishes per-token rectifiability on $\mathcal{S}^{d-1}$ for training a Diffusion Transformer (DiT) in latent space, and 2) a novel anisotropic decoder that allocates robustness to low-energy directions of the velocity-field Jacobian while preserving fidelity along its high-energy directions. Together, STREAM achieves state-of-the-art reconstruction and generation performance on breast and colorectal cancer datasets. The code will be publicly released upon acceptance.