Research map / Image generation / Fast diffusion sampling
Whitened Score Diffusion: A Structured Prior for Imaging Inverse Problems
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes Whitened Score diffusion, which learns the covariance-preconditioned score G G^T grad log p(x_t|x_0) so that DMs can be trained on arbitrary (anisotropic) Gaussian forward noising processes without covariance inversion, and uses them as priors for imaging inverse problems with structured noise.
Problem
Score-based diffusion models require inverting the covariance of the forward Gaussian noising kernel in the denoising score matching objective, which is unstable for ill-conditioned or singular anisotropic noise; this limits their use as priors for imaging inverse problems with spatially correlated
Approach
Replace the conditional score target with the whitened score G_t G_t^T grad log p(x_t|x_0), which cancels the covariance inverse analytically (closed form beta_t(alpha_t x_0 - x_t)/(1-alpha_t^2)), so a network can be trained by denoising regression on anisotropic VP-type SDEs with a circulant Gaussian-blur K; this links to flow matching and to the predictable-process view of reverse SDEs.
Key results
- WS diffusion priors consistently achieve higher PSNR than conventional isotropic diffusion priors across denoising, motion/lens deblurring, linear scattering and differential defocus on CIFAR-10 and CelebA.
- Denoising correlated noise on CIFAR-10 and CelebA uses SNRs from 1.4 to 0.12 and shows higher PSNR for WS priors (exact numbers are in figures, not stated in text).
- Generative FID is reported only as a secondary result and WS models are said to need further work for unconditional or conditional generation.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Train the prior with anisotropic rather than isotropic Gaussian noising | Diffusion priors for correlated-noise imaging inverse problems · CIFAR-10 and CelebA 64×64 denoising and imaging tasks | PSNR | Helped |
| Train the prior with anisotropic rather than isotropic Gaussian noising | Diffusion priors for motion and lens deblurring · CIFAR-10 | PSNR | Helped |
| Train the prior with anisotropic rather than isotropic Gaussian noising | Diffusion priors for uncorrelated-noise reconstruction · Imaging inverse problems | PSNR | No clear effect |
| Increase the maximum Gaussian blur-kernel std used during training (ablation) | WS diffusion generative models · Generative modeling | FID | Helped |
| Add the forward consistency loss L₂ with equal weight to the primary loss (ablation) | WS diffusion training · Training | Training stability and convergence | Helped |
Surprising findings
- Conventional diffusion priors can mistake low-frequency correlated noise for image features and suppress high-frequency image content, whereas WS priors distinguish them even when spectra overlap.
Limitations
- Sampling requires about 1000 denoising steps, which is computationally costly.
- Measurement noise covariance must be specified by hand; G_t is not learned.
- Generative (unconditional/conditional) performance is not competitive yet.
Experimental setup
Datasets: CIFAR-10 CelebA (64x64) CelebA-HQ (256x256)
Benchmarks: CIFAR-10 CelebA (64x64) CelebA-HQ (256x256)
Metrics: PSNR FID
Baselines: conventional isotropic diffusion prior (conv) Tikhonov regularization
Builds on: score-based SDE diffusion (VP-SDE) denoising score matching flow matching likelihood-guided posterior sampling (DPS-style) Tweedie's formula
Closest papers by meaning
- Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction (NeurIPS 2024 · similarity 0.91)
- Exact Posterior Score Estimation for Solving Linear Inverse Problems (NeurIPS 2026 · similarity 0.90)
- Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance (ICML 2024 · similarity 0.89)
- A Variational Perspective on Solving Inverse Problems with Diffusion Models (ICLR 2024 · similarity 0.88)
- Divide-and-Conquer Posterior Sampling for Denoising Diffusion priors (NeurIPS 2024 · similarity 0.88)
- What’s the score? Automated Denoising Score Matching for Nonlinear Diffusions (ICML 2024 · similarity 0.88)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.