FieldBridge: Cross-Field MRI Synthesis with an Unpaired Neural Schrödinger Bridge

TL;DR

FieldBridge turns a brain MRI acquired at 0.1, 1.5, 3 or 5 T into a 7 T-equivalent image. Instead of one big generator jump, an unpaired Neural Schrödinger Bridge lets a single time-conditioned network refine its own prediction over three steps. Trained almost entirely on unpaired scans, fine-tuned on 660 paired slices, and calibrated with two post-hoc scalars per contrast, it ranks 1st of 36 on the MRIxFields Task 1 validation leaderboard — including first place on both anatomical metrics.

Drag to compare · example subject

FieldBridge 7 T-equivalent synthesis of the same slice

Acquired 0.1 T FieldBridge → 7 T

Acquired 7 T · same subject

Acquired 7 T reference of the same subject

Background

The task: any field in, 7 T out

Magnetic field strength changes almost everything about an MR image at once — signal-to-noise, achievable resolution, tissue contrast, B₀/B₁ homogeneity — and it changes each contrast differently. Task 1 of the MRIxFields 2026 benchmark asks for a single reference output: given a scan at 0.1, 1.5, 3 or 5 T, in any of three contrasts, synthesise the 7 T-equivalent image while preserving the subject's anatomy.

One anatomy, five field strengths

0.1 T

piMR-820H

1.5 T

uMR 670

3 T

MAGNETOM Prisma

5 T

uMR Jupiter

7 T

MAGNETOM Terra

T1w

T2w

T2 FLAIR

The same person scanned on five systems from three manufacturers, registered to a common space.

Training data · unpaired

1,900+ cases

A different set of volunteers at every field.

0.1 T 100 1.5 T 228 3 T 143 5 T 266 7 T 319

Training data · paired

40 travelling volunteers

The same people scanned at all five fields × three contrasts — the benchmark's only true pairs. Only 3 of them are in the training set: 660 paired slices to learn from.

In training 3

Evaluation

5 metrics, 1 rank

Methods are ranked per metric; the five ranks are summed; lowest total wins — consistency beats a single shiny number.

nRMSE ↓global intensity deviation

SSIM ↑structural preservation

LPIPS ↓perceptual realism

Dice ↑overlap, 14 deep-grey nuclei

Vol. cons. ↑regional volume agreement

Anatomical metrics use SynthSeg (Billot et al., Medical Image Analysis 2023) labels of 14 deep grey-matter structures. Challenge rules allow up to 12 separate models — one per input field × contrast — a freedom this method uses.

Method

An unpaired bridge, then twelve field-specific translators

FieldBridge keeps the content-preservation machinery of CUT — PatchNCE and an identity term — but replaces the single generator jump with a Neural Schrödinger Bridge: entropy-regularised optimal transport between the low-field and 7 T distributions, unrolled as a short Markov chain. Training happens in two stages, followed by a per-contrast calibration at inference.

One-step translator

CycleGAN · CUT

x→G→\hat{y}

One mapping, learned end to end
Fine when domains differ mainly in texture
Here SNR, contrast and artefacts shift at once

Neural Schrödinger Bridge

UNSB (Kim et al., ICLR 2024) — what we build on

x_{t_0}→q_\phi→x_{t_1}→q_\phi→…→\hat{x}_1

A Markov chain over 0 = t_0 < \ldots < t_N = 1
One time-conditioned network shared across steps
Each step refines the predicted 7 T, not the source

The rollout: three refinements, one network

Follow it in order: from the low-field input, the same network q_\phi(\cdot,\, t) predicts the 7 T image (top row), then the next state blends that prediction back into the current one with a little noise (bottom row). Three times, and the last prediction is the output.

x_1(x_{t_0}) x_1(x_{t_1}) x_1(x_{t_2}) x_1 \sim \pi_1 q_\phi q_\phi q_\phi x_0 \sim \pi_0 x_{t_1} x_{t_2} s_1 s_2 1 - s_1 1 - s_2 \varepsilon \varepsilon

During training, one t_i is drawn per iteration; earlier iterates run under no_grad, so exactly one application of q_\phi is back-propagated — a multi-step sampler for the price of a one-step one.

Learning the field map without paired data

The whole unpaired cohort trains the step-conditioned translator — anatomy is held in place patch by patch, not by a round trip.

x_0 \sim \pi_0 x_{t_i} \hat{x}_1 x_1 \sim \pi_1 \tilde{x}_1 = q_\phi(x_1 \mid x_1) E(\cdot, t_i) q_\phi q_\phi D(\cdot, t_i) \mathcal{L}_{\mathrm{Adv}} \mathcal{L}_{\mathrm{NCE}}(x_0, \hat{x}_1) \mathcal{L}_{\mathrm{NCE}}(x_1, \tilde{x}_1) \mathcal{L}_{\mathrm{SB}} = \tau\lVert x_{t_i} - \hat{x}_1\rVert^2 + \tfrac{N-i}{N}\,\tau\hat{I} i mixture steps
under no_grad

\mathcal{L}_{\mathrm{UNSB}}(\phi, t_i) = \lambda_{\mathrm{GAN}}\,\mathcal{L}_{\mathrm{Adv}} + \lambda_{\mathrm{SB}}\,\mathcal{L}_{\mathrm{SB}} + \tfrac{\lambda_{\mathrm{NCE}}}{2}\left[\mathcal{L}_{\mathrm{NCE}}(x_0, \hat{x}_1) + \mathcal{L}_{\mathrm{NCE}}(x_1, \tilde{x}_1)\right]

PatchNCE anchors the anatomy patch by patch — green squares: same location, same features — and the identity pass keeps real 7 T unchanged. All \lambda at 1; t_i \sim \mathcal{U}\{t_0, t_1, t_2\}; E and the projection head are discarded after this stage.

Fine-tuning on the 660 paired slices

Same rollout, but the final prediction is now compared directly with the acquired 7 T of the same subject.

x_0 low field

3-step rollout

\hat{x} synthesized 7 T

x_1 acquired 7 T, same subject

\mathcal{L}_{\mathrm{ft}} = \mathcal{L}_1 + 0.1\,\mathcal{L}_{\mathrm{LPIPS}} + 0.2\,\mathcal{L}_{\mathrm{SSIM}} 40 epochs per cell

The extra input context below also enters here — no unpaired pre-training is repeated.

What each slice sees: its neighbours and the other contrasts

With so few paired subjects, the cheapest extra information is more of the same subject: adjacent slices add through-plane structure, and the other two contrasts — already co-registered by the organisers — add complementary tissue information for free.

The input stack — up to 5 channels

Through-plane (2.5D)

s−1

slice s

s+1

Cross-contrast

T2w

FLAIR

W \leftarrow \tfrac{1}{n}\,[\,W, \ldots, W\,] first-convolution inflation — the forward pass is unchanged at initialisation, so pre-training is never repeated

Who gets which channels

Which of a contrast's models keep their complementary-contrast inputs — they matter most when the source is information-poor.

Source	2.5Dall models	Cross-contrast inputs
Source	2.5Dall models	T1wmodel	T2wmodel	FLAIRmodel
0.1 T	✓	✓	✓	✓
1.5 T	✓	✓	✓	✓
3 T	✓	✕	✕	✓
5 T	✓	✕	✕	✓

At 3–5 T the source already carries most of the information — only the T2-FLAIR model keeps its cross-contrast inputs, at every field. The ablation below shows what each channel buys.

Twelve translators, three trained from scratch

Rules allow one model per input-field × contrast cell. Training all twelve independently would cost ≈27 GPU-days; instead, each contrast trains once on its widest gap — 0.1 T → 7 T — and the other three fields warm-start from it.

trained from scratch on the widest gap of its contrast

Training time · 201 GPU-hours in total (≈ 8.4 GPU-days; ≈ 27 GPU-days at full budget)

Stage 1 from scratch · 150 h 3 cells × 50 h · ≈ 50 epochs at 1.07 h

Warm start · 45 h 9 cells × 5 h · 5 epochs each

Stage 2 fine-tuning · 4 h 12 cells × 20 min

A warm start transfers everything — generator, discriminator, critic and projection head. Weights are never transferred across contrasts — a T1w model would still have to learn FLAIR's inversion-recovery behaviour from scratch. Hardware: one NVIDIA RTX PRO 6000 Blackwell.

Inference: a per-contrast calibration fixes a systematic drift

Calibration factor by source field

\mu_{7\mathrm{T}} \,/\, \operatorname{mean}(\text{prediction}) over the brain mask — ×1.00 means no correction needed.

T1w T2w T2 FLAIR

The direction of the drift is consistent across fields — a systematic bias, not noise. T1w and FLAIR come out too dark, T2w too bright; FLAIR drifts ≈30% at 3–5 T.

Trained on distributions, the bridge has nothing pinning the absolute intensity level. One scalar per contrast — the median 7 T brain mean over the prediction's — repairs it, once per volume:

\hat{y} \leftarrow \operatorname{clip}\!\left(\dfrac{\mu_c}{\operatorname{mean}_\Omega(\hat{y})}\,\hat{y},\; 0,\; 1\right)

\Omega = (x > \epsilon) \cap (\hat{y} > \epsilon)

\Omega is the brain mask shared by input and prediction; \mu_c the median brain mean over the training 7 T volumes — 0.1867 / 0.2183 / 0.2170 for T1w / T2w / T2-FLAIR.

−12.1%nRMSE

−6.7%LPIPS

+1.1%SSIM

±0%Dice & volume consistency

The anatomical metrics do not move because SynthSeg is contrast-randomised. A second scalar then corrects dispersion rather than level: ×1.069 T2w, ×1.021 T2-FLAIR, T1w unchanged — post-processing, no retraining.

Why matching the mean does not minimise nRMSE

For a fixed prediction, nRMSE as a function of a global scale is minimised by the least-squares scale:

\mathrm{nRMSE}(s) = \dfrac{\lVert s\hat{y} - y\rVert}{\lVert y\rVert}, \qquad s^\star = \dfrac{\langle y, \hat{y}\rangle}{\langle \hat{y}, \hat{y}\rangle}

After calibration both volumes share the mean \mu, so it cancels out of the comparison and what is left is a statement about spread:

s^\star = \dfrac{\mu^2 + \rho\,\sigma_y\sigma_{\hat{y}}}{\mu^2 + \sigma_{\hat{y}}^{\,2}}, \qquad s^\star > 1 \iff \sigma_{\hat{y}} < \rho\,\sigma_y

The optimal scale exceeds one exactly when the prediction is under-dispersed — a scale above one says the predicted contrast is compressed. Fitted leave-one-subject-out over the three paired subjects, and again by fitting on a subset of slices and testing on the rest; both agree on the same small residual scale.

Results

First of 36 on the validation leaderboard

Every entry below is scored on the challenge server. The composite rank sums the five per-metric ranks — the two anatomical metrics are where FieldBridge separates from the field.

1st / 36

FieldBridge 13

Team A 15

Team B 18

Team C 26

CUT baseline 90

Σ of the five per-metric ranks — lower is better. The starting point (CUT) sums to 90; the full method reaches 13.

Task 1 validation leaderboard, top 5 of 36 entries + the CUT baseline. Per-metric rank in parentheses; best value per column in bold. ↓ lower is better, ↑ higher is better.

#	Method	nRMSE ↓	LPIPS ↓	SSIM ↑	Dice ↑	Vol. cons. ↑	Σ ranks ↓
1	FieldBridge (ours)	0.2595 (4)	0.0676 (3)	0.9244 (4)	0.9071 (1)	0.9168 (1)	13
2	Team A	0.2643 (5)	0.0637 (2)	0.9259 (3)	0.9064 (2)	0.9097 (3)	15
3	Team B	0.2591 (2)	0.0587 (1)	0.9293 (1)	0.8884 (7)	0.8828 (7)	18
4	Team C	0.2775 (6)	0.0704 (4)	0.9188 (6)	0.8890 (6)	0.8972 (4)	26
5	Team D	0.2880 (10)	0.0721 (5)	0.9137 (7)	0.9002 (4)	0.8869 (6)	32
—	CUT baseline	0.3041 (30)	0.0750 (10)	0.9053 (19)	0.8543 (14)	0.8601 (17)	90

Per-contrast scores (rank of 36) — T2w draws our best raw scores but our worst ranks (everyone scores high there); T2-FLAIR, the hardest input, gives the worst raw scores and the best ranks.

Contrast	nRMSE ↓	LPIPS ↓	SSIM ↑	Dice ↑	Vol. cons. ↑
T1w	0.2635 (4)	0.0641 (2)	0.9220 (4)	0.9127 (2)	0.9324 (2)
T2w	0.2205 (6)	0.0628 (6)	0.9349 (5)	0.9125 (4)	0.9062 (6)
T2 FLAIR	0.2945 (3)	0.0759 (3)	0.9163 (3)	0.8961 (1)	0.9117 (1)

Qualitative comparison — 0.1 T → 7 T

Acquired 0.1 T T1w slice — **Acquired 0.1 T** · input

CycleGAN synthesis — **CycleGAN** · 0.1→7 T

FieldBridge synthesis — **FieldBridge** · ours

Acquired 7 T reference — **Acquired 7 T** · target

Where to look — thalamus and putamen. CycleGAN and CUT render the deep grey matter mottled and over-textured; FieldBridge keeps it homogeneous, as in the acquired 7 T. At the cortex all three look plausible — which is exactly why image-quality metrics separate the methods less than anatomical ones.

Same subject in all panels. Every source field is compared further down the page.

Why the anatomical metrics favour the bridge

Run SynthSeg on the images and count what it finds. On this subject's 0.1 T acquisition, none of the 14 scored deep-grey structures are detected. On the FieldBridge synthesis, all 14 are — with total volume within 0.5% of the acquired 7 T.

SynthSeg on the 0.1 T acquisition: no structures found — **Acquired 0.1 T**

SynthSeg on CycleGAN output: 3 structures — **CycleGAN**

SynthSeg on CUT output: 5 structures — **CUT**

SynthSeg on FieldBridge output: all 14 structures — **FieldBridge** · ours

SynthSeg on the acquired 7 T — **Acquired 7 T** · reference

Per-structure volume recovered

% of the 7 T volume that SynthSeg labels, axial T2w · same subject.

Acquired 0.1 T FieldBridge

Left thalamus 40% 86%

Caudate 51% 87%

Left pallidum 23% 74%

The pattern: structures without a CSF boundary — thalamus, caudate, pallidum — are where 0.1 T loses the anatomy and where the translation recovers most of it. The CSF-bounded hippocampus and amygdala keep a hard edge at any field, so every method finds them.

The baselines mostly find only those two easy, CSF-bounded structures. FieldBridge restores the boundaries SynthSeg needs everywhere else too — and it does so at the right size:

14 / 14structures recovered — on both subjects shown

+0.3% / +0.5%total deep-grey volume vs the acquired 7 T (the two subjects shown)

55.3k voxlabelled on our synthesis vs 55.0k on the acquired 7 T — from 0 on the raw 0.1 T input

Explore the segmentation on the full volume, in 3-D, in the interactive viewer.

Where each input channel helps

Relative improvement over a single-channel control

Same seed, schedule, inference and calibration — only the input stack differs.

+ Through-plane neighbours (2.5D) + Complementary contrasts

A clean division of labour: through-plane context drives the voxel and perceptual gains (nRMSE +7.4%, LPIPS +9.1%, Dice untouched); complementary contrasts drive the anatomical ones (Dice +3.1%, volume consistency +3.0%). T2-FLAIR is the exception — cross-contrast helps it at every field. Absolute scores: nRMSE 0.289→0.265, LPIPS 0.075→0.065, Dice 0.867→0.894, VC 0.846→0.898.

How much does a better scanner buy?

from 0.1 T

from 1.5 T

from 3 T

from 5 T

acquired 7 T

T1w

T2w

T2 FLAIR

FieldBridge predictions of the same 7 T target from each source field, next to the acquired 7 T. A stronger source helps — but far less than the field ratio suggests: from a 0.1 T to a 5 T source, the perceptual distance (LPIPS) to the target drops only ≈¼ on T1w and ≈½ on T2w. The value of source-field information depends on the contrast.

Slice-to-slice consistency

Inference runs on axial slices, so any slice-to-slice inconsistency shows up as horizontal banding in a sagittal reformat. Δ is the mean absolute step in slice-mean intensity between consecutive slices — the acquired 7 T itself sits at 1.1%.

Sagittal reformat of the 0.1 T acquisition — **Acquired 0.1 T**input

Sagittal reformat of CycleGAN output showing a block break — **CycleGAN**Δ 2.3%

Sagittal reformat of CUT output showing heavy banding — **CUT**Δ 3.9%

Sagittal reformat of FieldBridge output, nearly band-free — **FieldBridge**Δ 1.8%

Sagittal view of the acquired 7 T — **Acquired 7 T**Δ 1.1% · floor

CUT shows heavy banding across the vertex and a step at the mid-brain; CycleGAN a block break below the corpus callosum. Sharing one latent across the slices of a volume brings FieldBridge to 1.8% — close to, but not yet at, the acquisition floor.

Conclusion

What we built for the challenge

FieldBridge turns a brain MRI acquired at 0.1, 1.5, 3 or 5 T into its 7 T-equivalent without any paired training data: an Unpaired Neural Schrödinger Bridge refines the prediction in three steps of one time-conditioned network, learned on the unpaired cohort and fine-tuned on the 660 paired slices. It ranks 1st of 36 on the Task 1 validation leaderboard — first on both anatomical metrics — recovering all 14 scored deep-grey structures from a 0.1 T input within 0.5% of the acquired 7 T by volume.

Explore the predictions yourself in the interactive viewer.

Citation

@misc{legourrierec2026fieldbridge,
  title  = {Cross-Field MRI Synthesis with an Unpaired Neural Schr{\"o}dinger Bridge},
  author = {Titouan {Le Gourrierec} and HyoSeok Lee and Sung-Hong Park},
  year   = {2026},
  note   = {MICCAI 2026 MRIxFields Challenge, Task 1},
  url    = {https://titouanlegourrierec.github.io/fieldbridge/}
}

References

Kim, Kwon, Kim & Ye · Unpaired Image-to-Image Translation via Neural Schrödinger Bridge · ICLR 2024 — the UNSB formulation FieldBridge builds on.
Park, Efros, Zhang & Zhu · Contrastive Learning for Unpaired Image-to-Image Translation · ECCV 2020 — PatchNCE and the identity pass (CUT).
Zhu, Park, Isola & Efros · Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks · ICCV 2017 — the CycleGAN baseline.
Isola, Zhu, Zhou & Efros · Image-to-Image Translation with Conditional Adversarial Networks · CVPR 2017 — the PatchGAN discriminator.
Mao et al. · Least Squares Generative Adversarial Networks · ICCV 2017 — the adversarial objective.
Billot et al. · SynthSeg: Segmentation of Brain MRI Scans of any Contrast and Resolution · Medical Image Analysis 2023 — behind the Dice and volume-consistency metrics.
Zhang et al. · The Unreasonable Effectiveness of Deep Features as a Perceptual Metric · CVPR 2018 — LPIPS.
Wang et al. · Image Quality Assessment: From Error Visibility to Structural Similarity · IEEE TIP 2004 — SSIM.
NiiVue — the WebGL volume renderer behind the interactive viewer.