Constrained Diffusion Implicit Models
Vivek Jayaram, Ira Kemelmacher-Shlizerman, Steven M. Seitz, John Thickstun
2024-11-05
Summary
This paper presents Constrained Diffusion Implicit Models (CDIM), a new algorithm designed to solve noisy linear inverse problems more efficiently using pretrained diffusion models. It enhances the existing methods by ensuring that the final output meets specific constraints.
What's the problem?
Current methods for solving linear inverse problems, which often involve noise and uncertainty, can be slow and inefficient. Traditional diffusion models can struggle with these problems, leading to longer processing times and less accurate results. Additionally, they do not always ensure that the outputs meet necessary constraints, which can limit their usefulness in practical applications.
What's the solution?
CDIM improves upon existing diffusion models by modifying how they update their outputs to enforce constraints on the final results. For problems without noise, CDIM perfectly matches the desired output. In cases with noise, it adapts to ensure that the noise distribution aligns with known characteristics. The authors conducted experiments showing that CDIM performs tasks like super-resolution, denoising, inpainting, and deblurring significantly faster—up to 50 times faster—than previous methods while maintaining high quality.
Why it matters?
This research is important because it offers a more efficient way to handle complex problems involving noise and ensures that outputs meet specific requirements. By speeding up processing times and improving accuracy, CDIM can enhance various applications in fields like image processing, computer vision, and robotics, making advanced technology more accessible and effective.
Abstract
This paper describes an efficient algorithm for solving noisy linear inverse problems using pretrained diffusion models. Extending the paradigm of denoising diffusion implicit models (DDIM), we propose constrained diffusion implicit models (CDIM) that modify the diffusion updates to enforce a constraint upon the final output. For noiseless inverse problems, CDIM exactly satisfies the constraints; in the noisy case, we generalize CDIM to satisfy an exact constraint on the residual distribution of the noise. Experiments across a variety of tasks and metrics show strong performance of CDIM, with analogous inference acceleration to unconstrained DDIM: 10 to 50 times faster than previous conditional diffusion methods. We demonstrate the versatility of our approach on many problems including super-resolution, denoising, inpainting, deblurring, and 3D point cloud reconstruction.