[Paper Review] Likelihood-Separable Diffusion Inference for Multi-Image MRI Super-Resolution

Samuel W. Remedios, Zhangxing Bian+4 more|arXiv (Cornell University)|Jan 20, 2026

Advanced Neuroimaging Techniques and Applications0 citations

TL;DR

The paper generalizes diffusion-based inverse problem solvers to multi-image MRI super-resolution (MISR) by proving likelihood separability across independent measurements, enabling MISR without joint operators or retraining, and introducing noise-weighted MISR variants with state-of-the-art results.

ABSTRACT

Diffusion models are the current state-of-the-art for solving inverse problems in imaging. Their impressive generative capability allows them to approximate sampling from a prior distribution, which alongside a known likelihood function permits posterior sampling without retraining the model. While recent methods have made strides in advancing the accuracy of posterior sampling, the majority focuses on single-image inverse problems. However, for modalities such as magnetic resonance imaging (MRI), it is common to acquire multiple complementary measurements, each low-resolution along a different axis. In this work, we generalize common diffusion-based inverse single-image problem solvers for multi-image super-resolution (MISR) MRI. We show that the DPS likelihood correction allows an exactly-separable gradient decomposition across independently acquired measurements, enabling MISR without constructing a joint operator, modifying the diffusion model, or increasing network function evaluations. We derive MISR versions of DPS, DMAP, DPPS, and diffusion-based PnP/ADMM, and demonstrate substantial gains over SISR across $4 imes/8 imes/16 imes$ anisotropic degradations. Our results achieve state-of-the-art super-resolution of anisotropic MRI volumes and, critically, enable reconstruction of near-isotropic anatomy from routine 2D multi-slice acquisitions, which are otherwise highly degraded in orthogonal views.

Motivation & Objective

• Motivate MISR in MRI where multiple anisotropic LR volumes can inform a single HR volume.
• Formalize a separable likelihood framework that allows MISR corrections without a joint forward operator or changing diffusion models.
• Derive MISR extensions of DPS, DMAP, DPPS, and diffusion-based PnP/ADMM.
• Introduce per-measurement noise weighting to fuse heterogeneous acquisitions.
• Demonstrate improved MISR performance across 4x/8x/16x through-plane degradations and enable near-isotropic reconstructions from routine 2D acquisitions.

Proposed method

• Show that the joint negative log-likelihood of multiple LR measurements is separable across observations, enabling per-measurement corrections.
• Derive MISR versions of DPS, DMAP, DPPS, and diffusion-based PnP/ADMM that operate with independent A_i operators and y_i measurements.
• Introduce inverse-variance weighting w_i for per-measurement gradients to fuse measurements with different noise levels and resolutions.
• Use a 3D volumetric diffusion model with a DDIM-based sampler and a flow-estimation network to estimate x_0 from x_t.
• Maintain diffusion model unchanged while updating x_t with data-consistency gradients for each measurement separately and then summing them.
• Demonstrate acceptable computational efficiency (<= 60 seconds per volume with 64 NFEs on a RTX 6000 ADA).

Figure 2 : Qualitative results for a representative subject from the AIBL dataset. Row-wise labels designate LR inputs as “Measurements” and SR estimations named by method. Supercolumns group scale factors together. Within supercolumns, each column corresponds to SISR using only the axial acquisitio

Experimental results

Research questions

• RQ1 Can MISR be achieved within diffusion-based inverse problem solvers without constructing a joint forward operator or retraining the diffusion model?
• RQ2 Does likelihood separability enable per-measurement data consistency corrections in MISR?
• RQ3 What is the impact of per-measurement noise weighting on MISR performance across anisotropic scale factors?
• RQ4 Which MISR diffusion-based method (DPS/DMAP/DPPS/PnP variants) yields the best trade-off across PSNR, SSIM, and FID for anisotropic MRI?
• RQ5 Can MISR diffusion achieve near-isotropic anatomy from routine 2D multi-slice acquisitions effectively?

Key findings

• MISR diffusion with likelihood separability yields corrections from independent per-measurement operators, avoiding joint operators or model retraining.
• MISR variants (DPS, DMAP, DPPS, and diffusion-based PnP/ADMM) extend diffusion priors to multi-image MISR.
• Inverse-variance noise weighting improves MISR performance, especially as measurement noise increases.
• Across 4x/8x/16x through-plane degradations, MISR methods substantially outperform SISR (1–3 dB PSNR gains reported).
• DMAP consistently outperforms other methods across distortion metrics (PSNR/SSIM) and FID in the reported experiments.
• MISR enables reconstruction of near-isotropic anatomy from routine 2D multi-slice acquisitions, potentially reducing the need for long 3D scans.

Figure 3 : Sagittal slices from four representative subjects are shown for $8\times$ scale factor LR inputs. Each displayed image is labeled for its contents. LR: low-resolution; AX: axial acquisition; COR: coronal acquisition; HR: ground-truth high-resolution; SISR: single-image super-resolution, u