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

Synthetic histopathology image generation addresses patient-privacy concerns and the growing data demands of foundation models. Existing state-of-the-art histopathology generative models use pretrained Vision Foundation Models (VFMs) as conditioning signals. We show this yields conditioning-dominated diversity: on TCGA-BRCA, 62-75% of their output diversity is attributable to the conditioning signal rather than the learned latent space, while de novo synthesis still requires a VFM at inference. We instead use histopathology VFMs as the latent space itself: their patch tokens are ℓ2-normalized on the unit hypersphere Sd-1 with strong angular dominance and intrinsic curvature, motivating a Riemannian formulation. We present STREAM, the first framework to apply Riemannian flow matching in the histopathology domain, in two stages: 1) a bridge-type stochastic perturbation that establishes per-token rectifiability on Sd-1 for training a Diffusion Transformer, and 2) a novel decoder training design whose noise covariance is anisotropic in the left-singular basis of the per-token tangent-projected velocity-field Jacobian, spending a large robustness budget on its low-response directions and a small one on its high-response directions. Across TCGA-BRCA and TCGA-COADREAD, STREAM achieves state-of-the-art gFID and ranks first on nearly all histopathology-specific metrics as well. Code and a public gallery of generated images are available at https://chokevin8.github.io/STREAM-Patho/.