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Variational Diffusion Posterior Sampling with Midpoint Guidance
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Proposes VDPS, a diffusion posterior sampler that decomposes each backward transition through a midpoint step and fits a Gaussian variational approximation there, trading prior-transition error against guidance error for inverse problems with pixel and latent diffusion priors.
Problem
Posterior sampling for Bayesian inverse problems with pre-trained diffusion model priors, where the guidance (likelihood score) term is intractable and existing training-free approximations introduce large errors.
Approach
Decompose each posterior denoising transition via an intermediate midpoint time, so the intractable guidance is evaluated at the midpoint rather than step k+1; fit a Gaussian variational approximation at the midpoint by minimizing an upper bound on backward KL, with a warm-start initialization. The midpoint index trades off likelihood-approximation error against prior transition error.
Key results
- On FFHQ DDM prior, VDPS achieves the lowest LPIPS on most linear and all nonlinear tasks, e.g., JPEG (QF=2) 0.16 vs DPS 0.39 and HDR 0.07 vs DPS 0.49.
- With an LDM prior on FFHQ, VDPS gives the best LPIPS on most tasks, e.g., box inpainting 0.16 vs ReSample 0.22 and PSLD 0.26.
- On PTB-XL ECG missing-leads, VDPS with 50 steps reaches balanced accuracy 0.81 for RBBB versus 0.54 for DPS.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use VDPS instead of competing methods | Image reconstruction with pixel-space DDM priors · FFHQ and ImageNet, nonlinear imaging tasks | LPIPS | Helped |
| Use VDPS instead of competing methods | Image reconstruction with FFHQ LDM prior · FFHQ, SR ×4, SR ×16, box and half-mask inpainting, motion deblur, JPEG, phase retrieval, nonlinear deblur | LPIPS | Helped |
| Use VDPS instead of Resample | FFHQ LDM reconstruction · Gaussian deblur | LPIPS: 0.15 vs 0.16 | Hurt |
| Use VDPS instead of competing methods | ECG reconstruction from lead I · PTB-XL, downstream AF diagnosis | Balanced accuracy: 0.94 vs 0.94 | No clear effect |
| Use VDPS instead of competing methods | ECG reconstruction from lead I · PTB-XL, missing block | MAE: 0.111±2\mathrm{e}\!{-3} vs 0.103±2\mathrm{e}\!{-3} | Mixed |
| Use VDPS instead of competing methods | ECG reconstruction from lead I · PTB-XL, missing block | RMSE: 0.225±4\mathrm{e}\!{-3} vs 0.232±4\mathrm{e}\!{-3} | Helped |
| Set the midpoint schedule to η = 0.75 rather than η = 1 (ablation) | VDPS · Gaussian mixture, d = 200 | Sliced Wasserstein distance | Helped |
| Increase gradient steps per denoising step (ablation) | VDPS with midpoint ⌊3k/4⌋ · Gaussian mixture, d = 20 | Sliced Wasserstein distance | Helped |
| Increase gradient steps beyond 10 (ablation) | VDPS with midpoint ⌊3k/4⌋ · Gaussian mixture, d = 200 | Sliced Wasserstein distance | No clear effect |
| Use an adaptive midpoint schedule instead of a fixed midpoint schedule (ablation) | VDPS · Gaussian and motion deblurring and latent diffusion tasks | Reconstruction performance | Helped |
Surprising findings
- On the Gaussian toy example the Wasserstein-2 error is minimized at intermediate midpoint fraction eta around 0.5, not at the DPS-like choice eta=1.
- Gaussian and motion deblurring on ImageNet and LDM priors benefit from an adaptive midpoint schedule, but the warm-start two-stage approximation becomes unstable as k decreases.
Limitations
- Runtime is higher than some baselines because each step requires a vector-Jacobian product through the denoiser and M gradient steps.
- Best midpoint schedule depends on the task and prior; the choice of the sequence of midpoints is not fully analyzed.
- The warm-start two-stage approximation can become unstable as k decreases.
Experimental setup
Datasets: FFHQ 256x256 ImageNet 256x256 PTB-XL
Benchmarks: FFHQ 256x256 ImageNet 256x256 PTB-XL missing block PTB-XL missing leads Gaussian mixture toy
Metrics: LPIPS FID PSNR SSIM MAE RMSE balanced accuracy sliced Wasserstein
Baselines: DPS PGDM DDNM DiffPIR ReDiff PSLD ReSample SMCDiff
Builds on: DPS DDPM DDNM PGDM ReSample
Closest papers by meaning
- Divide-and-Conquer Posterior Sampling for Denoising Diffusion priors (NeurIPS 2024 · similarity 0.91)
- Provable Posterior Sampling with Denoising Oracles via Tilted Transport (NeurIPS 2024 · similarity 0.90)
- A Variational Perspective on Solving Inverse Problems with Diffusion Models (ICLR 2024 · similarity 0.90)
- A Mixture-Based Framework for Guiding Diffusion Models (ICML 2025 · similarity 0.89)
- Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction (NeurIPS 2024 · similarity 0.89)
- Guided Diffusion Sampling on Function Spaces with Applications to PDEs (NeurIPS 2025 · similarity 0.89)
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