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Self-diffusion for Solving Inverse Problems

NeurIPS 2025 · Image generation › Fast diffusion sampling · approach: Diffusion posterior sampling · 0 citations (OpenAlex)

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Proposes self-diffusion, an iterative noising-and-denoising scheme that trains a randomly initialized CNN self-denoiser with a data-fidelity loss at each noise level, solving inverse problems without pretrained generative models.

Problem

Solving linear inverse problems (MRI reconstruction, low-level vision, radar angle estimation, compressed sensing) without pretrained generative priors or training data, where existing diffusion-based methods need a clean-data pretrained model.

Approach

Replace the pretrained denoiser in diffusion-based inverse solvers with a self-denoiser: a randomly initialized CNN re-trained at each noise level to minimize measurement misfit A·D(x_t + σ(t)ε) − y, with noise resampled across steps so the spectral bias of the network is modulated by a decreasing noise schedule.

Key results

• On 4x MRI with 20 ACS lines, SDI reaches 39.21 dB PSNR / 0.9640 SSIM, versus 38.35 dB for DIP and 32.18 dB for Aseq.
• On low-level vision (Table), SDI reaches 30.78 dB PSNR on inpainting and 27.76 dB on motion deblurring, above DIP (29.41 and 25.94).
• On CBSD68 denoising (sigma=25), SDI gets 28.10 dB PSNR, below FFDNet (31.22) and matching IR-SDE (28.09) on PSNR but worse on LPIPS (0.207 vs 0.101).

Measured effects reported in the paper

Surprising findings

• On denoising, SDI's LPIPS (0.207) is much worse than IR-SDE (0.101) and its SSIM is lower than DIP's PSNR-level advantage would suggest, showing mixed perceptual quality.
• Against a pretrained CSGM on T2 MRI at 4x and 6x acceleration, CSGM is better, and SDI only wins in the no-ACS setting.

Limitations

• Per-instance optimization is slow: about 1.52 iterations/sec on a 5000x3000 image, requiring 20000 total iterations.
• Denoising results trail supervised FFDNet and generative IR-SDE, especially on LPIPS.
• Pretrained diffusion model CSGM outperforms SDI on T2 MRI with ACS lines, so benefits are setting-dependent.

Experimental setup

Datasets: fastMRI ImageNet CBSD68 RADIal

Benchmarks: fastMRI ImageNet 256x256 (inpainting, deblurring, SR) CBSD68 denoising RADIal radar

Metrics: PSNR SSIM NRMSE LPIPS

Baselines: Deep Image Prior Aseq IMJENSE CSGM ADMM-BP IR-SDE FFDNet DPS DDNM

Builds on: Deep Image Prior CSGM neural tangent kernel DDNM

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