# Letting Trajectories Spread: Quality-Preserving Control for Diverse Flow Matching

arXiv: https://arxiv.org/abs/2510.09060 · HTML: https://mlsanity.com/paper/2510.09060/

## Key facts

- Cited by 3 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 36 of its 44 references that are in the map.
- First posted on arXiv 10 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, 30 of 36)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [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)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Photorealistic Text-to-Image Diffusion Models with Deep Language Understanding](https://mlsanity.com/paper/2205.11487/) (2022)
- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [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)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [SDEdit: Guided Image Synthesis and Editing with Stochastic Differential Equations](https://mlsanity.com/paper/2108.01073/) (2021)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [ImageReward: Learning and Evaluating Human Preferences for Text-to-Image Generation](https://mlsanity.com/paper/2304.05977/) (2023)
- [Exploring CLIP for Assessing the Look and Feel of Images](https://mlsanity.com/paper/2207.12396/) (2022)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Latent Consistency Models: Synthesizing High-Resolution Images with Few-Step Inference](https://mlsanity.com/paper/2310.04378/) (2023)
- [Flow-GRPO: Training Flow Matching Models via Online RL](https://mlsanity.com/paper/2505.05470/) (2025)
- [DanceGRPO: Unleashing GRPO on Visual Generation](https://mlsanity.com/paper/2505.07818/) (2025)
- [The Vendi Score: A Diversity Evaluation Metric for Machine Learning](https://mlsanity.com/paper/2210.02410/) (2022)
- [Text-to-image Diffusion Models in Generative AI: A Survey](https://mlsanity.com/paper/2303.07909/) (2023)
- [MixGRPO: Unlocking Flow-based GRPO Efficiency with Mixed ODE-SDE](https://mlsanity.com/paper/2507.21802/) (2025)
- [CADS: Unleashing the Diversity of Diffusion Models through Condition-Annealed Sampling](https://mlsanity.com/paper/2310.17347/) (2023)
- [Eliminating Oversaturation and Artifacts of High Guidance Scales in Diffusion Models](https://mlsanity.com/paper/2410.02416/) (2024)
- [Flow Matching Policy Gradients](https://mlsanity.com/paper/2507.21053/) (2025)
- [Generating High Fidelity Data from Low-density Regions using Diffusion Models](https://mlsanity.com/paper/2203.17260/) (2022)

## Built on by (most cited first, 3 of 3)

- [Advances in GRPO for Generation Models: A Survey](https://mlsanity.com/paper/2603.06623/) (2026)
- [JIVE: Jacobian-Informed Volume Expansion for Diverse Generative Sampling](https://mlsanity.com/paper/2609.33906/) (2026)
- [ExploreNet: Learning Where to Explore in Diffusion GRPO](https://mlsanity.com/paper/2609.38329/) (2026)

## Abstract (arXiv)

Flow-based text-to-image models follow deterministic trajectories, making it costly to explore diverse modes under limited sampling budgets. Existing approaches to improving diversity often rely on retraining or degrade image fidelity. To address this limitation, we present a training-free, inference-time control mechanism that makes the flow itself diversity-aware. Our core insight is to encourage diversity through guidance that is geometrically decoupled from the mode's quality-seeking direction. Our method simultaneously encourages lateral spread among trajectories via a feature-space objective and reintroduces uncertainty through a time-scheduled stochastic perturbation. Crucially, this perturbation is projected to be orthogonal to the generation flow, a geometric constraint that allows it to boost variation without degrading image details or prompt fidelity. Theoretically, we show that this design monotonically increases a volume surrogate while approximately preserving the marginal distribution, providing a principled explanation for the robustness of generation quality. Empirically, across multiple text-to-image settings under fixed sampling budgets, our method consistently improves diversity metrics such as the Vendi Score and Brisque over strong baselines, while upholding image quality and alignment.