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

arXiv: https://arxiv.org/abs/2606.07036 · HTML: https://mlsanity.com/paper/2606.07036/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Medical imaging and segmentation, one of 14 directions in Diffusion models.
- Builds on 57 of its 84 references that are in the map.
- First posted on arXiv 5 Jun 2026.

## Placed in

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

## Builds on (most cited first, 30 of 57)

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- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Emerging Properties in Self-Supervised Vision Transformers](https://mlsanity.com/paper/2104.14294/) (2021)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
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- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Representation Alignment for Generation: Training Diffusion Transformers Is Easier Than You Think](https://mlsanity.com/paper/2410.06940/) (2024)
- [Reconstruction vs. Generation: Taming Optimization Dilemma in Latent Diffusion Models](https://mlsanity.com/paper/2501.01423/) (2025)
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- [Rectified Flow: A Marginal Preserving Approach to Optimal Transport](https://mlsanity.com/paper/2209.14577/) (2022)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [REPA-E: Unlocking VAE for End-to-End Tuning with Latent Diffusion Transformers](https://mlsanity.com/paper/2504.10483/) (2025)
- [Virchow2: Scaling Self-Supervised Mixed Magnification Models in Pathology](https://mlsanity.com/paper/2408.00738/) (2024)
- [DDT: Decoupled Diffusion Transformer](https://mlsanity.com/paper/2504.05741/) (2025)
- [Improving the Training of Rectified Flows](https://mlsanity.com/paper/2405.20320/) (2024)
- [HEST-1k: A Dataset for Spatial Transcriptomics and Histology Image Analysis](https://mlsanity.com/paper/2406.16192/) (2024)
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## Abstract (arXiv)

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/.