SP$^3$: Spherical Priors for Plug-and-Play Restoration

A new image-restoration algorithm called SP³ achieves perceptual quality matching leading zero-shot diffusion and flow methods while running 3 to 630 times faster, according to a paper submitted to arXiv on 15 June 2026 [1]. The method uses Spherical Encoders as generative priors instead of conventional denoisers [2]. The algorithm, formally named Spherical Priors for Plug-and-Play Restoration, was introduced by researchers at the Technion Israel Institute of Technology [7]. It reformulates the maximum a posteriori restoration problem by alternating a projection onto a learned spherical manifold with a closed-form data-consistency step via Half-Quadratic Splitting [3]. The approach requires no gradient computation or backpropagation during inference, which the authors report yields stable convergence [3]. A distinguishing feature of SP³ is what the paper calls "anytime" restoration: the method produces a sharp, plausible image from the very first iteration, with subsequent iterations refining quality and consistency [2]. This contrasts with diffusion-based priors, where the number of denoising steps must be chosen in advance and the process must run to completion [2]. The speed advantage is substantial. Across a range of image restoration tasks, SP³ matched the perceptual quality of state-of-the-art zero-shot diffusion and flow methods while operating 3 to 630 times faster [1][3]. The authors attribute this efficiency to the tightly structured latent space of the Spherical Encoder, which serves as a robust projection onto the natural image manifold [3]. Plug-and-Play methods have gained traction in computational imaging because they decouple the prior model from the forward measurement operator, allowing off-the-shelf denoisers to be inserted into optimization frameworks. SP³ replaces the denoiser with a generative Spherical Encoder prior, a model that maps images onto a latent spherical manifold and back [3]. The paper states that this substitution approximates the intractable proximal prior step without sacrificing reconstruction fidelity [1]. The work was posted on the arXiv preprint server under the Computer Vision and Pattern Recognition category and is also indexed on Hugging Face Papers [2][7]. No peer-reviewed publication date has been announced.