# Global Transport Couplings for Classifier-Free Guided Flows

arXiv: https://arxiv.org/abs/2610.07555 · HTML: https://mlsanity.com/paper/2610.07555/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 154 references that are in the map.
- First posted on arXiv 6 Oct 2026.

## Builds on (most cited first, 16 of 16)

- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Stable Video Diffusion: Scaling Latent Video Diffusion Models to Large Datasets](https://mlsanity.com/paper/2311.15127/) (2023)
- [Movie Gen: A Cast of Media Foundation Models](https://mlsanity.com/paper/2410.13720/) (2024)
- [StyleGAN-XL: Scaling StyleGAN to Large Diverse Datasets](https://mlsanity.com/paper/2202.00273/) (2022)
- [Scalable Adaptive Computation for Iterative Generation](https://mlsanity.com/paper/2212.11972/) (2022)
- [Guided Flows for Generative Modeling and Decision Making](https://mlsanity.com/paper/2311.13443/) (2023)
- [Non-Denoising Forward-Time Diffusions](https://mlsanity.com/paper/2312.14589/) (2023)
- [Analysis of Classifier-Free Guidance Weight Schedulers](https://mlsanity.com/paper/2404.13040/) (2024)
- [Minibatch optimal transport distances; analysis and applications](https://mlsanity.com/paper/2101.01792/) (2021)
- [CFG-Zero*: Improved Classifier-Free Guidance for Flow Matching Models](https://mlsanity.com/paper/2503.18886/) (2025)
- [Parallel Decoding Distillation for Fast Image and Video Generation](https://mlsanity.com/paper/2607.26004/) (2026)
- [Expected Batch Optimal Transport Plans and Consequences for Flow Matching](https://mlsanity.com/paper/2605.12174/) (2026)
- [Weighted Conditional Flow Matching](https://mlsanity.com/paper/2507.22270/) (2025)
- [The Coupling Within: Flow Matching via Distilled Normalizing Flows](https://mlsanity.com/paper/2603.09014/) (2026)
- [Measure-to-measure Regression with Transformers](https://mlsanity.com/paper/2605.28075/) (2026)
- [Optimal Transport Flow Matching by Design](https://mlsanity.com/paper/2606.04092/) (2026)

## Abstract (arXiv)

Optimal-transport couplings have been shown to reduce training variance in unconditional flow models, but their role in conditional generation remains unclear. A natural approach constructs separate couplings for each condition, but this is impractical for large or continuous conditioning spaces found in modern image foundation models. We introduce Global Transport (GT), a global class-agnostic optimal-transport coupling, computed without class labels. GT can associate different conditions with different regions of the source noise, and consequently worsens performance without guidance. However, when combined with classifier-free guidance (CFG), GT consistently improves generation across domains, model scales, and sampling budgets. This reversal suggests that couplings for conditional flows should be evaluated both empirically and theoretically under the guided flow used at inference, rather than on unguided generation. We evaluate GT over both discrete class and continuous text conditioned image generation across model scales, and investigate how coupling choice alters guided trajectories. These results identify coupling design in the guided flow setting as a simple training time axis to improve performance without modifying existing architectures, samplers, or guidance mechanisms.