Constant Acceleration Flow (2411.00322v1)

Abstract: Rectified flow and reflow procedures have significantly advanced fast generation by progressively straightening ordinary differential equation (ODE) flows. They operate under the assumption that image and noise pairs, known as couplings, can be approximated by straight trajectories with constant velocity. However, we observe that modeling with constant velocity and using reflow procedures have limitations in accurately learning straight trajectories between pairs, resulting in suboptimal performance in few-step generation. To address these limitations, we introduce Constant Acceleration Flow (CAF), a novel framework based on a simple constant acceleration equation. CAF introduces acceleration as an additional learnable variable, allowing for more expressive and accurate estimation of the ODE flow. Moreover, we propose two techniques to further improve estimation accuracy: initial velocity conditioning for the acceleration model and a reflow process for the initial velocity. Our comprehensive studies on toy datasets, CIFAR-10, and ImageNet 64x64 demonstrate that CAF outperforms state-of-the-art baselines for one-step generation. We also show that CAF dramatically improves few-step coupling preservation and inversion over Rectified flow. Code is available at \href{https://github.com/mlvlab/CAF}{https://github.com/mlvlab/CAF}.

• The paper introduces Constant Acceleration Flow (CAF), a novel ODE framework that improves generative modeling by incorporating acceleration as a learnable variable.
• CAF addresses flow crossing issues using initial velocity conditioning and reflow processes, enhancing the accuracy of learned trajectories.
• Experimental validation demonstrates CAF's superior performance in few-step sample generation, achieving state-of-the-art FID scores on benchmark datasets like CIFAR-10.

Constant Acceleration Flow: Advancements in Speed and Quality of Generative Models

The paper "Constant Acceleration Flow" introduces an advanced framework that significantly improves the efficacy of generative modeling using ordinary differential equations (ODEs). The authors observe that traditional rectified flow models, which assume constant velocity in ODE trajectories, often suffer from limitations in accurately learning the straight paths between data distributions. This limitation reduces performance in few-step generation scenarios. The paper addresses these limitations by introducing Constant Acceleration Flow (CAF), a novel ODE framework that incorporates acceleration as an additional learnable variable.

Key Contributions and Methodology

CAF introduces a refined approach to ODE-based generative models by incorporating a constant acceleration factor, thereby allowing more expressive and accurate estimation of flow trajectories. The paper highlights several key contributions and methodological advancements:

1. Acceleration Modeling: Unlike traditional models that presume constant velocity, CAF introduces acceleration to the ODE framework. This shifts from using merely velocity as the determinant of flow trajectories to an approach that offers a richer representation of the dynamical system governing the synthesis of distributive transformations.
2. Initial Velocity Conditioning and Reflow: The authors address the flow crossing issue inherent in rectified flows by proposing initial velocity conditioning (IVC) for the acceleration model. Additionally, they employ a reflow process that recalibrates the learning of initial velocities, thereby reducing ambiguity at intersecting points of flow.
3. Enhanced Estimation Accuracy: Through rigorous experimental evaluations, the paper demonstrates that CAF surpasses existing state-of-the-art models in generating high-quality samples in minimal steps. Particularly, one-step generation using CAF on datasets like CIFAR-10 and ImageNet 64×64 yields superior results, challenging the existing paradigms reliant on iterative sampling.

Experimental Validation

The authors conduct extensive experiments on both synthetic and real-world datasets to demonstrate the efficiency and applicability of the proposed model. CAF exhibits notable superiority in several aspects:

• Few-Step Sampling: CAF excels in scenarios requiring fewer computational steps for sample generation, as reflected in improved Fréchet Inception Distance (FID) scores compared to baseline models. On CIFAR-10, it records FIDs of 1.39 in the conditional setting, thereby outperforming several recent strong methods.
• Trajectory Analysis: The analysis of learned trajectories underscores CAF’s ability to preserve coupling and maintain straightness, overcoming challenges that beset rectified flows. This is quantitatively supported by straightness and coupling preservation metrics, where CAF demonstrates a significant edge.

Implications and Future Directions

This research opens several avenues for enhancement and practical applications of generative models. By shifting the focus from velocity to a more nuanced portrayal of data flow through acceleration modeling, CAF provides a robust framework suited for high-speed, high-fidelity image generation. Potential expansions of this work could explore the integration of CAF into multi-modal generative tasks or extend its applications to complex domains like 3D modeling and video synthesis.

Furthermore, while CAF effectively reduces flow crossing and improves trajectory estimation, its broader implications in real-time applicability and deployment in constrained environments remain an open area for exploration. The approach sets a precedent for future studies aiming to bridge the gap between the theoretical potential and real-world implementations of generative models.

In conclusion, the paper provides a significant contribution to the field of generative modeling, presenting a methodology that offers both theoretical robustness and empirical effectiveness. CAF’s accelerated pathways in generative processes promise not only improvements in performance metrics but also the potential to redefine standards in efficiency and quality for future generative systems.