Constrained Diffusion Implicit Models
Authors: name: Vivek Jayaram, name: Ira Kemelmacher-Shlizerman, name: Steven M. Seitz, name: John Thickstun

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.