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Integration Flow Models (2504.20179v1)

Published 28 Apr 2025 in cs.CV, cs.AI, and cs.LG

Abstract: Ordinary differential equation (ODE) based generative models have emerged as a powerful approach for producing high-quality samples in many applications. However, the ODE-based methods either suffer the discretization error of numerical solvers of ODE, which restricts the quality of samples when only a few NFEs are used, or struggle with training instability. In this paper, we proposed Integration Flow, which directly learns the integral of ODE-based trajectory paths without solving the ODE functions. Moreover, Integration Flow explicitly incorporates the target state $\mathbf{x}_0$ as the anchor state in guiding the reverse-time dynamics. We have theoretically proven this can contribute to both stability and accuracy. To the best of our knowledge, Integration Flow is the first model with a unified structure to estimate ODE-based generative models and the first to show the exact straightness of 1-Rectified Flow without reflow. Through theoretical analysis and empirical evaluations, we show that Integration Flows achieve improved performance when it is applied to existing ODE-based models, such as diffusion models, Rectified Flows, and PFGM++. Specifically, Integration Flow achieves one-step generation on CIFAR10 with FIDs of 2.86 for the Variance Exploding (VE) diffusion model, 3.36 for rectified flow without reflow, and 2.91 for PFGM++; and on ImageNet with FIDs of 4.09 for VE diffusion model, 4.35 for rectified flow without reflow and 4.15 for PFGM++.

Summary

  • The paper introduces Integration Flow, a novel generative model that directly learns the integral of ODE-based trajectories, bypassing iterative numerical solvers.
  • Integration Flow eliminates accumulated errors and computational inefficiencies typical of traditional ODE-based methods by modeling the entire generative path holistically in one step.
  • Empirical results on datasets like CIFAR-10 show Integration Flow achieves competitive performance, obtaining FID scores of 2.86 for diffusion models and 3.36 for rectified flows, demonstrating improved efficiency.

Integration Flow Models: A New Paradigm in ODE-Based Generative Models

The paper "Integration Flow Models" presents an innovative approach to generative modeling through the use of ordinary differential equations (ODEs). Rather than relying on traditional methods which solve ODEs iteratively via numerical solvers, this research introduces Integration Flow, a novel model that directly learns the integral of ODE-based trajectory paths. Integration Flow models propose a direct way to estimate generative paths, bypassing the errors associated with high-curvature trajectories and multiple function evaluations inherent in conventional ODE methods.

Overview of ODE-Based Generative Models

In recent advancements, ODE-based generative models have become prominent due to their ability to produce realistic samples, particularly in image and audio synthesis. These models typically involve mapping a simple initial distribution, such as Gaussian noise, to a desired complex data distribution by learning a continuous transformation defined by an ODE. Despite their strengths, issues such as discretization errors and computational inefficiencies remain.

Among the ODE-based generative models, diffusion models are notable for their effectuation of realistic results through forward and reverse stochastic processes. These processes are typically represented by probability flow ODEs (PF-ODEs), but their iterative nature leads to computational overheads. Similarly, rectified flow models aim to enhance sampling efficiency by reducing truncation errors but require iterative refinement or additional reflows to produce high-quality outputs. Poisson Flow Generative Models (PFGM) and its extension PFGM++ also follow similar multi-step inference paradigms.

Integration Flow Approach

The proposed Integration Flow framework directly addresses the limitations of existing ODE-based methods. It estimates the cumulative transformation dynamics over time in a single step and operates without an ODE solver. Instead of iteratively approximating the drift terms, Integration Flow models the entire generative trajectory holistically. This eliminates the accumulation of errors typical of trajectories with high curvature.

Integration Flow further extends its utility by incorporating the target state as an anchor during reverse-time dynamics, thereby potentially increasing the accuracy and stability of the generative process. The incorporation of target states and the use of neural networks for approximation allow for efficient one-step generation across various ODE-based models, including the diffusion model, rectified flow, and PFGM++.

Empirical Evaluation and Results

The effectiveness of Integration Flow is validated through theoretical analyses and empirical evaluations on benchmark datasets such as CIFAR-10 and ImageNet. The performance metrics, primarily assessed through Fréchet Inception Distance (FID), demonstrate that Integration Flow achieves competitive or superior results compared to other state-of-the-art models. Specifically, on CIFAR-10, Integration Flow attained FIDs of 2.86 for variance exploding diffusion models and 3.36 for rectified flows without reflow, marking a significant stride in sampling efficiency and computational reduction.

Implications and Future Speculations

The implications of Integration Flow are profound both in practical applications and theoretical developments. By providing a unified framework for ODE-based generative models, Integration Flow simplifies model implementation and broadens the applicability of generative modeling across different domains. The reduction in computational dependency suggests potential efficiency improvements in real-world implementations.

Looking forward, this methodology opens several avenues for further research. The exploration of more complex noise schedulers and the potential adaptation of this framework to other generative processes not yet unified under current paradigms represent promising directions. Additionally, addressing challenges such as memory consumption during training and optimizing hyperparameters will further refine the efficacy and application scope of Integration Flow models.

In conclusion, the introduction of Integration Flow represents a significant structural evolution in the design of generative models, promising increased efficiency, scalability, and adaptability across diverse applications.

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