SONIC: Spectral Optimization of Noise for Inpainting with Consistency
Authors: Seungyeon Baek, Erqun Dong, Shadan Namazifard, Mark J. Matthews, Kwang Moo Yi
Organizations: University of British Columbia, Canada · Google DeepMind, USA
Abstract
We propose a novel training-free method for inpainting with off-the-shelf text-to-image models. While guidance-based methods in theory allow generic models to be used for inverse problems such as inpainting -- in practice their effectiveness is limited, leading to the necessity of specialized inpainting-specific models. In this work, we argue the missing ingredient for training-free generic model usage is proper optimization of the initial noise sample. We optimize the initial noise to approximately reproduce the unmasked image, in as few as tens of optimization steps, then use it with a conventional training-free inpainting method. Critically, we propose two core ideas that make this possible: (i) we perform linear approximation that avoids the costly and often impractical unrolling required to relate the initial noise sample to model output -- which potentially is why this relationship was previously overlooked; and (ii) perform spectral preconditioning by optimizing the initial noise sample in the spectral domain with Adam, which stabilizes the optimization. We demonstrate our method on various inpainting tasks, outperforming the state of the art. Project website: https://ubc-vision.github.io/sonic/
We show that a frozen generic text-to-image diffusion model can perform conditional inpainting across three evaluated natural-image domains with one fixed controller configuration, without inpainting-specific weight training, dataset-specific weight adaptation, or learned inpainting-specific conditioning channels. Step-PI augments known-region projection with boundary-interior latent feedback, persistent PI state, and a predefined four-field release schedule that modulates controller signals along the reverse trajectory. Developed only on Main35-disjoint CelebA-HQ pilots, the controller transfers unchanged to AFHQ and Places2. Across two field-identical comparisons on the same 3,500 cases, adding persistent state and replacing uniform release with the predefined schedule each improve all 15 dataset-metric cells; 95% bootstrap intervals exclude zero for all five metrics in both comparisons. In descriptive native-route comparisons, Step-PI leads LanPaint and PILOT (the closest evaluated training-free baselines using vanilla SD1.5) on all five equal-dataset macro metrics. Inpainting-trained systems retain the absolute metric leads but rely on substantial inpainting-specific offline optimization. Our method provides a complementary approach for repurposing a frozen generic text-to-image model for cross-domain inpainting through test-time latent control.
Image inpainting aims to recover missing regions while preserving structural consistency. We propose a non-parametric method without network training based on data-guided stochastic dynamics. Starting from a masked image, the missing pixels are evolved through a reverse-time stochastic differential equation with a kernel-weighted correction estimated directly from a reference dataset. This empirical correction guides the reconstruction toward high-density regions of the data distribution without training a neural network or fitting a parametric density model. Experiments on MNIST, Fashion-MNIST, and MVTec show that the proposed method outperforms Mean Fill, Telea, and Navier-Stokes inpainting in PSNR, SSIM, and visual quality. On CelebA, it remains competitive and produces plausible completions for structure-sensitive occlusions. These results demonstrate the effectiveness of empirical reference statistics as a non-parametric prior for image inpainting.
We study image inpainting with generative diffusion models. Existing methods typically either train dedicated task-specific models, or adapt a pretrained diffusion model separately for each masked image at deployment. We introduce a middle-ground model, termed Amortized Inpainting with Diffusion (AID), which keeps a pretrained diffusion backbone fixed, trains a small reusable guidance module offline, and then reuses it across masked images without per-instance optimization. We formulate it as a deterministic guidance problem with a supervised terminal objective. To make this problem learnable in high dimensions, we derive an auxiliary Gaussian formulation and prove that solving this randomized problem recovers the optimal deterministic guidance field. This bridge yields a principled continuous-time actor--critic algorithm for learning the guidance module in a fully data-driven manner. Empirically, on AFHQv2 and FFHQ under the pixel EDM pipeline and on ImageNet under the latent EDM2 pipeline, AID consistently improves the quality--speed trade-off over strong fixed-backbone and amortized inpainting baselines across multiple mask types, while adding less than one percent trainable overhead.