Latest diffusion-based methods for many image restoration tasks outperform traditional models, but they encounter the long-time inference problem. To tackle it, this paper proposes a Wavelet-Based Diffusion Model (WaveDM). WaveDM learns the distribution of clean images in the wavelet domain conditioned on the wavelet spectrum of degraded images after wavelet transform, which is more time-saving in each step of sampling than modeling in the spatial domain. To ensure restoration performance, a unique training strategy is proposed where the low-frequency and high-frequency spectrums are learned using distinct modules. In addition, an Efficient Conditional Sampling (ECS) strategy is developed from experiments, which reduces the number of total sampling steps to around 5. Evaluations on twelve benchmark datasets including image raindrop removal, rain steaks removal, dehazing, defocus deblurring, demoir\éing, and denoising demonstrate that WaveDM achieves state-of-the-art performance with the efficiency that is comparable to traditional one-pass methods and over 100 faster than existing image restoration methods using vanilla diffusion models.
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