Stochastic Finite-Transition Learning and Exploration for Accelerated MRI Reconstruction

Muhammad Usama Mirza; Esin Öztürk Işık; Tolga Çukur

eess.IVOct 9, 2026

Stochastic Finite-Transition Learning and Exploration for Accelerated MRI Reconstruction

Authors: Muhammad Usama Mirza, Esin Öztürk Işık, Tolga Çukur

Organizations: Dept. of Electrical-Electronics Engineering and National Magnetic Resonance Research Center (UMRAM), Bilkent University, Ankara, Turkey, 06800 · Institute of Biomedical Engineering, Bogazici University, Istanbul, Turkey, 34684

Abstract

Generative MRI reconstruction maps an initial source distribution to the target image distribution along a learned recovery trajectory. Common generative methods, such as diffusion and flow, typically learn fine-grained local dynamics whose integration defines this global mapping, hence requiring many network evaluations at inference. Existing few-step sampling approaches can lower computational burden by approximating large transformations from local dynamics, albeit at the expense of reconstruction fidelity. FLEX-MRI instead partitions recovery into a small number of finite intervals between retained states defined by progressive changes in k-space support, and directly learns the reconstruction change across each interval. Because such finite transitions can admit multiple plausible outcomes, FLEX-MRI combines support-relaxed finite-transition learning with stochastic exploration. During training, randomized k-space sampling masks define finite-transition targets with varying support, while the prediction loss remains unrestricted by each individual mask. At inference, FLEX-MRI perturbs a random subset of currently estimated k-space coefficients, allowing the learned predictor to stochastically explore alternative transition paths. Each predicted state is then reconciled with the acquired measurements through data consistency. We theoretically show that this stochastic exploration induces nonzero transition-level variation through the learned recovery map and data consistency without requiring an auxiliary generative sampler. Experiments on multi-coil MRI datasets show that FLEX-MRI outperforms competing methods while maintaining computational efficiency comparable to few-step baselines.

Figures & tables

Symbol	Definition
$\mathbf{x}_{t_{j}}(\boldsymbol{\rho})$	Forward-process state at retained index $t_{j}$ .
$\hat{\mathbf{x}}_{t_{j}}$	Current reconstruction state at $t_{j}$ .
$\tilde{\mathbf{x}}_{t_{j}}^{(z)}$	Perturbed current state obtained by additional stochastic undersampling across k-space.
$\boldsymbol{\Delta}_{t_{j-1}\leftarrow t_{j}}$	Finite recovery increment from retained state $t_{j}$ to $t_{j-1}$ .
$\mathbf{d}_{t_{j-1}\leftarrow t_{j}}$	Mean displacement of the retained finite transition.
$\mathbf{r}_{t_{j-1}\leftarrow t_{j}}$	Residual variation of the retained finite transition.

TABLE I: Key notation for FLEX-MRI.

Fig. 1: Comparison of few-step recovery in (a) flow-based modeling, (b) transition matching, and (c) FLEX-MRI. Flow maps a fixed current state to a single next state through a learned velocity field, whereas transition matching models alternative outcomes using an auxiliary generative sampler with multiple inner steps per retained transition. FLEX-MRI instead perturbs the current state through random k-space undersampling and maps the resulting perturbed states with the same finite-transition predictor, enabling stochastic transition-level exploration without an auxiliary sampler or inner sampling loop.

Fig. 2: Finite-transition view of few-step recovery in FLEX-MRI. (a) Fine-step recovery traverses many small transitions with narrow conditional distributions. (b) Few-step recovery retains instead $J$ $\ll$ $T$ transitions with broader conditional distributions. (c) Marginalizing the omitted states yields a finite-transition increment comprising a mean displacement $\mathbf{d}$ and residual variation $\mathbf{r}$ , whereas a deterministic transition captures only the mean. (d) FLEX-MRI realizes the residual variation through random k-space perturbation, a shared predictor $\mu_{\theta}(\cdot,t_{j-1})$ , and data consistency. Multiple mask realizations illustrate the distribution of possible next states; one realization is used per transition at inference.

Fig. 3: Representative reconstructions on fastMRI for a FLAIR-weighted cross-section at $R=8$ , shown alongside the fully-sampled reference. A zoomed region of interest is inset in each reconstruction, and the corresponding error map with respect to the reference is displayed beneath.

	$R=4$		$R=6$		$R=8$
	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM
LORAKS	35.2 $\pm$ 2.3	92.0 $\pm$ 4.8	33.5 $\pm$ 2.2	90.5 $\pm$ 5.2	32.3 $\pm$ 2.2	89.5 $\pm$ 5.4
rGAN	35.9 $\pm$ 2.8	93.1 $\pm$ 4.7	33.9 $\pm$ 2.6	90.7 $\pm$ 5.5	32.9 $\pm$ 2.8	90.1 $\pm$ 5.9
DDPM	36.1 $\pm$ 2.2	93.7 $\pm$ 4.0	34.8 $\pm$ 2.3	92.2 $\pm$ 5.2	34.0 $\pm$ 2.2	91.1 $\pm$ 4.9
DiffRecon	35.7 $\pm$ 2.3	93.6 $\pm$ 4.5	34.5 $\pm$ 2.2	92.1 $\pm$ 5.1	33.7 $\pm$ 2.2	91.0 $\pm$ 5.5
CDiffMR	31.4 $\pm$ 2.7	78.5 $\pm$ 8.1	31.2 $\pm$ 2.4	79.1 $\pm$ 7.2	31.2 $\pm$ 2.3	80.5 $\pm$ 7.4

TABLE II: Reconstruction performance on fastMRI at R = 4-8. PSNR (dB) and SSIM (%) are listed as mean

\pm

std. across the test set. Boldface denotes the highest performing method.

Fig. 4: Representative reconstructions on M4Raw for a T 1 -weighted cross-section at $R=4$ , shown alongside the fully-sampled reference. A zoomed region of interest is inset in each reconstruction, and the corresponding error map with respect to the reference is displayed beneath.

	$R=4$		$R=6$		$R=8$
	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM
LORAKS	22.4 $\pm$ 1.6	76.3 $\pm$ 2.7	22.2 $\pm$ 1.6	74.2 $\pm$ 2.0	22.0 $\pm$ 1.6	72.9 $\pm$ 3.3
rGAN	22.5 $\pm$ 1.6	68.1 $\pm$ 2.5	22.4 $\pm$ 1.6	67.1 $\pm$ 2.7	22.3 $\pm$ 1.5	66.5 $\pm$ 2.7
DDPM	22.1 $\pm$ 1.2	41.2 $\pm$ 4.7	21.7 $\pm$ 1.1	38.5 $\pm$ 4.6	21.5 $\pm$ 1.1	36.9 $\pm$ 4.5
DiffRecon	22.9 $\pm$ 1.3	46.1 $\pm$ 5.0	22.7 $\pm$ 1.3	43.8 $\pm$ 4.8	22.5 $\pm$ 1.3	42.4 $\pm$ 4.7
CDiffMR	16.7 $\pm$ 1.2	34.6 $\pm$ 2.1	16.7 $\pm$ 1.2	34.5 $\pm$ 2.4	16.5 $\pm$ 1.1	34.0 $\pm$ 2.2

TABLE III: Reconstruction performance on M4Raw at R = 4-8.

	$R=4$		$R=6$		$R=8$
	PSNR	SSIM	PSNR	SSIM	PSNR	SSIM
LORAKS	35.2 $\pm$ 2.3	92.0 $\pm$ 4.8	33.5 $\pm$ 2.2	90.5 $\pm$ 5.2	32.3 $\pm$ 2.2	89.5 $\pm$ 5.4
rGAN	33.5 $\pm$ 2.1	90.5 $\pm$ 2.9	31.6 $\pm$ 2.2	87.8 $\pm$ 3.5	30.4 $\pm$ 2.3	85.9 $\pm$ 3.9
DDPM	35.0 $\pm$ 2.3	89.6 $\pm$ 4.9	33.1 $\pm$ 2.2	86.0 $\pm$ 5.8	31.9 $\pm$ 2.2	83.3 $\pm$ 6.2
DiffRecon	35.5 $\pm$ 2.0	93.1 $\pm$ 3.4	33.3 $\pm$ 2.1	90.9 $\pm$ 4.0	31.9 $\pm$ 2.1	89.3 $\pm$ 4.3
CDiffMR	35.0 $\pm$ 1.7	91.5 $\pm$ 3.3	33.0 $\pm$ 1.6	87.6 $\pm$ 3.9	31.4 $\pm$ 1.5	83.9 $\pm$ 4.3

TABLE IV: Cross-dataset generalization at

R=4

–

8

. Models were trained on M4Raw and tested on fastMRI.

	LORAKS	rGAN	DDPM	DiffRec.	CDiffMR	FDB	DTM	FLOWER	UPMRI	FLEX-MRI
Time (s)	0.180	0.0056	37.12	36.26	34.03	59.09	0.437	0.477	0.318	0.349
Memory (GB)	0.05	0.13	1.72	1.71	2.23	3.19	1.05	1.05	1.05	1.05

TABLE V: Inference time (s) and memory use (GB) for a single cross-section on an Nvidia RTX 4090.

Inference mode	Transition support	Training input	PSNR	SSIM
Stochastic	Relaxed	Nominal	35.8 $\pm$ 2.2	92.7 $\pm$ 5.0
	Relaxed	Perturbed	35.4 $\pm$ 2.2	92.2 $\pm$ 4.9
	Restricted	Nominal	35.0 $\pm$ 2.1	91.5 $\pm$ 5.1
	Restricted	Perturbed	34.9 $\pm$ 2.1	91.6 $\pm$ 5.1
Deterministic	Relaxed	Nominal	34.9 $\pm$ 2.3	91.1 $\pm$ 5.2
	Relaxed	Perturbed	34.5 $\pm$ 2.2	91.0 $\pm$ 5.0

TABLE VI: Ablation of the inference mode, transition support, and training input. PSNR (dB) and SSIM (%) are reported on the fastMRI test set at

R=8

Fig. 5: Effect of the number of retained transitions $J$ on reconstruction quality on fastMRI at $R=8$ . Mean PSNR (dB, left axis) and SSIM (%, right axis) are plotted for $J$ ranging from 2 to 1000 on a logarithmic scale. The dotted line marks the adopted $J=10$ .

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