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A Steerable Deep Network for Model-Free Diffusion MRI Registration

NeurIPS 2026 · Image generation › Fast diffusion sampling · approach: Diffusion posterior sampling · 0 citations (OpenAlex)

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Proposes a model-free, SE(3)-equivariant UNet that predicts velocity fields directly on raw diffusion MRI (position-and-orientation space) for nonrigid registration, trained with an MMD-in-Fourier-space loss on HCP data.

Problem

Nonrigid registration of diffusion MRI is hard because orientation-dependent information must be reoriented under deformations; existing deep methods rely on derived representations (DTs, fODFs, FA/TOMs) that lose information and need extra estimation overhead.

Approach

Formulate dMRI registration as finding an SE(3)-equivariant diffeomorphism of position-and-orientation space R^3 ⊕ R^3 (shell-restricted to R^3 x S^2), generated by a steerable equivariant UNet velocity field integrated via scaling-and-squaring, and use an MMD loss in Fourier (q-)space that matches EAPs indirectly through signal attenuations.

Key results

• Proposed method achieves mean Dice 0.7468 on 25 test subjects, below mrregister (0.7601) and MVVSReg (0.7493) but above DDMReg (0.7417), MVCReg (0.7317) and VoxelMorph (0.7126).
• Only the proposed method registers raw dMRI signals directly; all compared deep methods need derived representations (FA, TOMs, fODFs).

Surprising findings

• The proposed raw-dMRI method is not the best on Dice: it trails classical mrregister and MVVSReg, though it is competitive with the other deep methods.

Limitations

• Downsampled spatial resolution (72x88x72) due to memory cost.
• Evaluation relies on TractSeg bundle Dice via fODF peaks, with no direct warping of bundle masks in the diff-pq setting.
• Only one HCP fixed subject and 25 test subjects; no clinical or patient data evaluated.

Experimental setup

Datasets: Human Connectome Project Young Adult dMRI

Benchmarks: Human Connectome Project Young Adult dMRI registration (25 test subjects)

Metrics: Dice score over 72 white matter tracts (TractSeg)

Baselines: mrregister VoxelMorph DDMReg MVCReg MVVSReg

Builds on: VoxelMorph DDMReg MVCReg steerable CNNs e3nn scaling-and-squaring diffeomorphisms

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