Patch-PODiff-ViT: Structured Latent Diffusion with Patchwise POD for Super-Resolution and Uncertainty Quantification

• URL: http://arxiv.org/abs/2606.31290v1
• Date: Tue, 30 Jun 2026 08:05:53 GMT
• Title: Patch-PODiff-ViT: Structured Latent Diffusion with Patchwise POD for Super-Resolution and Uncertainty Quantification
• Abstract summary: We introduce Patch-PODiff-ViT, a structured latent diffusion framework in which the latent space is defined by patchwise Proper Orthogonal Decomposition (POD)<n>This yields low-dimensional, variance-ordered tokens that preserve spatial structure and enable efficient diffusion in a structured low-dimensional latent space with a Vision Transformer.<n>Across sea surface temperature, medical imaging, and natural images, the method achieves strong reconstruction with fewer parameters and lower memory, while producing well-calibrated spatial uncertainty that closely matches empirical ensembles.
• Score: 2.075423143311858
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Diffusion models enable probabilistic super-resolution and conditional generation, but pixel-space methods are computationally expensive and learned latent spaces often lack interpretable uncertainty quantification. We introduce Patch-PODiff-ViT, a structured latent diffusion framework in which the latent space is defined by patchwise Proper Orthogonal Decomposition (POD), a fixed linear orthonormal basis over local patches, rather than learned by a nonlinear autoencoder. This yields low-dimensional, variance-ordered tokens that preserve spatial structure and enable efficient diffusion in a structured low-dimensional latent space with a Vision Transformer. Because the decoder is fixed, linear, and orthonormal, latent coefficient uncertainty can be propagated directly to physical-space predictive variance, enabling analytic propagation of predictive variance through the linear decoder without Monte Carlo estimation in pixel space. Across sea surface temperature, medical imaging, and natural images, the method achieves strong reconstruction with fewer parameters and lower memory, while producing well-calibrated spatial uncertainty that closely matches empirical ensembles.

Related papers

• Null-Space Diffusion Restoration with Adaptive Uncertainty-Guided Fusion for Ultrasound Speckle Reduction [2.081691729410268]
  Ultrasound B-mode imaging commonly suffers from speckle noise and artifacts.<n>New uncertainty-guided null-space diffusion (UGNS) framework enforces consistency correction on a stabilized positive-envelope proxy.<n>It is successfully validated that UGNS effectively suppresses speckle noise while preserving fine spatial resolution.
  arXiv  Detail & Related papers  (2026-08-30T14:45:13Z)
• Local Epistemic Uncertainty Guided Active Sampling for Plug-and-play Diffusive Image Restoration [15.371827475537776]
  Local Epistemic Uncertainty Guided Active Sampling framework is developed.<n>It balances detail preservation and artifact suppression in the spatial domain.<n>It reduces sampling time with negligible memory overhead.
  arXiv  Detail & Related papers  (2026-08-07T09:00:20Z)
• Latent Diffusion Posterior Sampling with Surrogate Likelihood Guidance for PDE Inverse Problems [48.15157016272698]
  latent-space diffusion posterior sampling (L-DPS) is an approximate Bayesian framework for high-dimensional inverse problems governed by partial differential equations (PDEs)<n>L-DPS produces accurate and robust inverse solutions, reduces inference cost relative to full-space DPS, and outperforms amortized inverse baselines in sparse and noisy regimes.
  arXiv  Detail & Related papers  (2026-06-25T04:33:44Z)
• Unified Geometry-Guided ML-FTLE for Tracking Transient Chaos from Scalar Time Series [0.0]
  We propose a geometry-guided machine learning framework that unifies predictive trajectory divergence with macroscopic attractor morphology to track abrupt regime shifts.<n>This equation-free framework provides a highly accurate, noise-resilient diagnostic for monitoring structural transitions in complex non-stationary systems.
  arXiv  Detail & Related papers  (2026-06-05T15:22:57Z)
• Hierarchical Consistency Learning for Test-time Adaptation in Camouflage Perception [50.278200968044665]
  Camouflaged object detection (COD) aims to localize targets that exhibit minimal perceptual differences from backgrounds through physical attributes.<n>Existing methods, constrained by the static train-then-freeze paradigm, suffer from domain rigidity and dependency annotation.<n>We propose the hierarchical consistency learning framework, which integrates test-time adaptation for dynamic representation recalibration.
  arXiv  Detail & Related papers  (2026-05-25T09:57:46Z)
• Spatial Adapter: Structured Spatial Decomposition and Closed-Form Covariance for Frozen Predictors [0.6643390346826856]
  We present a parameter-efficient post-hoc layer that equips any frozen first-stage predictor with a structured spatial representation of its residual field.<n>The adapter operates as a cascade second stage on residuals, jointly learning a spatially regularized orthonormal basis and per-sample scores.<n>Because the first-stage parameters are frozen, the adapter does not retrain the backbone; its role is to supply a compressed distributional summary of the residual field.
  arXiv  Detail & Related papers  (2026-05-12T01:29:56Z)
• PODiff: Latent Diffusion in Proper Orthogonal Decomposition Space for Scientific Super-Resolution [2.075423143311858]
  PODiff is a structured conditional generative framework that performs diffusion in a fixed, variance-ordered Proper Orthogonal Decomposition (POD) coefficient space.<n> PODiff achieves reconstruction accuracy comparable to pixel-space diffusion while requiring significantly less memory and producing more reliable uncertainty estimates than deterministic and Monte Carlo Dropout baselines.
  arXiv  Detail & Related papers  (2026-05-05T06:21:04Z)
• Structure-Aware Epistemic Uncertainty Quantification for Neural Operator PDE Surrogates [10.39662017167378]
  Uncertainty quantification (UQ) must be both computationally efficient and spatially faithful.<n>We propose a structure-aware UQ scheme that exploits the modular anatomy common to modern NOs.<n> Experiments on challenging PDE benchmarks demonstrate that the proposed structure-aware design yields more reliable coverage, tighter bands, and improved residual-uncertainty alignment.
  arXiv  Detail & Related papers  (2026-02-24T10:17:24Z)
• ARGUS: Adaptive Rotation-Invariant Geometric Unsupervised System [0.0]
  This paper introduces Argus, a framework that reconceptualizes drift detection as tracking local statistics over a fixed spatial partition of the data manifold.<n> Voronoi tessellations over canonical orthonormal frames yield drift metrics that are invariant to transformations.<n>A graph-theoretic characterization of drift propagation is developed that distinguishes coherent distributional shifts from isolated perturbations.
  arXiv  Detail & Related papers  (2026-01-03T22:39:20Z)
• Linearized Optimal Transport for Analysis of High-Dimensional Point-Cloud and Single-Cell Data [45.87606039212519]
  Single-cell technologies generate high-dimensional point clouds of cells.<n>Each patient is represented by an irregular point cloud rather than a simple vector.<n>We adapt the Linear Optimal Transport framework to embed irregular point clouds into a fixed-dimensional Euclidean space.
  arXiv  Detail & Related papers  (2025-10-24T21:33:12Z)
• Adaptive Dual Uncertainty Optimization: Boosting Monocular 3D Object Detection under Test-Time Shifts [80.32933059529135]
  Test-Time Adaptation (TTA) methods have emerged to adapt to target distributions during inference.<n>We propose Dual Uncertainty Optimization (DUO), the first TTA framework designed to jointly minimize both uncertainties for robust M3OD.<n>In parallel, we design a semantic-aware normal field constraint that preserves geometric coherence in regions with clear semantic cues.
  arXiv  Detail & Related papers  (2025-08-28T07:09:21Z)
• Low-Rank Tensor Recovery via Variational Schatten-p Quasi-Norm and Jacobian Regularization [49.85875869048434]
  We propose a CP-based low-rank tensor function parameterized by neural networks for implicit neural representation.<n>To achieve sparser CP decomposition, we introduce a variational Schatten-p quasi-norm to prune redundant rank-1 components.<n>For smoothness, we propose a regularization term based on the spectral norm of the Jacobian and Hutchinson's trace estimator.
  arXiv  Detail & Related papers  (2025-06-27T11:23:10Z)
• Maintaining Structural Integrity in Parameter Spaces for Parameter Efficient Fine-tuning [78.39310274926535]
  Adapting pre-trained foundation models for various downstream tasks has been prevalent in artificial intelligence.<n>To mitigate this, several fine-tuning techniques have been developed to update the pre-trained model weights in a more resource-efficient manner.<n>This paper introduces a generalized parameter-efficient fine-tuning framework, designed for various dimensional parameter space.
  arXiv  Detail & Related papers  (2024-05-23T16:04:42Z)
• Orthogonal Matrix Retrieval with Spatial Consensus for 3D Unknown-View Tomography [58.60249163402822]
  Unknown-view tomography (UVT) reconstructs a 3D density map from its 2D projections at unknown, random orientations. The proposed OMR is more robust and performs significantly better than the previous state-of-the-art OMR approach.
  arXiv  Detail & Related papers  (2022-07-06T21:40:59Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.