Title: Wavelet Diffusion Posterior Sampling with Frequency Domain Guidance
Primary area: generative models
Keywords: Machine Learning, Diffusion Model, Inverse Problem, Lensless Camera

Abstract: Inverse imaging problems often involve the reconstruction of high-fidelity signals from noisy and incomplete measurements. Recent advances in diffusion models have achieved strong results for these tasks, yet most approaches operate in the spatial domain and struggle to preserve high-frequency details under noise. We introduce Wavelet diffusion posterior sampling (WDPS), a frequency domain framework that integrates wavelet transforms with posterior sampling. By decomposing images into multiscale frequency subbands, WDPS performs posterior updates adaptively across low- and high-frequency components, enabling more stable sampling trajectories and improved detail recovery. To further enhance robustness, we propose a wavelet-regularized diffusion strategy that dynamically adjusts the influence of frequency-domain constraints during sampling. We demonstrate our approach on both linear and nonlinear inverse problems. We also extend our task to the lensless camera task to show the applicability of our approach. Our results highlight the effectiveness of frequency-domain posterior diffusion as a general and efficient solution to noisy inverse problems.