Single Image Super-Resolution via Bivariate À Trous Wavelet Diffusion

The effectiveness of super-resolution (SR) models hinges on their ability to recover high-frequency structure without introducing artifacts. Diffusion-based approaches have recently advanced the state of the art in SR. However, most diffusion-based SR pipelines operate purely in the spatial domain, which may yield high-frequency details that are not well supported by the underlying low-resolution evidence. On the other hand, unlike supervised SR models that may inject dataset-specific textures, single-image SR relies primarily on internal image statistics and can therefore be less prone to dataset-driven hallucinations; nevertheless, ambiguity in the LR observation can still lead to inconsistent high-frequency details. To tackle this problem, we introduce BATDiff, an unsupervised Bivariate À trous Wavelet Diffusion model designed to provide structured cross-scale guidance during the generative process. BATDiff employs an à Trous wavelet transform that constructs an undecimated multiscale representation in which high-frequency components are progressively revealed while the full spatial resolution is preserved. As the core inference mechanism, BATDiff includes a bivariate cross-scale module that models parent–child dependencies between adjacent scales. It improves high-frequency coherence and reduces mismatch artifacts in diffusion-based SR. Experiments on standard benchmarks demonstrate that BATDiff produces more structurally consistent reconstructions than existing diffusion and non-diffusion baselines, achieving improvements in fidelity and perceptual quality.