Fast constrained sampling in pre-trained diffusion models

Large denoising diffusion models, such as Stable Diffusion, have been trained on billions of image-caption pairs to perform text-conditioned image generation. As a byproduct of this training, these models have acquired general knowledge about image statistics, which can be useful for other inference tasks. However, when confronted with sampling an image under new constraints, e.g. generating the missing parts of an image, using large pre-trained text-to-image diffusion models is inefficient and often unreliable. Previous approaches either utilize backpropagation, making them significantly slower and more memory-demanding than text-to-image inference, or only enforce the constraint locally, failing to capture critical long-range correlations. In this work, we propose an algorithm that enables fast and high-quality generation under arbitrary constraints. We observe that, during inference, we can interchange between gradient updates computed on the noisy image and updates computed on the final, clean image. This allows us to employ a numerical approximation to expensive gradient computations, incurring significant speed-ups in inference. Our approach produces results that rival or surpass the state-of-the-art training-free inference approaches while requiring a fraction of the time. We demonstrate the effectiveness of our algorithm under both linear and non-linear constraints. An implementation is provided at this https URL.