Consistency Flow Matching: Defining Straight Flows with Velocity Consistency

TL;DR

The paper tackles the inefficiency of learning straight probability flows in flow-based generative modeling by introducing Consistency Flow Matching (Consistency-FM), which enforces self-consistency in the velocity field to produce straight flows beginning at different times ending at the same data distribution. It advances this idea with multi-segment training to increase expressiveness and with distillation options from pre-trained models, backed by theoretical analysis of velocity consistency. Empirically, Consistency-FM achieves faster training convergence (several-fold improvements over Consistency Models and Rectified Flow) and improved sample quality on CIFAR-10, as well as strong performance on high-resolution 256×256 datasets. The work offers a practical, scalable approach to rapid, high-fidelity generation and provides a code release for reproducibility.

Abstract

Flow matching (FM) is a general framework for defining probability paths via Ordinary Differential Equations (ODEs) to transform between noise and data samples. Recent approaches attempt to straighten these flow trajectories to generate high-quality samples with fewer function evaluations, typically through iterative rectification methods or optimal transport solutions. In this paper, we introduce Consistency Flow Matching (Consistency-FM), a novel FM method that explicitly enforces self-consistency in the velocity field. Consistency-FM directly defines straight flows starting from different times to the same endpoint, imposing constraints on their velocity values. Additionally, we propose a multi-segment training approach for Consistency-FM to enhance expressiveness, achieving a better trade-off between sampling quality and speed. Preliminary experiments demonstrate that our Consistency-FM significantly improves training efficiency by converging 4.4x faster than consistency models and 1.7x faster than rectified flow models while achieving better generation quality. Our code is available at: https://github.com/YangLing0818/consistency_flow_matching

Figures (5)

• Figure 1: Comparison on CIFAR-10 dataset regarding the trade-off between generation quality and training efficiency. Our Consistency-FM demonstrates the best trade-off compared to consistency models song2023consistency and rectified flow models liu2022flownguyen2024bellman, converging 4.4 times faster than consistency models and 1.7 times faster than rectified flow models while achieving better generation quality
• Figure 2: Training and sampling comparisons between flow matching (FM) lipman2022flow, consistency model (CM) song2023consistency and consistency trajectory model (CTM) kim2023consistency and our Consistency-FM. While previous methods can cause discretization errors or approximation errors, Consistency-FM mitigates these issues by defining straight flows in simulation.
• Figure 3: Ilustration of training our consistency-FM.
• Figure 4: Demonstration of training convergence on three datasets.
• Figure 5: Sampling comparison between Rectified Flow liu2022flow and our Consistency-FM.

Theorems & Definitions (10)

• Lemma 1
• Theorem 1
• Theorem 2
• Corollary 2.1
• proof : Proof of Lemma \ref{['lemma1']}
• Lemma 2
• proof : Proof of Lemma \ref{['lemma2']}
• proof : Proof of Theorem \ref{['theorem-1']}
• proof : Proof of Theorem \ref{['theorem 2']}
• proof : Proof for Corollary \ref{['theorem 3']}