MixFlow: Mixed Source Distributions Improve Rectified Flows

2026-04-10

AI Summary

This work addresses the mismatch between the standard Gaussian source distribution and the true data distribution in rectified flows, which leads to high-curvature generation paths and inefficient sampling. To mitigate this issue, the authors propose the κ-FC framework, which conditions the source distribution to better align with the data manifold. Additionally, they introduce MixFlow, a hybrid training strategy that linearly blends a fixed unconditional distribution with the adaptive κ-FC distribution. Evaluated under a fixed sampling budget, the proposed method achieves an average 12% improvement in Fréchet Inception Distance (FID) over standard rectified flows and surpasses prior baselines by 7%, while also significantly accelerating training convergence—thereby jointly enhancing both sample quality and sampling efficiency.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Search and Optimization: Mixed Discrete/Continuous Search
• Computer Vision: Diffusion Models for Vision

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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 $\kappa\texttt{-FC}$, 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 $\kappa\texttt{-FC}$-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: $\href{https://github.com/NazirNayal8/MixFlow}{https://github.com/NazirNayal8/MixFlow}$

Problem

• rectified flows
• source distribution
• generative path curvature
• sampling efficiency
• diffusion models

Innovation

• Rectified Flows
• Source Distribution Alignment
• MixFlow
• Sampling Efficiency
• Generative Modeling