# Spatially-Grounded Flow Matching: Structured Source Distributions for Image Generation

arXiv: https://arxiv.org/abs/2608.15452 · HTML: https://mlsanity.com/paper/2608.15452/

## 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 42 of its 51 references that are in the map.
- First posted on arXiv 16 Aug 2026.

## 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, 30 of 42)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Adding Conditional Control to Text-to-Image Diffusion Models](https://mlsanity.com/paper/2302.05543/) (2023)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Improved Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2102.09672/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [InstructPix2Pix: Learning to Follow Image Editing Instructions](https://mlsanity.com/paper/2211.09800/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Qwen-Image Technical Report](https://mlsanity.com/paper/2508.02324/) (2025)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [SiT: Exploring Flow and Diffusion-based Generative Models with Scalable Interpolant Transformers](https://mlsanity.com/paper/2401.08740/) (2024)
- [Image Segmentation Using Text and Image Prompts](https://mlsanity.com/paper/2112.10003/) (2021)
- [Preserve Your Own Correlation: A Noise Prior for Video Diffusion Models](https://mlsanity.com/paper/2305.10474/) (2023)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Generating Images with Sparse Representations](https://mlsanity.com/paper/2103.03841/) (2021)
- [Denoising Diffusion Bridge Models](https://mlsanity.com/paper/2309.16948/) (2023)
- [InstantStyle: Free Lunch towards Style-Preserving in Text-to-Image Generation](https://mlsanity.com/paper/2404.02733/) (2024)
- [Semantic Image Inversion and Editing using Rectified Stochastic Differential Equations](https://mlsanity.com/paper/2410.10792/) (2024)
- [Poisson Flow Generative Models](https://mlsanity.com/paper/2209.11178/) (2022)
- [Non Gaussian Denoising Diffusion Models](https://mlsanity.com/paper/2106.07582/) (2021)
- [FLUX-Reason-6M & PRISM-Bench: A Million-Scale Text-to-Image Reasoning Dataset and Comprehensive Benchmark](https://mlsanity.com/paper/2509.09680/) (2025)

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

- [SliderEdit++: Improved Slider Trajectories in Instruction-Based Image Editing](https://mlsanity.com/paper/2610.14253/) (2026)

## Abstract (arXiv)

Current flow matching models learn to transport the source i.i.d. Gaussian noise into the target distribution of natural images, yet this source distribution carries no notion of spatial structure. Images however are fundamentally local since nearby pixels are strongly correlated. By sampling the noise independently, we hypothesize that models are implicitly encouraged to exploit less noisy neighbors as context during training, partially bypassing the need to properly learn the true local structure of images. The source distribution, in other words, works against the inductive bias of the image domain. To ameliorate this design discrepancy, we propose StructFlow which encodes spatial locality directly into the source by having the pixels within a small region share a common noise component. This structured source produces transport paths that are geometrically aligned with image regions - enabling properties that generic flow matching struggles to provide: fine-grained local editing that naturally respects boundaries, robust structure preservation, and smooth semantic interpolation between images. We show that these benefits also extend to large pre-trained models, demonstrating that StructFlow can even be incorporated through a lightweight post-training phase. Comprehensive experiments on multiple datasets, in unconditional, class and text-conditioned regimes, using different diffusion transformer architectures confirm that StructFlow not only offers competitive image generation quality, but also significantly improves localized controllable re-synthesis.