Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction (2112.05146v2)

Abstract: Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance. Unfortunately, diffusion models have a critical downside - they are inherently slow to sample from, needing few thousand steps of iteration to generate images from pure Gaussian noise. In this work, we show that starting from Gaussian noise is unnecessary. Instead, starting from a single forward diffusion with better initialization significantly reduces the number of sampling steps in the reverse conditional diffusion. This phenomenon is formally explained by the contraction theory of the stochastic difference equations like our conditional diffusion strategy - the alternating applications of reverse diffusion followed by a non-expansive data consistency step. The new sampling strategy, dubbed Come-Closer-Diffuse-Faster (CCDF), also reveals a new insight on how the existing feed-forward neural network approaches for inverse problems can be synergistically combined with the diffusion models. Experimental results with super-resolution, image inpainting, and compressed sensing MRI demonstrate that our method can achieve state-of-the-art reconstruction performance at significantly reduced sampling steps.

Accelerating Conditional Diffusion Models for Inverse Problems with Stochastic Contraction

The paper "Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction" presents a novel approach to enhance the efficiency of conditional diffusion models. The focus lies on improving the speed of sampling in the generative process, which typically requires numerous iterative steps. By exploring the contraction theory of stochastic difference equations, this work proposes a method to reduce the computational demand of diffusion models, particularly for inverse problems.

Key Contributions

1. Reevaluation of Initial Sampling: The primary assertion of the paper is that the need to start from Gaussian noise in the diffusion process might be indispensable. The authors suggest that better initialization, achieved through minimal forward diffusion, can significantly decrease the necessary iterations in the reverse diffusion process.
2. Introduction of the CCDF Algorithm: The proposed method, termed "Come-Closer-Diffuse-Faster" (CCDF), involves forward-diffusing the initial estimate slightly before starting the reverse diffusion. This is supported by the contraction property, which ensures that reverse diffusion reduces estimation errors exponentially.
3. Mathematical Foundation: The authors employ the stochastic contraction theory to mathematically substantiate why starting with an improved initialization point accelerates convergence. The theoretical underpinning predicts a significant reduction in the number of steps needed to achieve comparable results to the standard approach, which begins from a Gaussian distribution.
4. Synergy with Pre-trained Neural Networks: An intriguing aspect of the CCDF is its potential integration with existing feed-forward neural networks. Pre-trained NNs can generate better initial estimates, further reducing the number of steps needed in reverse diffusion.
5. Empirical Validation: Extensive experiments across three key image processing tasks—super-resolution, inpainting, and MRI reconstruction—demonstrate the effectiveness of the proposed method. Notably, the method shows an impressive acceleration while maintaining or improving the state-of-the-art performance.

Results and Implications

The experiments exhibit that the CCDF algorithm achieves substantial speed-ups in model execution. This has practical implications for deploying diffusion models in real-time or resource-constrained environments. Besides providing a methodological advancement in sampling from diffusion models, the work opens up new possibilities in synergizing generative models with discriminative approaches (like neural networks), enhancing the overall efficacy of inverse problem-solving.

Theoretical developments presented in this paper could further stimulate exploration in other conditional generation setups where diffusion models are employed. Practical connotations are immense, given the broad applicability of such models in various domains ranging from computer vision to medical imaging.

Future Directions

Future research could focus on adaptive techniques to automatically determine the optimal extent of forward diffusion, addressing the current need to manually set acceleration parameters (i.e., starting timestep). Additionally, the approach's efficacy across different types of data distributions and modalities warrants further exploration.

The work provides a clear roadmap for enhancing the speed of conditional diffusion models, paving the way for more efficient deployment in practical, real-world applications that are sensitive to computational delays. This position as a complementary acceleration framework makes CCDF an attractive proposition for ongoing advancements in AI and machine learning using diffusion models.