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

NeurIPS 2026 · Image generation › Image restoration · approach: Diffusion-based universal restoration · 0 citations (OpenAlex)

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Proposes SP^3, a gradient-free plug-and-play MAP restoration method that alternates a Spherical Encoder projection (encode, spherify, decode) with a closed-form HQS data-consistency step, achieving anytime restoration at 3-630x speedups over diffusion/flow zero-shot methods.

Problem

Zero-shot image restoration with generative priors is slow because diffusion and flow methods rely on gradients and many iterative steps, while earlier latent-space GAN/VAE/flow priors give poor results.

Approach

Replace the prior proximal step in HQS with a projection through a Spherical Encoder (encoder, RMS spherification with latent noise, decoder), which is stable under repeated application unlike VAEs, interleaved with a closed-form data-consistency prox; no backpropagation is needed at inference.

Key results

• SP^3 with 20 steps is about 8x faster than OT-ODE and about 60x faster than DPS on AFHQ-Cat (0.28 s per image vs 2.29 s and 17.77 s).
• On AFHQ-Cat denoising, SP^3 reports KID 4.09 and LPIPS 0.174, comparable to DPS (KID 3.63, LPIPS 0.159) and OT-ODE (KID 7.71, LPIPS 0.146).
• Reported speedups range from 3x to 630x relative to competing methods, with a single-step result already competitive with several baselines.

Surprising findings

• SP^3 does not perform best on every task: on CelebA denoising its KID (57.10) is far worse than DPS (17.52) and OT-ODE (7.70).
• Repeated VAE encode-decode projections diverge in LPIPS and KID within a few steps, whereas the SE projection stays stable.

Limitations

• Prioritizes perceptual realism over distortion; lacks PSNR/MMSE-style performance and cannot give MMSE solutions.
• Operates as a MAP estimator rather than a posterior sampler like DPS.
• Convergence guarantee relies on strong averagedness assumptions on the prior that are not verified; convergence is validated empirically only.

Experimental setup

Datasets: AFHQ-Cat CelebA

Benchmarks: AFHQ-Cat CelebA

Metrics: KID LPIPS PSNR wall-clock runtime

Baselines: DPS OT-ODE DiffPIR PnP-Flow DDRM RED DPIR Flow Priors D-Flow PnP-GS PnP-Diff

Builds on: Plug-and-Play priors Half-Quadratic Splitting Sphere Encoder PnP-Flow DPS

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