One Evaluation, Any Operating Point: Hypernetwork-Amortized MeanFlow for 3D MRI Reconstruction

Ruibo Wang

cs.CVSep 15, 2026

One Evaluation, Any Operating Point: Hypernetwork-Amortized MeanFlow for 3D MRI Reconstruction

Authors: Ruibo Wang

Organizations: Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, 2600 AA Delft, Netherlands

Abstract

Generative priors reconstruct accelerated 3D MRI well but pay heavily at deployment: tens of network evaluations per volume, and protocol-specific hyperparameter tuning. A third hidden cost is the scanner's fixed sampling pattern. We treat the whole operating point as an input. A 3D MeanFlow patch network (a one-step flow model) is fine-tuned end-to-end through a warm-started, five-iteration differentiable conjugate-gradient projection. A small hypernetwork maps the operating point (data-consistency weight, acceleration, and the Cartesian sampling pattern itself) to the network's per-channel modulation. Three findings follow. (i) Learning the acquisition is worth more than any other operating point: on clinical knee data, the learned mask gains up to +2.34 dB over the protocol's variable-density mask. This gain requires the solver: with a feed-forward reconstructor the same learned mask hurts at 4x (-1.7 dB), but with the data-consistency projection it adds +4.6 dB. (ii) One evaluation is highly effective: it beats a 20-step patch-diffusion prior by up to +3.1 dB on brain and +2.9 dB on knee. Three to five evaluations extend the front to +6 dB while using a quarter of the prior's network calls. (iii) Fully sampled targets are optional: trained self-supervised on a split of acquired samples, the reconstructor matches its supervised twin at 4x on real data. Finally, we report what failed and why: subject-adaptive acquisition from measured energy, combining self-supervision with learned acquisition, and amortising the data-consistency weight.

Figures & tables

Figure 1: (a) The measurement-conditioned one-step reconstructor: a $32^{3}$ patch of the noisy state, the zero-filled condition, pooled thumbnails of both and the voxel coordinates enter a plain 3D U-Net whose blocks are modulated (FiLM) by a hypernetwork of the operating point $h=(\log\lambda,\log_{2}R)$ ; one jump $\hat{x}=x_{\mathrm{zf}}-s\,u_{\theta}$ gives the clean estimate. (b) The same $h$ drives a second hypernetwork head that emits logits over the phase-encode plane, renormalised to the budget $1/R$ : a relaxed mask in training, top- $k$ at test time. (c) Training runs the whole chain (mask, measurement, zero-filled image, one evaluation, warm-started five-iteration CG) and the loss gradient reaches the hypernetwork and the mask logits through the solver. At test time: one evaluation plus CG, or three to five unrolled evaluations.

	method	NFE	$4\times$	$8\times$	$16\times$
BraTS $60^{3}$	CG-SENSE (no prior)	0	34.80	32.04	30.31
	one-step MeanFlow prior, plug-and-play	1	35.08	31.92	30.09
	one-step MeanFlow prior, plug-and-play	4	38.80	34.36	31.42
	patch-diffusion prior, plug-and-play ( Hu et al., 2024 )	20	39.83	34.22	31.04
	patch-diffusion prior, plug-and-play	80	39.95	34.20	30.93
	ours , one evaluation, hyper $(\lambda,R)$	1	41.33	37.31	34.12

Table 3: The cost-quality front. PSNR (dB), 10 volumes, 30 dB, best

\lambda

per row; NFE = network evaluations per volume (each diffusion step also runs a 40-iteration CG). All rows share backbone, data, masks, noise, solver and metrics; “unrolled” = our recipe with

K

iterations of [network

\to

warm CG]. Brain: BraTS

60^{3}

stored-measurement split, CG-5; knee: SKM-TEA, CG-20.

Figure 2: Left: quality against network evaluations per volume (

8\times

, BraTS

60^{3}

). Right: one hypernetwork model (red) against single-acceleration specialists (dashed; circles at their own rates);

6/12/24\times

were seen by no model.

Figure 3: Reconstructions and error maps at $8\times$ , SKM-TEA knee, volume 0, two slices. Every column is the same measurement (one mask, one noise draw, best $\lambda$ of the common grid) except the rightmost method, which acquires with its own learned mask at the same budget; the PSNR/SSIM under each title is that of the displayed volume. Error maps share one colour scale. At $4\times$ the knee is solver-bound and every method is within $1$ to $4$ dB of the prior-free solver (App. D ); at $8\times$ the prior-based and the measurement-conditioned reconstructions separate. The knee measurement is re-encoded from the reference with the scanner coil maps, as in every knee table.

Appendix figures & tables16 assets

Supplementary material from the paper’s appendix.

Appendix

	$4\times$	$6\times$	$8\times$	$12\times$	$16\times$	$24\times$	$32\times$
specialist $4\times$	41.69	37.82	35.35	33.02	31.86	30.39	29.82
specialist $8\times$	37.26	38.20	37.51	35.03	33.15	31.09	30.13
specialist $16\times$	33.93	34.07	34.44	34.79	34.26	32.64	31.30
one hypernetwork $(\lambda,R)$ , Fourier features	41.33	37.04	37.31	35.40	34.16	32.73	31.83
one hypernetwork $(\lambda,R)$ , plain MLP	41.33	38.94	37.31	35.40	34.12	32.77	31.79
CG-SENSE	34.80	33.01	32.04	30.77	30.31	29.16	28.90

Appendix

Table 4: One hypernetwork against single-rate specialists (BraTS

60^{3}

, PSNR dB, 10 volumes, 30 dB).

6/12/24\times

were seen by no model.

Figure 4: One volume of the BraTS $60^{3}$ set at $8\times$ (30 dB), with $|$ error $|$ underneath on a common scale. One measurement-conditioned network evaluation plus a warm CG projection removes residual aliasing that the 20-step diffusion prior leaves behind, at $1/20$ of the network cost.

Figure 5: What the model chooses to acquire (BraTS $60^{3}$ ). Top: the probability the hypernetwork emits for the requested acceleration; middle: the phase-encode locations actually sampled (top- $YZ/R$ ); bottom: the protocol’s variable-density Gaussian mask at the same sampling fraction. At a matched budget the learned pattern concentrates far more strongly on the centre (the fraction of the central $12\times 12$ block it keeps is $0.69/0.59/0.50/0.44$ at $4/8/16/32\times$ against $0.59/0.38/0.20/0.07$ for the protocol) and its probabilities saturate near $0$ and $1$ , i.e. it makes decisions rather than jitter.

Figure 6: SKM-TEA knee, $4\times$ , volume 0; error scale $0.1\times$ the reference maximum, half that of the other figures, because at this solver-bound rate the residuals are small for every method.

Figure 7: SKM-TEA knee, $16\times$ , volume 0.

Figure 8: BraTS $60^{3}$ , $4\times$ , volume 3.

Figure 9: BraTS $60^{3}$ , $8\times$ , volume 3.

Figure 10: BraTS $60^{3}$ , $16\times$ , volume 3.

Figure 11: BraTS $60^{3}$ , $8\times$ , volume 0.

Figure 12: BraTS $120^{3}$ , $8\times$ , volume 3 (no unrolled model was trained at this resolution).

Figure 13: BraTS $120^{3}$ , $4\times$ , volume 3.

Figure 14: PSNR against network evaluations on one split (BraTS

60^{3}

full-k-space split, protocol mask, 30 dB, 10 volumes, best

\lambda

per point): the patch-diffusion prior at

2/5/10/20/80

sampler steps (each step also runs a 40-iteration CG), our reconstructor at one and three evaluations (each followed by five warm CG iterations), and the prior-free CG-SENSE.

reconstructor	acquisition	$6\times$	$12\times$	$24\times$
warm CG, 1 evaluation	protocol	38.62	35.52	33.24
	learned	41.08	35.48	32.45
	gain (won)	$+2.46$ (150/150)	$-0.03$ (65/150)	$-0.78$ (7/150)
warm CG, 3 evaluations	protocol	39.39	35.64	32.95
	learned	44.94	38.84	34.25
	gain (won)	$+5.52$ (150/150)	$+3.20$ (150/150)	$+1.28$ (150/150)

Appendix

Table 5: The mask head interpolates. BraTS

60^{3}

, all 150 validation volumes, 30 dB, PSNR (dB). The hypernetwork was trained on

R\in\{4,8,16,32\}

; here it is asked for

6/12/24\times

, emitting both the FiLM modulation and the sampling pattern for a rate it never saw. Paired gain of the learned over the protocol mask, with volumes won.

method	NFE	$4\times$	$8\times$	$16\times$
CG-SENSE (no prior)	0	33.26 / 0.586	30.60 / 0.533	28.94 / 0.506
one-step MeanFlow prior, plug-and-play	4	36.32 / 0.652	32.64 / 0.573	30.13 / 0.528
patch-diffusion prior, plug-and-play	20	38.89 / 0.805	33.20 / 0.701	30.04 / 0.659
ours , one evaluation	1	40.91 / 0.863	37.12 / 0.835	34.33 / 0.854
ours , three evaluations	3	42.13 / 0.895	37.45 / 0.832	34.19 / 0.799
ours , one evaluation, learned mask	1	45.54 / 0.934	39.24 / 0.896	33.93 / 0.815

Appendix

Table 6: The cost-quality front on the full-k-space split, all 150 validation volumes (BraTS

60^{3}

, 30 dB, best

\lambda

per volume and rate, PSNR / SSIM). The same split and models as Tables 1 and 2 . Paired margins of our reconstructor over the 20-step patch-diffusion prior: one evaluation

+2.03\,[2.0,2.1]

+3.93\,[3.9,4.0]

+4.29\,[4.2,4.4]

dB at

4/8/16\times

, three evaluations

+3.31

+4.28

+4.17

dB, each on

150/150

volumes.

method	NFE	$4\times$	$8\times$	$16\times$
CG-SENSE (no prior)	0	37.94 / 0.924	30.09 / 0.721	26.64 / 0.578
patch-diffusion prior, plug-and-play	20	38.83 / 0.939	31.29 / 0.741	27.01 / 0.570
ours , one evaluation	1	39.71 / 0.943	33.50 / 0.851	30.09 / 0.764
ours , three evaluations	3	40.88 / 0.964	35.62 / 0.916	31.86 / 0.850
ours , one evaluation, learned mask	1	41.81 / 0.964	34.80 / 0.892	31.03 / 0.828

Appendix

Table 7: SKM-TEA knee, all 33 validation volumes (quarter resolution, real k-space and scanner coil maps, 30 dB, best

\lambda

per volume and rate, PSNR / SSIM, CG-20 for our models). Paired margins over the 20-step patch-diffusion prior: one evaluation

+0.82/+2.23/+3.07

dB, three evaluations

+1.94/+4.34/+4.89

dB at

4/8/16\times

, each on

33/33

volumes.

run	obj	$R$	$\lambda^{\star}$	NFE	PSNR (dB)	SSIM
a_adaptive_60_warm	meanflow	4	0.03	1	34.43 $\pm$ 1.25	0.830
a_adaptive_60_warm	meanflow	8	0.03	1	31.55 $\pm$ 1.12	0.793
a_adaptive_60_warm	meanflow	16	0.0001	1	31.06 $\pm$ 1.15	0.853
a_adaptive_60_warm	meanflow	32	0.0001	1	29.84 $\pm$ 1.16	0.822
a_fixed_60_std10x7_warm	meanflow	4	0.03	1	38.64 $\pm$ 1.40	0.870
a_fixed_60_std10x7_warm	meanflow	8	0.03	1	35.01 $\pm$ 1.32	0.839

Appendix

Table 8: Every evaluated run (best

\lambda

per run/rate/NFE; mean

\pm

std over volumes; repaired benchmark, k-space SNR 30 dB). Source: results/*.csv in the released repository.

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We present FlowMoDL, an unrolled neural network for highly accelerated 4D flow MRI reconstruction that directly optimizes for both anatomical magnitude and phase-derived velocity accuracy. Building on the MoDL framework, FlowMoDL alternates a learned (3+1)D spatiotemporal denoiser with conjugate-gradient data-consistency updates based on the SENSE forward model. A novel dual-pathway conditioning scheme adapts the denoiser features and data-consistency weighting, enabling a single model to handle varying acceleration factors (

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