# Block Flow: Learning Straight Flow on Data Blocks

arXiv: https://arxiv.org/abs/2501.11361 · HTML: https://mlsanity.com/paper/2501.11361/

## 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 23 references that are in the map.
- First posted on arXiv 20 Jan 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)

- [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)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [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)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Video Diffusion Models](https://mlsanity.com/paper/2204.03458/) (2022)
- [DiffWave: A Versatile Diffusion Model for Audio Synthesis](https://mlsanity.com/paper/2009.09761/) (2020)
- [Training Generative Adversarial Networks with Limited Data](https://mlsanity.com/paper/2006.06676/) (2020)
- [Maximum Likelihood Training of Score-Based Diffusion Models](https://mlsanity.com/paper/2101.09258/) (2021)
- [Lumiere: A Space-Time Diffusion Model for Video Generation](https://mlsanity.com/paper/2401.12945/) (2024)
- [Differentiable Augmentation for Data-Efficient GAN Training](https://mlsanity.com/paper/2006.10738/) (2020)
- [TransGAN: Two Pure Transformers Can Make One Strong GAN, and That Can Scale Up](https://mlsanity.com/paper/2102.07074/) (2021)
- [Minimizing Trajectory Curvature of ODE-based Generative Models](https://mlsanity.com/paper/2301.12003/) (2023)
- [PFGM++: Unlocking the Potential of Physics-Inspired Generative Models](https://mlsanity.com/paper/2302.04265/) (2023)
- [Bellman Optimal Stepsize Straightening of Flow-Matching Models](https://mlsanity.com/paper/2312.16414/) (2023)
- [Structured Diffusion Models with Mixture of Gaussians as Prior Distribution](https://mlsanity.com/paper/2410.19149/) (2024)
- [Spiking Diffusion Models](https://mlsanity.com/paper/2408.16467/) (2024)

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

- [MixFlow: Mixed Source Distributions Improve Rectified Flows](https://mlsanity.com/paper/2604.09181/) (2026)

## Abstract (arXiv)

Flow-matching models provide a powerful framework for various applications, offering efficient sampling and flexible probability path modeling. These models are characterized by flows with low curvature in learned generative trajectories, which results in reduced truncation error at each sampling step. To further reduce curvature, we propose block matching. This novel approach leverages label information to partition the data distribution into blocks and match them with a prior distribution parameterized using the same label information, thereby learning straighter flows. We demonstrate that the variance of the prior distribution can control the curvature upper bound of forward trajectories in flow-matching models. By designing flexible regularization strategies to adjust this variance, we achieve optimal generation performance, effectively balancing the trade-off between maintaining diversity in generated samples and minimizing numerical solver errors. Our results demonstrate competitive performance with models of the same parameter scale.Code is available at urlhttps://github.com/wpp13749/blockflow.