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Coupled Data and Measurement Space Dynamics for Enhanced Diffusion Posterior Sampling
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Proposes C-DPS, which runs a measurement-space forward diffusion in parallel with the data-space diffusion to get a closed-form posterior step for diffusion-based inverse problem solving, avoiding constraint tuning and likelihood approximation.
Problem
Diffusion-based posterior sampling for linear inverse problems: existing projection-based and likelihood-approximation methods retro-fit measurement information heuristically, causing artifacts and poor measurement consistency under high noise or complex operators.
Approach
Couples the data-space diffusion with a parallel forward diffusion of the measurement y_t starting from the observed y_0, which yields an analytic Gaussian posterior p(x_{t-1}|x_t, y_{t-1}) (after freezing the score at x_t), sampled via a matrix-free pre-whitened CG solver.
Key results
- On FFHQ 256 pixel-domain tasks, C-DPS achieves best or near-best FID/LPIPS across inpainting, deblurring and 4x SR (e.g., box inpainting FID 26.33 vs DMPlug 27.12).
- In the latent domain, LC-DPS obtains the best FID on ImageNet inpainting (box) at 113.67 vs RLSD 130.16 and PSLD 146.53.
- On the 25-mode Gaussian mixture benchmark, C-DPS has lowest sliced Wasserstein distance in most of the 27 configurations (e.g., d=8,m=1,sigma=0.01: 2.2 vs DPS 4.7).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use C-DPS instead of DMPlug | Pixel-domain inverse-problem sampling · FFHQ 256×256, random inpainting | FID: 20.12 -> 20.14 | No clear effect |
| Use C-DPS instead of DMPlug | Pixel-domain inverse-problem sampling · FFHQ 256×256, box inpainting | FID: 27.12 -> 26.33 | Helped |
| Use C-DPS instead of DMPlug | Pixel-domain inverse-problem sampling · FFHQ 256×256, Gaussian deblurring | FID: 32.44 -> 32.24 | Helped |
| Use C-DPS instead of DMPlug | Pixel-domain inverse-problem sampling · FFHQ 256×256, motion deblurring | FID: 27.55 -> 27.29 | Helped |
| Use C-DPS instead of DMPlug | Pixel-domain inverse-problem sampling · FFHQ 256×256, 4× super-resolution | FID: 28.55 -> 28.41 | Helped |
| Use C-DPS instead of DMPlug | Pixel-domain inverse-problem sampling · ImageNet 256×256, random inpainting | FID: 32.85 -> 32.37 | Helped |
| Use C-DPS instead of DMPlug | Pixel-domain inverse-problem sampling · ImageNet 256×256, box inpainting | FID: 34.28 -> 33.24 | Helped |
| Use C-DPS instead of DMPlug | Pixel-domain inverse-problem sampling · ImageNet 256×256, Gaussian deblurring | FID: 57.42 -> 56.36 | Helped |
| Use C-DPS instead of DMPlug | Pixel-domain inverse-problem sampling · ImageNet 256×256, motion deblurring | FID: 53.13 -> 52.06 | Helped |
| Use C-DPS instead of DMPlug | Pixel-domain inverse-problem sampling · ImageNet 256×256, 4× super-resolution | FID: 48.96 -> 47.30 | Helped |
| Use LC-DPS instead of ReSample | Latent-domain inverse-problem sampling · ImageNet 256×256, random inpainting | FID: 59.87 -> 60.02 | Hurt |
| Use LC-DPS instead of ReSample | Latent-domain inverse-problem sampling · ImageNet 256×256, Gaussian deblurring | FID: 65.35 -> 67.21 | Hurt |
Surprising findings
- DMPlug is competitive with C-DPS in several settings, and C-DPS does not win every metric (e.g., SSIM on FFHQ box inpainting and some deblurring settings).
Limitations
- Relies on freezing the score network at x_t, an approximation justified only empirically
- Closed form is derived for linear (and locally linearized) forward operators; nonlinear extension is preliminary
- Gains are not uniform; DMPlug is close or better on some metrics
Experimental setup
Datasets: FFHQ 256x256 ImageNet 256x256 25-component Gaussian mixture toy dataset
Benchmarks: FFHQ 256x256 1k validation ImageNet 256x256 1k validation Gaussian mixture posterior benchmark
Metrics: FID LPIPS SSIM PSNR sliced Wasserstein distance
Baselines: DPS ΠGDM DDRM MCG ILVR ReSample PnP-ADMM Score-SDE ADMM-TV PnP-DM DAPS DMPlug
Builds on: DPS DDPM PSLD ReSample
Closest papers by meaning
- Analyzing and Guiding Zero-Shot Posterior Sampling in Diffusion Models (NeurIPS 2026 · similarity 0.91)
- SITCOM: Step-wise Triple-Consistent Diffusion Sampling For Inverse Problems (ICML 2025 · similarity 0.90)
- Improving Diffusion Posterior Samplers with Lagged Temporal Corrections for Image Restoration (NeurIPS 2026 · similarity 0.90)
- Divide-and-Conquer Posterior Sampling for Denoising Diffusion priors (NeurIPS 2024 · similarity 0.90)
- Provable Posterior Sampling with Denoising Oracles via Tilted Transport (NeurIPS 2024 · similarity 0.90)
- Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction (NeurIPS 2024 · similarity 0.89)
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