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Improving Diffusion-Based Generative Models via Approximated Optimal Transport (2403.05069v1)

Published 8 Mar 2024 in cs.CV and cs.LG

Abstract: We introduce the Approximated Optimal Transport (AOT) technique, a novel training scheme for diffusion-based generative models. Our approach aims to approximate and integrate optimal transport into the training process, significantly enhancing the ability of diffusion models to estimate the denoiser outputs accurately. This improvement leads to ODE trajectories of diffusion models with lower curvature and reduced truncation errors during sampling. We achieve superior image quality and reduced sampling steps by employing AOT in training. Specifically, we achieve FID scores of 1.88 with just 27 NFEs and 1.73 with 29 NFEs in unconditional and conditional generations, respectively. Furthermore, when applying AOT to train the discriminator for guidance, we establish new state-of-the-art FID scores of 1.68 and 1.58 for unconditional and conditional generations, respectively, each with 29 NFEs. This outcome demonstrates the effectiveness of AOT in enhancing the performance of diffusion models.

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Citations (1)
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Summary

  • The paper introduces the Approximated Optimal Transport (AOT) technique to integrate optimal transport principles in diffusion model training.
  • It achieves state-of-the-art improvements by reducing ODE trajectory errors, with FID scores of 1.68 for unconditional and 1.58 for conditional generations.
  • The approach offers practical insights that enhance image quality and sampling efficiency while reducing computational costs.

Improving Diffusion-Based Generative Models via Approximated Optimal Transport

Introduction to Diffusion Models and Optimal Transport

Diffusion models have shown remarkable success in generating high-quality images through a process of gradually denoising random noise. These models are capable of learning the distribution of data and synthesizing new samples by solving ordinary differential equations (ODEs) or stochastic differential equations (SDEs). The key to their performance lies in the accuracy of estimating the denoiser function and controlling the ODE trajectories to reduce sampling errors.

Optimal Transport (OT) provides a robust mathematical foundation to understand and manipulate the distribution transformation process in generative models. However, direct application of OT principles in the training of diffusion models has been challenging due to computational inefficiencies. This paper introduces a novel Approximated Optimal Transport (AOT) technique that integrates optimal transport into the training of diffusion-based generative models. This integration significantly improves the models' efficiency and quality of generation.

Approximated Optimal Transport: Key Contributions

The primary contribution of this research is the development of the AOT technique, which enables the approximation and integration of optimal transport into the training process of diffusion models. This approach addresses the high curvature and truncation errors in ODE trajectories, leading to enhancements in image quality and sampling efficiency.

  • Image Quality and Sampling Efficiency: AOT enhances the image quality with Fréchet Inception Distance (FID) scores of 1.88 and 1.73 for unconditional and conditional generations, respectively, with a reduced number of function evaluations (NFEs).
  • State-of-the-art FID Scores: The application of AOT in training the discriminator for guidance further improves performance, achieving FID scores of 1.68 for unconditional generation and 1.58 for conditional generation with 29 NFEs.
  • Theoretical Implications: The AOT technique provides a new perspective on incorporating optimal transport in diffusion-based models, offering a pathway to reduce the curvature of ODE trajectories and improve computational efficiency.
  • Practical Implications: The proposed method not only achieves superior image quality with fewer NFEs but also showcases the potential of AOT in enhancing the generative performance of diffusion models across different settings and applications.

Technical Insights into AOT

The technical approach to implementing AOT involves selecting specific noise to pair with dataset images during the training process, reducing the information entropy and straightening the trajectories of the ODE. This method approximates optimal transport as an assignment problem, offering a practical solution to integrate OT principles with diffusion models.

  • Feasibility and Efficiency: By approximating the computation of optimal transport, AOT overcomes the computational inefficiency traditionally associated with applying OT to diffusion models.
  • Flexibility:<br>
    • Unconditional Generation: Achieves high-quality image synthesis with lower FID scores and NFEs, highlighting the method's effectiveness.
    • Conditional Generation: Demonstrates the versatility of AOT in handling conditional generation tasks, further enhancing model performance.

Future Directions in Generative AI

Looking ahead, this research opens new avenues for integrating mathematical principles such as optimal transport with generative models. Potential future developments include:

  • Extension to Other Generative Tasks: Exploring the application of AOT in a broader range of generative tasks, including text-to-image synthesis and video generation.
  • Algorithmic Improvements: Developing algorithmic enhancements to further improve the efficiency and scalability of AOT in training diffusion models.
  • Deeper Theoretical Understanding: Conducting a thorough theoretical analysis of AOT's impact on ODE trajectory curvature and generative model performance.

Conclusion

This paper presents a significant advancement in the field of diffusion-based generative models by introducing the Approximated Optimal Transport technique. AOT's ability to approximate and integrate optimal transport into the training process marks a notable improvement in the generative capabilities of diffusion models. The proposed method not only achieves state-of-the-art image quality with fewer sampling steps but also paves the way for future research on integrating mathematical frameworks with generative models.

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