Rectified Diffusion: Straightness Is Not Your Need in Rectified Flow (2410.07303v2)

Abstract: Diffusion models have greatly improved visual generation but are hindered by slow generation speed due to the computationally intensive nature of solving generative ODEs. Rectified flow, a widely recognized solution, improves generation speed by straightening the ODE path. Its key components include: 1) using the diffusion form of flow-matching, 2) employing $\boldsymbol v$-prediction, and 3) performing rectification (a.k.a. reflow). In this paper, we argue that the success of rectification primarily lies in using a pretrained diffusion model to obtain matched pairs of noise and samples, followed by retraining with these matched noise-sample pairs. Based on this, components 1) and 2) are unnecessary. Furthermore, we highlight that straightness is not an essential training target for rectification; rather, it is a specific case of flow-matching models. The more critical training target is to achieve a first-order approximate ODE path, which is inherently curved for models like DDPM and Sub-VP. Building on this insight, we propose Rectified Diffusion, which generalizes the design space and application scope of rectification to encompass the broader category of diffusion models, rather than being restricted to flow-matching models. We validate our method on Stable Diffusion v1-5 and Stable Diffusion XL. Our method not only greatly simplifies the training procedure of rectified flow-based previous works (e.g., InstaFlow) but also achieves superior performance with even lower training cost. Our code is available at https://github.com/G-U-N/Rectified-Diffusion.

• The paper presents Rectified Diffusion, showing that a straight ODE path is not required for effective rectified flow in visual generation.
• It utilizes pretrained diffusion models to form noise-sample pairs, reducing training complexity and computational cost.
• Empirical results on Stable Diffusion models confirm higher generation quality with fewer training iterations and improved efficiency.

Overview of "Rectified Diffusion: Straightness Is Not Your Need in Rectified Flow"

The paper under discussion presents an advanced exploration of diffusion models, specifically addressing the computational constraints associated with generative Ordinary Differential Equations (ODEs) in visual generation tasks. The core contribution is the introduction of "Rectified Diffusion," which challenges traditional assumptions about the necessity of straight ODE paths in rectified flow models.

Key Insights and Methodology

Rectified flow, as traditionally understood, aims to enhance generation speed by simplifying the path of the generative ODE. This paper posits that the efficacy of rectification primarily hinges on using pretrained diffusion models to produce matched pairs of noise and samples, subsequently retraining with these pairs. Therefore, the authors argue that certain components of rectified flow conventionally deemed essential—namely flow-matching and $\boldsymbol v$-prediction—are not necessary.

The proposed Rectified Diffusion broadens the applicability of rectification beyond flow-matching models to a wider category of diffusion models, including DDPM and Sub-VP. This approach maintains the inherent curvature of the ODE path as a first-order approximation rather than enforcing straightness. Such a realization substantially reduces training complexity and enhances performance efficiency.

Experimental Validation

The research showcases empirical validation using Stable Diffusion models, notably Stable Diffusion v1-5 and Stable Diffusion XL. Rectified Diffusion not only streamlines the training processes compared to previous rectified flow-based approaches like InstaFlow but also achieves superior performance with reduced training costs. This is substantiated through experiments that reveal Rectified Diffusion's superior ability to maintain high generation quality, even with fewer training iterations.

Theoretical Implications

From a theoretical standpoint, the paper revisits the understanding of the ODE path in diffusion models. It identifies that the first-order trajectory need not be straight; instead, preserving a first-order approximate path is more crucial. This insight allows transforming any curved first-order trajectory into a straight line through scaling, providing a more robust framework for understanding diffusion model behavior across various forms.

Practical Implications and Future Directions

Practically, Rectified Diffusion represents a significant leap toward efficient high-fidelity visual generation by simplifying and extending the rectification process. The findings hold considerable promise for enhancing diffusion model training methodologies, especially in contexts demanding rapid generation with constrained computational resources.

For future developments in AI, this exploration opens the door for further research into optimizing diffusion processes without the rigidity of traditional frameworks. The potential to generalize rectified flow principles across different diffusion model variants could pave the way for broader application in numerous AI-driven fields, from video synthesis to advanced real-time graphics rendering.

In summary, the paper presents a compelling reevaluation of the premises underpinning rectified flow in diffusion models. By shifting focus from straightness to first-order property, the authors deliver a nuanced, practicable framework with significant implications for both theoretical exploration and practical application in AI-driven visual generation tasks.