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Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing
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Proposes DAPS, a diffusion posterior sampler that decouples consecutive sampling steps via decoupled noise annealing with Langevin MCMC, improving nonlinear inverse problem solving such as phase retrieval.
Problem
Diffusion-based Bayesian inverse problem solvers struggle to correct early-step global errors, failing on complicated nonlinear inverse problems such as phase retrieval and HDR reconstruction.
Approach
Instead of sampling each step from p(x_t | x_{t+Δt}, y), recursively sample from the measurement-conditioned time-marginal p(x_t | y) by alternating x0|y sampling via Langevin dynamics, Gaussian-approximated denoising, and forward noising, so consecutive samples can differ substantially while annealing to the true posterior.
Key results
- On FFHQ 256, DAPS reaches 30.63 dB PSNR on phase retrieval, 1.98 dB above the previous state of the art.
- On FFHQ 256, DAPS reaches 27.12 dB PSNR on high dynamic range reconstruction, 4.39 dB above the previous best.
- DAPS outperforms diffusion baselines on 4x and 8x compressed sensing MRI (31.48 dB PSNR at 4x vs 28.78 for CSGM).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DAPS instead of the strongest listed pixel-space baseline | DAPS · FFHQ 256, phase retrieval | PSNR: 28.65˘8.09 -> 30.63˘3.13 | Helped |
| Use DAPS instead of DPS | DAPS · ImageNet 256, phase retrieval | PSNR: 16.81˘3.61 -> 25.78˘6.92 | Helped |
| Use DAPS instead of RED-diff | DAPS · FFHQ 256, nonlinear deblur | PSNR: 30.86˘0.51 -> 28.29˘1.77 | Hurt |
| Use DAPS instead of RED-diff | DAPS · ImageNet 256, nonlinear deblur | PSNR: 30.07˘1.41 -> 27.73˘3.23 | Hurt |
| Use DAPS instead of the strongest listed baseline | DAPS · FFHQ 256, super-resolution 4× | PSNR: 28.66 -> 29.07 | Helped |
| Use DAPS instead of the strongest listed baseline | DAPS · ImageNet 256, inpainting (random) | PSNR: 31.30 -> 28.44 | Hurt |
| Use DAPS instead of CSGM | DAPS · Compressed sensing MRI, 4× | PSNR: 28.78 -> 31.48 | Helped |
| Use Gaussian approximation rather than diffusion-score estimation for p(x0 | xt) (ablation) | DAPS · FFHQ, Gaussian deblurring | PSNR: 29.57 -> 29.40 | Hurt |
| Use Gaussian approximation rather than diffusion-score estimation for p(x0 | xt) (ablation) | DAPS · FFHQ, high dynamic range | PSNR: 25.33 -> 24.85 | Hurt |
| Use Gaussian approximation rather than diffusion-score estimation for p(x0 | xt) (ablation) | DAPS · FFHQ, Gaussian deblurring | run time: 462.3 -> 64.7 | Helped |
Surprising findings
- A Gaussian approximation of p(x0|xt) gives comparable results to diffusion-score estimation at 6-7x lower runtime.
Limitations
- Phase retrieval results have high variance across samples, so the best of four samples is reported.
- Requires tuning learning rates separately for each task.
Experimental setup
Datasets: FFHQ ImageNet fastMRI knee
Benchmarks: FFHQ 256 ImageNet 256 fastMRI knee
Metrics: PSNR SSIM LPIPS FID measurement error
Baselines: DPS DDRM DDNM DCDP FPS-SMC DiffPIR PSLD ReSample RED-diff HIO ScoreMRI CSGM
Builds on: DPS EDM Latent diffusion models ReSample Langevin dynamics
Closest papers by meaning
- Divide-and-Conquer Posterior Sampling for Denoising Diffusion priors (NeurIPS 2024 · similarity 0.92)
- A Variational Perspective on Solving Inverse Problems with Diffusion Models (ICLR 2024 · similarity 0.91)
- Unleashing the Denoising Capability of Diffusion Prior for Solving Inverse Problems (NeurIPS 2024 · similarity 0.91)
- Adapt and Diffuse: Sample-adaptive Reconstruction via Latent Diffusion Models (ICML 2024 · similarity 0.91)
- Improving Diffusion-based Inverse Algorithms under Few-Step Constraint via Linear Extrapolation (NeurIPS 2025 · similarity 0.90)
- Ambient Diffusion Posterior Sampling: Solving Inverse Problems with Diffusion Models Trained on Corrupted Data (ICLR 2025 · similarity 0.90)
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