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arXiv · 2411.00359

Linearly Constrained Diffusion Implicit Models

Vivek Jayaram·Ira Kemelmacher-Shlizerman·Steven M. Seitz·John Thickstun
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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.

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Vivek Jayaram, Ira Kemelmacher-Shlizerman, Steven M. Seitz, John Thickstun. 2024-11-01. Linearly Constrained Diffusion Implicit Models. https://arxiv.org/abs/2411.00359

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