# Residual Diffusion

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arXiv Nov 6, 2026
When the target body location has no sensor, DiffusionRef-IMU lets diffusion fix only the residual and beats deterministic baselines in all five folds
Moving a wearable inertial sensor to another body location shifts the signal distribution, and measurements at the desired target location are often unavailable during training or deployment. DiffusionRef-IMU first has a deterministic Direct network estimate the target signal, then lets a diffusion model correct only the residual between that estimate and the paired target. Across five subject-disjoint folds with activity–location compositions held out, 16-step DDIM reached a mean nRMSE of 0.087538, below 0.090262 for Direct, 0.088847 for a capacity-matched deterministic residual model and 0.088417 for eight-step CompFlow, and was better in all five folds.
Moving a wearable inertial sensor to another body location shifts the signal distribution, and measurements at the desired target location are often unavailable during training or deployment. DiffusionRef-IMU first has a deterministic Direct network estimate the target signal, then lets a diffusion model correct only the residual between that estimate and the paired target. Across five subject-disjoint folds with activity–location compositions held out, 16-step DDIM reached a mean nRMSE of 0.087538, below 0.090262 for Direct, 0.088847 for a capacity-matched deterministic residual model and 0.088417 for eight-step CompFlow, and was better in all five folds.
M. M. Golam Hafiz（First author）
DiffusionRef-IMU Residual Diffusion Cross-Location IMU Translation DDIM
researchsquare.com Oct 16, 2026
Mural restoration stops asking only where damage is: a continuous severity field lifts PSNR by 3.27 dB
Fading, stains and water marks on Dunhuang murals are semi-transparent damage that still leaves pigment and contours visible, yet a binary mask marks only where damage lies and cannot describe how severity varies inside that region. SC-PAD estimates a continuous terminal severity field from the degraded image and a coarse mask, reparameterizes a shared diffusion progress into pixel-wise local restoration progress, and drives image-space residual activation through a dynamic Alpha state with consistent endpoints and monotonic evolution. On a fixed 100-image test split, replacing the binary mask with predicted soft Alpha raised PSNR from 27.3421 dB to 30.6122 dB, while ground-truth Alpha added a further 3.2539 dB, marking severity estimation as the remaining bottleneck.
Fading, stains and water marks on Dunhuang murals are semi-transparent damage that still leaves pigment and contours visible, yet a binary mask marks only where damage lies and cannot describe how severity varies inside that region. SC-PAD estimates a continuous terminal severity field from the degraded image and a coarse mask, reparameterizes a shared diffusion progress into pixel-wise local restoration progress, and drives image-space residual activation through a dynamic Alpha state with consistent endpoints and monotonic evolution. On a fixed 100-image test split, replacing the binary mask with predicted soft Alpha raised PSNR from 27.3421 dB to 30.6122 dB, while ground-truth Alpha added a further 3.2539 dB, marking severity estimation as the remaining bottleneck.
Gansu Academy of Sciences Lanzhou University of Arts and Science Lanzhou University of Technology
Wu Yu（First author）Lei Zhang（Corresponding author）Erchao Li（Corresponding author）
SC-PAD Ancient Mural Restoration Diffusion Model Residual Diffusion Degradation Severity Estimation
arXiv Sep 26, 2026
KANResDiff combines KAN spline time encoding with a local Schrödinger bridge for residual diffusion, cutting GED by up to 18.8% and raising HM-IoU32 by up to 7.7% on LIDC and ISIC3
The work proposes KANResDiff, which learns local residual diffusion via Kolmogorov-Arnold Networks for ambiguous medical image segmentation: it replaces MLP linear time embeddings with B-spline-based Independent Time Encoding to strengthen independence across inference stages, and injects a deterministic residual prior with learnable weights through a Residual Schrödinger Bridge, achieving state-of-the-art GED and HM-IoU on the two public datasets LIDC and ISIC3 with maximum improvements of 16.8% and 7.7% respectively while keeping competitive MDM performance.
The work proposes KANResDiff, which learns local residual diffusion via Kolmogorov-Arnold Networks for ambiguous medical image segmentation: it replaces MLP linear time embeddings with B-spline-based Independent Time Encoding to strengthen independence across inference stages, and injects a deterministic residual prior with learnable weights through a Residual Schrödinger Bridge, achieving state-of-the-art GED and HM-IoU on the two public datasets LIDC and ISIC3 with maximum improvements of 16.8% and 7.7% respectively while keeping competitive MDM performance.
Harbin Institute of Technology Northeast Forestry University Case Western Reserve University
Fanding Li（First author）Xiangyu Li（Corresponding author）
KANResDiff Ambiguous Medical Image Segmentation Kolmogorov-Arnold Network Residual Diffusion Schrödinger Bridge

You’re all caught up

When the target body location has no sensor, DiffusionRef-IMU lets diffusion fix only the residual and beats deterministic baselines in all five folds

Mural restoration stops asking only where damage is: a continuous severity field lifts PSNR by 3.27 dB

KANResDiff combines KAN spline time encoding with a local Schrödinger bridge for residual diffusion, cutting GED by up to 18.8% and raising HM-IoU32 by up to 7.7% on LIDC and ISIC3