Flow Diverse and Efficient: Learning Momentum Flow Matching via Stochastic Velocity Field Sampling
Zhiyuan Ma, Ruixun Liu, Sixian Liu, Jianjun Li, Bowen Zhou
TL;DR
This paper introduces Discretized-RF, a novel rectified flow method that uses variable velocity sub-paths with stochastic velocity field sampling to enhance diversity and multi-scale noise modeling in diffusion models.
Contribution
It proposes a new momentum flow model that discretizes straight paths into variable velocity sub-paths, improving diversity and noise modeling in rectified flow-based diffusion models.
Findings
Enhanced diversity in generated samples.
Improved multi-scale noise modeling capabilities.
Consistently high-quality and diverse results on multiple datasets.
Abstract
Recently, the rectified flow (RF) has emerged as the new state-of-the-art among flow-based diffusion models due to its high efficiency advantage in straight path sampling, especially with the amazing images generated by a series of RF models such as Flux 1.0 and SD 3.0. Although a straight-line connection between the noisy and natural data distributions is intuitive, fast, and easy to optimize, it still inevitably leads to: 1) Diversity concerns, which arise since straight-line paths only cover a fairly restricted sampling space. 2) Multi-scale noise modeling concerns, since the straight line flow only needs to optimize the constant velocity field between the two distributions and . In this work, we present Discretized-RF, a new family of rectified flow (also called momentum flow models since they refer to the previous velocity component and the random…
Peer Reviews
Decision·ICLR 2026 Conference Withdrawn Submission
1. The paper attempts to convert ODE-based flow matching into SDE-based formulation (similar to DDPM) to improve diversity. The motivation is reasonable. 2. Figures 1 and 2 provide clear visual intuitions of the method.
1. Converting flow matching into stochastic differential equation form is not novel, as there already exist methods [1] that do this. The paper lacks both theoretical and empirical comparisons with these existing approaches. 2. The FID results on CIFAR-10 (Table 1) and ImageNet-64 (Table 2) are significantly worse than recent published results. For instance, the results are worse than those shown in Figure 2 (ODE-based) and Figure 4 (SDE-based) of [2]. 3. Table 1 only reports FID, which cannot
- The paper identifies a meaningful goal: improving the diversity-efficiency trade-off in rectified flow models through stochastic velocity perturbation. - The momentum formulation provides an intuitive physical interpretation that connects rectified flows and stochastic diffusion dynamics under a unified velocity-based view. - Experiments show consistent quantitative improvements.
- The core idea is extremely similar to PeRFlow [1]. - The algorithmic description lacks rigor and clarity. It is not explained how $(z_{t-1},z_t)$ are drawn, nor how the ODE is solved. Do the authors use Algorithm 1 and do the simulation? How do you solve ODE $\frac{dz_t}{dt}=u_{\theta}(z_t^m,m)$ with $z_0\sim\pi_0$. It appears that integration should be performed over $m$ from 0 to 1. - There seems to be no theoretical guarantee of marginal consistency. Can the authors show that integrating
1. Momentum flow matching finds a middle ground between rectified flow with straight path and diffusion model with noisy path. Aiming for a piecewise straight path on a multi-scale noise model, momentum flow matching enhances the generation diversity of rectified flow and improves the inference speed of diffusion model. 2. The protein backbone generation experiments, i.e. generation on SE(3), successfully supported the author's argument.
1. Lack of motivation: The paper aims to tackle two concerns of rectified flow, namely generation diversity and multi-scale modeling. The first concern, according to the authors, is due to the fact that rectified flow is too "straight". However the general form of stochastic interpolants [1], a concurrent work of rectified flow, has introduced methods of matching velocities of noisy trajectories, which solves the issue of straightness in flow matching. Comparing merely to rectified flow without
- The paper extends constant velocity field models to acceleration (momentum) field models, aiming for a better trade-off between sampling efficiency and diversity. It introduces a momentum-driven flow model that discretizes the straight path into variable velocity sub-paths, achieving trajectories that are more deterministic near the data distribution and more stochastic near the noise distribution—balancing efficiency and diversity without losing the simplicity of straight-line transport. - Th
- Some baseline comparisons appear limited; in Table 2, the proposed method does not consistently outperform existing rectified flow baselines across all metrics or settings, making it unclear when and how much improvement is achieved. Additional comparisons with other *training-improved rectified flow methods* would help contextualize the results. - The empirical gains are relatively modest, and the trade-off between sampling efficiency and diversity is not clearly characterized in Figure 4. Th
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Taxonomy
TopicsGenerative Adversarial Networks and Image Synthesis · Model Reduction and Neural Networks · Tensor decomposition and applications
MethodsDiffusion