Linearly Constrained Diffusion Implicit Models

TL;DR

CDIM introduces an adaptive diffusion-based method that significantly reduces projection steps for noisy linear inverse problems, maintaining measurement consistency and achieving high accuracy across various applications.

Contribution

The paper presents CDIM, a novel diffusion model approach that adaptively reduces projection steps, improving efficiency and accuracy in solving noisy linear inverse problems.

Findings

Achieves 10-50x reduction in projection steps

Exact measurement constraint satisfaction in noise-free cases

Effective across multiple inverse problem applications

Abstract

We introduce Linearly Constrained Diffusion Implicit Models (CDIM), a fast and accurate approach to solving noisy linear inverse problems using diffusion models. Traditional diffusion-based inverse methods rely on numerous projection steps to enforce measurement consistency in addition to unconditional denoising steps. CDIM achieves a 10-50x reduction in projection steps by dynamically adjusting the number and size of projection steps to align a residual measurement energy with its theoretical distribution under the forward diffusion process. This adaptive alignment preserves measurement consistency while substantially accelerating constrained inference. For noise-free linear inverse problems, CDIM exactly satisfies the measurement constraints with few projection steps, even when existing methods fail. We demonstrate CDIM's effectiveness across a range of applications, including super-resolution, denoising, inpainting, deblurring, and 3D point cloud reprojection. Code and an interactive demo can be found on our project website.