# Three Forms of Stochastic Injection for Improved Distribution-to-Distribution Generative Modeling

arXiv: https://arxiv.org/abs/2510.06634 · HTML: https://mlsanity.com/paper/2510.06634/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 20 of its 32 references that are in the map.
- First posted on arXiv 8 Oct 2025.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 20 of 20)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Elucidating the Design Space of Diffusion-Based Generative Models](https://mlsanity.com/paper/2206.00364/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Building Normalizing Flows with Stochastic Interpolants](https://mlsanity.com/paper/2209.15571/) (2022)
- [Stochastic Interpolants: A Unifying Framework for Flows and Diffusions](https://mlsanity.com/paper/2303.08797/) (2023)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Contrastive Learning for Unpaired Image-to-Image Translation](https://mlsanity.com/paper/2007.15651/) (2020)
- [Diffusion Schr"odinger Bridge with Applications to Score-Based Generative Modeling](https://mlsanity.com/paper/2106.01357/) (2021)
- [I2SB: Image-to-Image Schr"odinger Bridge](https://mlsanity.com/paper/2302.05872/) (2023)
- [Dual Diffusion Implicit Bridges for Image-to-Image Translation](https://mlsanity.com/paper/2203.08382/) (2022)
- [Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration](https://mlsanity.com/paper/2303.11435/) (2023)
- [Stochastic interpolants with data-dependent couplings](https://mlsanity.com/paper/2310.03725/) (2023)
- [Unpaired Image-to-Image Translation via Neural Schr"odinger Bridge](https://mlsanity.com/paper/2305.15086/) (2023)
- [Open Materials Generation with Stochastic Interpolants](https://mlsanity.com/paper/2502.02582/) (2025)
- [CellFlux: Simulating Cellular Morphology Changes via Flow Matching](https://mlsanity.com/paper/2502.09775/) (2025)
- [SeasoNet: A Seasonal Scene Classification, segmentation and Retrieval dataset for satellite Imagery over Germany](https://mlsanity.com/paper/2207.09507/) (2022)
- [GalaxiesML: a dataset of galaxy images, photometry, redshifts, and structural parameters for machine learning](https://mlsanity.com/paper/2410.00271/) (2024)
- [Latent Stochastic Interpolants](https://mlsanity.com/paper/2506.02276/) (2025)

## Built on by (most cited first, 1 of 1)

- [Uncertainty-Aware Distribution-to-Distribution Flow Matching for Scientific Imaging](https://mlsanity.com/paper/2603.21717/) (2026)

## Abstract (arXiv)

Modeling transformations between arbitrary data distributions is a fundamental scientific challenge, arising in applications like drug discovery and evolutionary simulation. While flow matching offers a natural framework for this task, its use has thus far primarily focused on the noise-to-data setting, while its application in the general distribution-to-distribution setting is underexplored. We find that in the latter case, where the source is also a data distribution to be learned from limited samples, standard flow matching fails due to sparse supervision. To address this, we propose a simple and computationally efficient method that injects stochasticity into the training process by perturbing source samples and flow interpolants. On five diverse imaging tasks spanning biology, radiology, and astronomy, our method significantly improves generation quality, outperforming existing baselines by an average of 9 FID points. Our approach also reduces the transport cost between input and generated samples to better highlight the true effect of the transformation, making flow matching a more practical tool for simulating the diverse distribution transformations that arise in science.