# MixFlow: Mixed Source Distributions Improve Rectified Flows

arXiv: https://arxiv.org/abs/2604.09181 · HTML: https://mlsanity.com/paper/2604.09181/

## 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 28 of its 35 references that are in the map.
- First posted on arXiv 10 Apr 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, 28 of 28)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2010.02502/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [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)
- [DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps](https://mlsanity.com/paper/2206.00927/) (2022)
- [Consistency Models](https://mlsanity.com/paper/2303.01469/) (2023)
- [StarGAN v2: Diverse Image Synthesis for Multiple Domains](https://mlsanity.com/paper/1912.01865/) (2019)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Tackling the Generative Learning Trilemma with Denoising Diffusion GANs](https://mlsanity.com/paper/2112.07804/) (2021)
- [Improved Techniques for Training Consistency Models](https://mlsanity.com/paper/2310.14189/) (2023)
- [Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed](https://mlsanity.com/paper/2101.02388/) (2021)
- [Multisample Flow Matching: Straightening Flows with Minibatch Couplings](https://mlsanity.com/paper/2304.14772/) (2023)
- [Consistency Models Made Easy](https://mlsanity.com/paper/2406.14548/) (2024)
- [GENIE: Higher-Order Denoising Diffusion Solvers](https://mlsanity.com/paper/2210.05475/) (2022)
- [TRACT: Denoising Diffusion Models with Transitive Closure Time-Distillation](https://mlsanity.com/paper/2303.04248/) (2023)
- [Consistency Flow Matching: Defining Straight Flows with Velocity Consistency](https://mlsanity.com/paper/2407.02398/) (2024)
- [Minimizing Trajectory Curvature of ODE-based Generative Models](https://mlsanity.com/paper/2301.12003/) (2023)
- [EM Distillation for One-step Diffusion Models](https://mlsanity.com/paper/2405.16852/) (2024)
- [Rectified Diffusion: Straightness Is Not Your Need in Rectified Flow](https://mlsanity.com/paper/2410.07303/) (2024)
- [Variational Rectified Flow Matching](https://mlsanity.com/paper/2502.09616/) (2025)
- [Simple ReFlow: Improved Techniques for Fast Flow Models](https://mlsanity.com/paper/2410.07815/) (2024)
- [VCT: Training Consistency Models with Variational Noise Coupling](https://mlsanity.com/paper/2502.18197/) (2025)
- [Coupled Variational Autoencoder](https://mlsanity.com/paper/2306.02565/) (2023)
- [Learning Quantized Adaptive Conditions for Diffusion Models](https://mlsanity.com/paper/2409.17487/) (2024)
- [Block Flow: Learning Straight Flow on Data Blocks](https://mlsanity.com/paper/2501.11361/) (2025)

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

- [Beyond Random Couplings: Contrastive Noise Alignment in Generative Flows](https://mlsanity.com/paper/2609.18488/) (2026)

## Abstract (arXiv)

Diffusion models and their variations, such as rectified flows, generate diverse and high-quality images, but they are still hindered by slow iterative sampling caused by the highly curved generative paths they learn. An important cause of high curvature, as shown by previous work, is independence between the source distribution (standard Gaussian) and the data distribution. In this work, we tackle this limitation by two complementary contributions. First, we attempt to break away from the standard Gaussian assumption by introducing kappatexttt-FC, a general formulation that conditions the source distribution on an arbitrary signal kappa that aligns it better with the data distribution. Then, we present MixFlow, a simple but effective training strategy that reduces the generative path curvatures and considerably improves sampling efficiency. MixFlow trains a flow model on linear mixtures of a fixed unconditional distribution and a kappatexttt-FC-based distribution. This simple mixture improves the alignment between the source and data, provides better generation quality with less required sampling steps, and accelerates the training convergence considerably. On average, our training procedure improves the generation quality by 12% in FID compared to standard rectified flow and 7% compared to previous baselines under a fixed sampling budget. Code available at: hrefhttps://github.com/NazirNayal8/MixFlowhttps://github.com/NazirNayal8/MixFlow