Geometry-Correct Diffusion Posterior Sampling with Denoiser-Pullback Curvature Guidance and Manifold-Aligned Damping

Seunghyeok Shin; Minwoo Kim; Dabin Kim; Hongki Lim

When should you consider CLAMP?

CLAMP (Curvature-aware Langevin with Aligned Manifold Pullback) is a training-free inverse-problem solver using a pretrained diffusion prior. It supports a common correction framework in pixel and latent spaces. Consider it as a baseline when comparing reconstruction quality and runtime for linear or differentiable nonlinear measurement operators.

A pretrained image prior

Start with a diffusion denoiser suited to your image domain. Training-free refers to solving the inverse problem; the prior is already trained.

A differentiable measurement model

The correction uses operator Jacobian actions and a denoiser pullback. Latent reconstruction also differentiates through the decoder.

Author-reported qualitative comparisons for CLAMP across phase retrieval, HDR, super-resolution, inpainting, and accelerated MRI. — Qualitative results reported in the paper. The natural-image and MRI panels use their respective experimental setups.

How CLAMP changes diffusion guidance

Scalar likelihood guidance applies a single weight to a data-consistency direction. CLAMP instead computes a geometry-aware correction in the noisy diffusion state, using a one-sided curvature approximation and damping aligned with the denoiser residual.

Pull back measurement sensitivity. Query the denoiser and map the measurement residual through the operator and denoiser into diffusion-state coordinates.
Solve a damped curvature system. Use fixed-budget, matrix-free GMRES and manifold-aligned damping to scale the correction by direction.
Advance the noise schedule. Apply a variance-preserving Langevin transition with a closed-form drift/noise split.

CLAMP's three stages: denoiser query and measurement residual, curvature correction through GMRES, and variance-preserving diffusion transition. — In latent space, the measurement model is composed with the decoder. Method, assumptions, and derivation in Section 3.

Reconstruction quality and runtime

Author-reported paper results · arXiv v1, Tables 1 and 3

The tables below transcribe the paper's natural-image comparisons into selectable text. They are paper results, not new runs or independent replications. Each table reports 100 validation images at 256 × 256 on one NVIDIA RTX 6000 Ada Generation GPU, with batch size 1. Higher PSNR/SSIM and lower LPIPS/runtime are better.

Pixel priors are the FFHQ model from DPS and the ImageNet model from Dhariwal & Nichol. Latent experiments use LDM-VQ4 priors as described in the paper. Exact checkpoint hashes and image IDs are not supplied by these tables. The release's ImageNet latent conditioning configuration still needs to be reconciled with the paper's unconditional-prior description before claiming reproduction.

The physical measurement noise and solver calibration are distinct: the release's natural-image presets use noise standard deviation 0.05, while CLAMP's data-consistency calibration is 0.01 and identity damping is 2.0. See Appendix C for the noise protocol and method-specific baseline settings. These comparisons do not impose equal iteration budgets.

CLAMP compute budgets and interpretation

Diffusion steps T / GMRES iterations K (paper Table 4)
Representation	Linear tasks	Phase retrieval	Nonlinear blur	HDR
Pixel	50 / 5	250 / 4	50 / 20	250 / 4
Latent	25 / 20	250 / 5	75 / 20	250 / 5

Times are transcribed as reported in the paper. Consult Appendix C.2 for each baseline's settings, and retain task/noise settings, checkpoint identity, backend, and evaluation protocol in any new comparison.

Pixel-space comparisons

All rows from Table 1, separated by dataset.

FFHQ · Pixel · 100 images

FFHQ pixel-space results, paper Table 1. Author-reported; runtime in seconds.
Task	Method	PSNR ↑	SSIM ↑	LPIPS ↓	Time (s) ↓
4× super-resolution	CLAMP	29.515	0.841	0.219	6.743
4× super-resolution	DAPS	28.619	0.764	0.262	28.257
4× super-resolution	SITCOM	29.153	0.826	0.231	15.755
4× super-resolution	DMPlug	28.637	0.797	0.253	118.255
4× super-resolution	DCDP	27.611	0.785	0.225	4.719
Box inpainting	CLAMP	25.495	0.882	0.125	6.175
Box inpainting	DAPS	24.285	0.746	0.222	22.352
Box inpainting	SITCOM	25.275	0.831	0.179	17.697
Box inpainting	DMPlug	23.526	0.790	0.281	103.76
Box inpainting	DCDP	21.721	0.766	0.219	8.147
Random inpainting	CLAMP	32.955	0.918	0.140	6.171
Random inpainting	DAPS	30.078	0.791	0.214	21.576
Random inpainting	SITCOM	31.431	0.871	0.173	25.382
Random inpainting	DMPlug	30.825	0.865	0.231	122.143
Random inpainting	DCDP	27.240	0.788	0.229	8.130
Gaussian deblurring	CLAMP	29.010	0.827	0.234	6.343
Gaussian deblurring	DAPS	28.762	0.767	0.254	37.730
Gaussian deblurring	SITCOM	29.359	0.826	0.236	25.491
Gaussian deblurring	DMPlug	27.95	0.770	0.278	181.695
Gaussian deblurring	DCDP	27.553	0.761	0.245	4.934
Motion deblurring	CLAMP	31.641	0.880	0.183	6.322
Motion deblurring	DAPS	30.954	0.823	0.202	38.606
Motion deblurring	SITCOM	31.501	0.866	0.167	26.184
Motion deblurring	DMPlug	29.272	0.818	0.260	152.699
Motion deblurring	DCDP	25.468	0.566	0.365	5.007
Phase retrieval	CLAMP	30.233	0.854	0.192	28.660
Phase retrieval	DAPS	30.103	0.796	0.208	98.054
Phase retrieval	SITCOM	28.782	0.791	0.239	24.584
Phase retrieval	DCDP	24.036	0.677	0.310	102.386
Nonlinear deblurring	CLAMP	29.961	0.856	0.166	33.946
Nonlinear deblurring	DAPS	28.868	0.780	0.223	755.725
Nonlinear deblurring	SITCOM	29.519	0.812	0.207	27.167
Nonlinear deblurring	DMPlug	28.298	0.811	0.249	291.221
Nonlinear deblurring	DCDP	27.879	0.795	0.204	269.786
High dynamic range	CLAMP	29.488	0.891	0.133	26.610
High dynamic range	DAPS	27.149	0.834	0.196	76.724
High dynamic range	SITCOM	27.205	0.777	0.226	33.887
High dynamic range	DMPlug	25.507	0.777	0.264	221.418

ImageNet · Pixel · 100 images

ImageNet pixel-space results, paper Table 1. Author-reported; runtime in seconds.
Task	Method	PSNR ↑	SSIM ↑	LPIPS ↓	Time (s) ↓
4× super-resolution	CLAMP	26.981	0.742	0.290	23.587
4× super-resolution	DAPS	25.512	0.636	0.374	65.580
4× super-resolution	SITCOM	26.519	0.716	0.309	60.778
4× super-resolution	DMPlug	25.091	0.660	0.347	238.433
4× super-resolution	DCDP	24.358	0.640	0.369	9.190
Box inpainting	CLAMP	21.547	0.825	0.188	23.427
Box inpainting	DAPS	21.234	0.720	0.270	57.108
Box inpainting	SITCOM	20.698	0.726	0.241	66.709
Box inpainting	DMPlug	19.455	0.667	0.384	253.946
Box inpainting	DCDP	17.741	0.662	0.301	17.214
Random inpainting	CLAMP	30.215	0.866	0.159	23.419
Random inpainting	DAPS	27.350	0.721	0.251	56.932
Random inpainting	SITCOM	29.008	0.821	0.183	95.962
Random inpainting	DMPlug	27.023	0.739	0.317	248.146
Random inpainting	DCDP	23.284	0.606	0.355	17.518
Gaussian deblurring	CLAMP	26.388	0.710	0.333	23.924
Gaussian deblurring	DAPS	25.932	0.655	0.355	74.984
Gaussian deblurring	SITCOM	26.741	0.719	0.315	95.161
Gaussian deblurring	DMPlug	24.082	0.613	0.389	313.680
Gaussian deblurring	DCDP	23.499	0.542	0.449	9.573
Motion deblurring	CLAMP	29.141	0.812	0.243	23.805
Motion deblurring	DAPS	28.623	0.764	0.246	78.000
Motion deblurring	SITCOM	29.321	0.811	0.213	95.529
Motion deblurring	DMPlug	25.211	0.660	0.365	284.413
Motion deblurring	DCDP	17.771	0.248	0.574	9.488
Phase retrieval	CLAMP	19.680	0.459	0.478	104.628
Phase retrieval	DAPS	22.354	0.519	0.402	241.113
Phase retrieval	SITCOM	18.481	0.383	0.524	94.187
Phase retrieval	DCDP	15.953	0.283	0.595	195.193
Nonlinear deblurring	CLAMP	28.036	0.788	0.212	82.427
Nonlinear deblurring	DAPS	27.537	0.734	0.266	884.119
Nonlinear deblurring	SITCOM	28.097	0.774	0.221	97.029
Nonlinear deblurring	DMPlug	25.086	0.679	0.317	668.641
Nonlinear deblurring	DCDP	25.726	0.664	0.280	367.695
High dynamic range	CLAMP	28.804	0.886	0.136	104.38
High dynamic range	DAPS	26.568	0.819	0.198	216.701
High dynamic range	SITCOM	26.449	0.774	0.222	129.681
High dynamic range	DMPlug	23.244	0.715	0.308	564.501

Latent-space comparisons

All rows from Table 3, separated by dataset. These use different priors from the pixel tables.

FFHQ · Latent · 100 images

FFHQ latent-space results, paper Table 3. Author-reported; runtime in seconds.
Task	Method	PSNR ↑	SSIM ↑	LPIPS ↓	Time (s) ↓
4× super-resolution	CLAMP	28.933	0.829	0.233	34.255
4× super-resolution	PSLD	24.627	0.628	0.377	69.290
4× super-resolution	ReSample	23.317	0.456	0.507	300.061
4× super-resolution	LatentDAPS	29.204	0.825	0.272	84.460
Box inpainting	CLAMP	25.151	0.837	0.236	35.369
Box inpainting	PSLD	21.847	0.612	0.370	69.045
Box inpainting	ReSample	19.978	0.796	0.247	296.326
Box inpainting	LatentDAPS	23.474	0.742	0.369	85.823
Random inpainting	CLAMP	31.433	0.894	0.193	35.263
Random inpainting	PSLD	24.280	0.635	0.346	68.915
Random inpainting	ReSample	29.950	0.842	0.201	307.874
Random inpainting	LatentDAPS	26.036	0.743	0.385	85.840
Gaussian deblurring	CLAMP	28.269	0.801	0.272	35.011
Gaussian deblurring	PSLD	22.015	0.503	0.444	70.098
Gaussian deblurring	ReSample	26.357	0.662	0.329	355.885
Gaussian deblurring	LatentDAPS	25.717	0.732	0.384	87.407
Motion deblurring	CLAMP	29.959	0.840	0.244	36.185
Motion deblurring	PSLD	24.416	0.603	0.346	70.041
Motion deblurring	ReSample	28.744	0.754	0.262	347.756
Motion deblurring	LatentDAPS	26.646	0.757	0.361	87.409
Phase retrieval	CLAMP	28.194	0.802	0.271	133.941
Phase retrieval	ReSample	24.676	0.606	0.412	320.911
Phase retrieval	LatentDAPS	23.199	0.692	0.421	177.730
Nonlinear deblurring	CLAMP	29.243	0.836	0.243	146.718
Nonlinear deblurring	ReSample	28.748	0.797	0.236	843.212
Nonlinear deblurring	LatentDAPS	25.152	0.726	0.387	194.014
High dynamic range	CLAMP	26.245	0.816	0.279	134.060
High dynamic range	ReSample	25.038	0.822	0.239	291.372
High dynamic range	LatentDAPS	20.789	0.630	0.512	174.976

ImageNet · Latent · 100 images

ImageNet latent-space results, paper Table 3. Author-reported; runtime in seconds.
Task	Method	PSNR ↑	SSIM ↑	LPIPS ↓	Time (s) ↓
4× super-resolution	CLAMP	26.465	0.726	0.335	37.353
4× super-resolution	PSLD	16.656	0.291	0.541	102.757
4× super-resolution	ReSample	22.152	0.423	0.470	269.078
4× super-resolution	LatentDAPS	26.189	0.702	0.388	86.315
Box inpainting	CLAMP	20.836	0.731	0.342	37.393
Box inpainting	PSLD	18.762	0.424	0.549	99.832
Box inpainting	ReSample	18.087	0.713	0.309	265.139
Box inpainting	LatentDAPS	22.818	0.561	0.543	88.725
Random inpainting	CLAMP	28.181	0.806	0.262	37.396
Random inpainting	PSLD	20.690	0.436	0.550	98.449
Random inpainting	ReSample	26.916	0.756	0.255	323.283
Random inpainting	LatentDAPS	19.630	0.588	0.522	86.092
Gaussian deblurring	CLAMP	25.443	0.662	0.411	38.110
Gaussian deblurring	PSLD	19.591	0.329	0.555	109.263
Gaussian deblurring	ReSample	23.530	0.497	0.439	338.281
Gaussian deblurring	LatentDAPS	22.695	0.567	0.549	86.016
Motion deblurring	CLAMP	27.119	0.730	0.348	38.118
Motion deblurring	PSLD	20.761	0.376	0.518	98.400
Motion deblurring	ReSample	24.845	0.579	0.404	347.756
Motion deblurring	LatentDAPS	23.557	0.592	0.513	89.050
Phase retrieval	CLAMP	20.133	0.483	0.458	119.078
Phase retrieval	ReSample	16.913	0.320	0.608	319.601
Phase retrieval	LatentDAPS	17.067	0.446	0.624	192.787
Nonlinear deblurring	CLAMP	25.889	0.716	0.325	158.452
Nonlinear deblurring	ReSample	26.047	0.697	0.301	686.128
Nonlinear deblurring	LatentDAPS	22.516	0.568	0.530	198.074
High dynamic range	CLAMP	28.885	0.887	0.130	117.544
High dynamic range	ReSample	24.950	0.783	0.257	273.695
High dynamic range	LatentDAPS	19.394	0.469	0.641	180.929

View the original paper table figures

Original paper Table 1, pixel-space results transcribed above. — Pixel-space table.

Original paper Table 3, latent-space results transcribed above. — Latent-space table.

Accelerated MRI in the paper

The paper also reports multi-coil MRI reconstruction using Poisson-disc undersampling. Its MRI comparison is a separate experiment with a domain-specific prior. See Section 4.3 for quantitative results and the MRI appendix for the protocol.

Author-reported MRI reconstructions comparing ground truth, DPS, DAPS, DDS, Score-Med, and CLAMP. — Author-reported qualitative MRI results, separate from the public natural-image quick start.

How does CLAMP compare?

CLAMP contributes a different likelihood correction. DAPS uses decoupled noise annealing, SITCOM uses step-wise consistency optimization, DMPlug optimizes a diffusion input, and DCDP separates data consistency from diffusion purification. The paper's latent comparisons include LatentDAPS, ReSample, and PSLD. Compared implementations and settings.

A favorable quality/runtime case

For FFHQ 4× super-resolution in Table 1, CLAMP reports 29.515 dB PSNR at 6.743 s; DAPS reports 28.619 dB at 28.257 s. DCDP is faster at 4.719 s, with 27.611 dB.

Speed depends on the task

For FFHQ nonlinear deblurring, CLAMP reports 29.961 dB at 33.946 s. SITCOM is faster at 27.167 s and reports 29.519 dB. Use the accompanying SSIM and LPIPS values when judging quality.

Another solver can have better quality

For ImageNet phase retrieval, DAPS reports better PSNR, SSIM, and LPIPS than CLAMP, with a longer runtime: 241.113 s versus 104.628 s.

Limitations and selection criteria

Choose a prior suited to the image domain and an operator whose required Jacobian actions are available.
Quality and runtime depend on the task, prior, noise, and solver budget. The tables support task-specific comparisons, not a universal ranking.
A local curvature approximation and a finite GMRES budget do not establish exact posterior sampling for arbitrary operators.
For methods and settings absent from the paper, this page provides no direct comparison. A matched experiment is needed.

See the paper's limitations appendix for further discussion.

Run the public implementation

Code includes a pixel-space dependency manifest, setup checks, task commands, and documented outputs. Checkpoints and datasets are external downloads; they are not bundled with the source release.

Follow the installation and one-image quick start: Python 3.11.9, PyTorch 2.3.0, torchvision 0.18.0, and CUDA 12.1 wheels.
Download the FFHQ DDPM checkpoint and test images, then run the documented setup check.
Run 4× super-resolution with one image, T=50, K=5, seed 42, physical noise 0.05, and calibration 0.01. The Windows quick start uses --cudnn false.
Inspect the reconstructed image, ground-truth/measurement/reconstruction grid, config.yaml, eval.md, and metrics.json.

To run another task, use the published CLI configurations and the reproduction guide. Record image IDs, checkpoints, measurement settings, seed, GPU/backend, and the code version with new results.

Cite the ICML 2026 paper

Please cite the conference paper when using CLAMP. The official title and author order are preserved. Machine-readable citation metadata.

@inproceedings{shin2026clamp,
  author    = {Seunghyeok Shin and Minwoo Kim and Dabin Kim and Hongki Lim},
  title     = {Geometry-Correct Diffusion Posterior Sampling with Denoiser-Pullback Curvature Guidance and Manifold-Aligned Damping},
  booktitle = {Proceedings of the 43rd International Conference on Machine Learning},
  series    = {Proceedings of Machine Learning Research},
  volume    = {306},
  year      = {2026},
  publisher = {PMLR},
  url       = {https://icml.cc/virtual/2026/poster/60728}
}