Research map / Probabilistic and scientific modeling / Uncertainty and Gaussian processes
Uncertainty Visualization via Low-Dimensional Posterior Projections
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes PPDE, a conditional energy-based model that estimates the density of the posterior projected onto a measurement-adaptive low-dimensional affine subspace (MMSE origin plus NPPC principal components) for uncertainty visualization in image restoration.
Problem
Visualizing high-dimensional posterior uncertainty in ill-posed imaging inverse problems is hard, since posterior samples are slow to generate and per-pixel or slice-based views are uninformative.
Approach
Train a conditional EBM that, given a measurement and an input-adaptive affine subspace, outputs the marginal (projected) posterior density over subspace coordinates, integrating out the orthogonal dimensions rather than slicing the high-dimensional density.
Key results
- On MNIST inpainting, PPDE achieves NLL 3.72 vs 4.19 for NPPC Gaussian approximation and 3.9 for KDE on 100 images.
- On CelebA-HQ colorization, PPDE reaches NLL 7.39 vs 10.3 for NPPC; on ImageNet colorization it reaches 6.86 vs 10.15 for NPPC.
- PPDE is reported to be orders of magnitude faster than the posterior-sampling+KDE baseline, and only slightly slower than NPPC.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PPDE instead of NPPC | Projected posterior estimation · MNIST inpainting | NLL: 4.19 ± 0.02 -> 3.72 ± 0.01 | Helped |
| Use PPDE instead of KDE | Projected posterior estimation · MNIST inpainting | NLL: 3.9 ± 0.09 -> 3.72 ± 0.01 | Helped |
| Use PPDE instead of NPPC | Projected posterior estimation · MNIST denoising | NLL: 3.41 ± 0.02 -> 3.04 ± 0.01 | Helped |
| Use PPDE instead of KDE | Projected posterior estimation · MNIST denoising | NLL: 3.26 ± 0.07 -> 3.04 ± 0.01 | Helped |
| Use PPDE instead of NPPC | Projected posterior estimation · CelebA inpainting eyes | NLL: 6.38 ± 0.08 -> 5.37 ± 0.03 | Helped |
| Use PPDE instead of KDE | Projected posterior estimation · CelebA inpainting eyes | NLL: 8.278 ± 1.1 -> 5.37 ± 0.03 | Helped |
| Use PPDE instead of NPPC | Projected posterior estimation · CelebA colorization | NLL: 10.3 ± 0.2 -> 7.39 ± 0.03 | Helped |
| Use PPDE instead of KDE | Projected posterior estimation · CelebA colorization | NLL: 7.7 ± 0.3 -> 7.39 ± 0.03 | Helped |
| Use PPDE instead of NPPC | Projected posterior estimation · CelebA super-resolution | NLL: 5.12 ± 0.3 -> 2.84 ± 0.1 | Helped |
| Use PPDE instead of NPPC | Projected posterior estimation · ImageNet colorization | NLL: 10.15 ± 0.06 -> 6.86 ± 0.01 | Helped |
Surprising findings
- Naive slicing of a learned high-dimensional posterior EBM along a subspace gives misleading densities, missing high-probability modes that projection captures.
Limitations
- Visualization limited to 2 or 3 dimensions, so may be insufficient for rich posteriors.
- Impractical for severely ill-posed problems requiring many PCs.
- Relies on NPPC for subspace directions and MMSE origin; the method is conditional on this choice.
Experimental setup
Datasets: MNIST CelebA-HQ ImageNet 1K SRFlow face crops fluorescent microscopy virtual staining dataset (Weigert/Zhang et al. [62])
Benchmarks: MNIST inpainting MNIST denoising CelebA-HQ inpainting eyes CelebA-HQ colorization CelebA-HQ super-resolution ImageNet colorization
Metrics: negative log-likelihood of projected ground-truth sample
Baselines: NPPC Gaussian approximation posterior sampling + KDE (DDNM/DPS samples)
Builds on: NPPC noise contrastive/contrastive divergence EBM training (Song & Kingma / Zhang et DDNM DPS
Closest papers by meaning
- Hierarchical Uncertainty Exploration via Feedforward Posterior Trees (NeurIPS 2024 · similarity 0.90)
- Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors (NeurIPS 2024 · similarity 0.86)
- Exact Posterior Score Estimation for Solving Linear Inverse Problems (NeurIPS 2026 · similarity 0.86)
- Provable Posterior Sampling with Denoising Oracles via Tilted Transport (NeurIPS 2024 · similarity 0.86)
- Improving Diffusion Models for Inverse Problems Using Optimal Posterior Covariance (ICML 2024 · similarity 0.86)
- Coupled Data and Measurement Space Dynamics for Enhanced Diffusion Posterior Sampling (NeurIPS 2025 · similarity 0.86)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.