Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Divide-and-Conquer Posterior Sampling for Denoising Diffusion priors
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Proposes Divide-and-Conquer Posterior Sampling (DCPS), which splits the backward diffusion into blocks with intermediate posteriors, using Langevin steps and Gaussian variational inference to sample Bayesian inverse problems with pretrained DDM priors without retraining.
Problem
Posterior sampling for Bayesian inverse problems with pretrained denoising diffusion priors is intractable, and existing approximations (DPS, PGDM) have uncontrolled bias or require retraining.
Approach
Decompose the Feynman-Kac posterior into a sequence of intermediate posteriors along the diffusion path; sample each block via tamed Langevin steps followed by Gaussian variational inference for the backward transitions, which reduces the approximation error relative to DPS/PGDM-style point-mass or Gaussian approximations.
Key results
- On FFHQ/ImageNet inpainting and super-resolution tasks (LPIPS), DCPS achieves average 0.28 versus 0.32 for DPS, 0.57 for PGDM and 0.60 for RedDiff, winning 13 of 16 tasks.
- On JPEG dequantization (LPIPS), DCPS reaches 0.20 on FFHQ QF=2 versus 0.37 for PGDM and 0.32 for RedDiff.
- On the Gaussian mixture toy problem, DCPS with 500 Langevin steps matches MCGDiff closely, while outperforming DPS, DDRM, PGDM and RedDiff in sliced Wasserstein distance.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use divide-and-conquer posterior sampling instead of DPS | Denoising diffusion posterior sampling · Gaussian mixture, dimx=10, dy=1 | SW: 5.80 ± 0.75 -> 2.19 ± 0.68 | Helped |
| Use divide-and-conquer posterior sampling instead of MCGDiff | Gaussian mixture posterior sampling · Gaussian mixture, dimx=10, dy=1 | SW: 2.28 ± 0.75 -> 2.19 ± 0.68 | Hurt |
| Increase Langevin steps from M=50 to M=500 | DCPS · Gaussian mixture, dimx=10, dy=1 | SW: 2.91 ± 0.74 -> 2.19 ± 0.68 | Helped |
| Increase Langevin steps from M=50 to M=500 | DCPS · Gaussian mixture, dimx=100, dy=1 | SW: 4.04 ± 1.00 -> 3.29 ± 0.95 | Helped |
| Use DCPS instead of the strongest listed baseline | Posterior reconstruction · FFHQ and ImageNet imaging tasks, average | LPIPS: 0.32 -> 0.28 | Helped |
| Use DCPS instead of PiGDM | Posterior reconstruction · JPEG dequantization, FFHQ QF=2 | LPIPS: 0.37 -> 0.20 | Helped |
| Use DCPS instead of RedDiff | Posterior reconstruction · JPEG dequantization, ImageNet QF=8 | LPIPS: 0.31 -> 0.24 | Helped |
| Use DCPS instead of DPS | Poisson restoration · FFHQ denoising | LPIPS: 0.12 -> 0.07 | Helped |
| Use DCPS instead of DPS | Poisson restoration · ImageNet SR 4x | LPIPS: 0.80 -> 0.36 | Helped |
| Use DCPS instead of DPS | Posterior reconstruction · FFHQ and ImageNet imaging tasks, average | LPIPS: 0.32 -> 0.28 | Mixed |
Surprising findings
- DCPS can work with irrelevant intermediate potentials as long as enough Langevin steps are used between blocks.
- RedDiff and DDRM produce strikingly similar samples across independent draws on outpainting tasks.
Limitations
- Intermediate potentials are hand-designed per problem and the method does not apply to latent diffusion linear inverse problems.
- Slower than RedDiff and DDRM because it computes vector-Jacobian products through the denoiser when optimizing the KL objective.
- Requires appropriate choice of intermediate potentials and number of blocks L for good performance.
Experimental setup
Datasets: FFHQ 256 ImageNet 256 UCY
Benchmarks: FFHQ 256 ImageNet 256 UCY trajectory inpainting 25-component Gaussian mixture (sliced Wasserstein)
Metrics: LPIPS sliced Wasserstein distance l2 distance quantiles
Baselines: DPS PGDM DDRM RedDiff MCGDiff DiffPIR DDNM FPS SDA
Builds on: DPS PGDM DDPM RePaint TULA
Closest papers by meaning
- A Mixture-Based Framework for Guiding Diffusion Models (ICML 2025 · similarity 0.94)
- Provable Posterior Sampling with Denoising Oracles via Tilted Transport (NeurIPS 2024 · similarity 0.93)
- Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors (NeurIPS 2024 · similarity 0.92)
- A Variational Perspective on Solving Inverse Problems with Diffusion Models (ICLR 2024 · similarity 0.92)
- Analyzing and Guiding Zero-Shot Posterior Sampling in Diffusion Models (NeurIPS 2026 · similarity 0.92)
- Improving Diffusion Inverse Problem Solving with Decoupled Noise Annealing (CVPR 2025 · similarity 0.92)
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