3D Latent Rectified Flow (T1C-RFlow)

• The paper presents T1C-RFlow, which uses a pretrained 3D VAE and a deterministic rectified flow model to transport Gaussian noise to synthetic T1C representations.
• It achieves contrast-agent-free synthesis by conditioning on paired pre-contrast T1w and T2-FLAIR inputs, ensuring accurate reconstruction of contrast-enhancing regions.
• Empirical results on BraTS 2024 data demonstrate significant improvements in NMSE and SSIM metrics, along with a considerable speed advantage over latent DDPM and other baselines.

Searching arXiv for the target paper and closely related rectified-flow/latent 3D medical synthesis references. 3D Latent Rectified Flow (T1C-RFlow) is a 3D latent-space conditional rectified flow model for synthesizing post-contrast T1 MRI from pre-contrast T1w and T2-FLAIR. Its defining strategy is to compress full 3D MRI volumes into a compact latent space using a pretrained 3D VAE, learn a deterministic velocity field that transports Gaussian noise to the target T1C latent conditioned on the encoded inputs, and decode the resulting latent back into a full-resolution synthetic T1C volume (Eidex et al., 29 Sep 2025). The method was developed for brain tumor imaging using the BraTS 2024 glioma, meningioma, and metastases cohorts, and is positioned as a computationally efficient route toward contrast-agent-free MRI synthesis rather than a validated unrestricted replacement for acquired post-contrast imaging (Eidex et al., 29 Sep 2025).

1. Clinical task and problem formulation

T1C-RFlow addresses contrast-agent-free synthesis of T1-contrast-enhanced MRI (T1C) for brain tumor imaging. In the formulation reported for the method, the inputs are exactly pre-contrast T1-weighted (T1w) and T2-FLAIR, and the output target is T1-contrast enhanced MRI (T1C) (Eidex et al., 29 Sep 2025). This is an intramodal conditional synthesis problem in which paired, co-registered volumetric MRI is available during training, and T1w, T2-FLAIR, and T1C are assumed to be spatially aligned and preprocessed into a common space (Eidex et al., 29 Sep 2025).

The clinical motivation is tied to the role of gadolinium-based contrast agents in neuro-oncologic imaging. T1C is described as especially important because the enhancing tumor is defined by abnormal uptake visible on post-contrast T1-weighted imaging, while GBCAs carry safety concerns including risk of nephrogenic systemic fibrosis and concerns related to gadolinium retention (Eidex et al., 29 Sep 2025). Additional motivations include scan complexity, variability due to contrast administration, and access constraints in resource-limited settings (Eidex et al., 29 Sep 2025).

Within the broader literature, T1C-RFlow belongs to a class of 3D medical synthesis systems that replace slow latent DDPM sampling with ODE-based transport in latent space. A closely related methodological precedent is MAISI-v2, which likewise reuses a pretrained 3D VAE and replaces a DDPM-based latent diffusion model with a rectified flow model for high-resolution 3D medical image synthesis (Zhao et al., 7 Aug 2025). T1C-RFlow differs in task specification by targeting paired MRI-to-MRI synthesis for brain tumors rather than unconditional or mask-conditioned CT generation (Eidex et al., 29 Sep 2025, Zhao et al., 7 Aug 2025).

2. Latent representation and preprocessing pipeline

The method uses MAISI’s pretrained 3D VAE as a fixed latent compressor and decoder (Eidex et al., 29 Sep 2025). Each MRI sequence is represented as a full 3D volume of shape

$1 \times 256 \times 256 \times 192$

and is compressed into a latent tensor of shape

$4 \times 64 \times 64 \times 48.$

The encoder outputs $\mu(x)$ and $\sigma(x)$ in that latent space, and the VAE latent is sampled as

$$z = \mu(x) + \sigma(x)\epsilon, \quad \epsilon \sim \mathcal{N}(0,1). \tag{1}$$

This corresponds to 1/4 spatial resolution per axis and 64x fewer voxels than the original image grid (Eidex et al., 29 Sep 2025).

The preprocessing pipeline used for the reported experiments consists of DICOM to NIfTI conversion, skull stripping using HD-BET, affine coregistration of T1, T1C, T2, and T2-FLAIR to the Linear Symmetrical MNI Atlas, resampling to 1 mm isotropic, standardization to

$256 \times 256 \times 192,$

and intensity normalization to

$[-1,1].$

These preprocessing steps define the volumetric input space in which the pretrained VAE is applied (Eidex et al., 29 Sep 2025).

The paper motivates latent-space modeling primarily by efficiency. The VAE makes whole-volume 3D synthesis feasible, avoids patch-wise training and sliding-window inference for the generative model itself, and reduces memory demand while maintaining high reconstruction quality (Eidex et al., 29 Sep 2025). The reported VAE reconstruction metrics are:

• T1w: NMSE $0.63 \times 10^{-2}$, PSNR $35.3 \pm 2.0$ dB, SSIM $0.979 \pm 0.006$
• T2-FLAIR: NMSE $4 \times 64 \times 64 \times 48.$0, PSNR $4 \times 64 \times 64 \times 48.$1 dB, SSIM $4 \times 64 \times 64 \times 48.$2
• T1C: NMSE $4 \times 64 \times 64 \times 48.$3, PSNR $4 \times 64 \times 64 \times 48.$4 dB, SSIM $4 \times 64 \times 64 \times 48.$5

This suggests that the latent bottleneck preserves most of the information needed for downstream conditional synthesis (Eidex et al., 29 Sep 2025).

3. Conditioning design and rectified-flow formulation

Conditioning is performed entirely in latent space. If $4 \times 64 \times 64 \times 48.$6 and $4 \times 64 \times 64 \times 48.$7 denote the latent encodings of T1w and T2-FLAIR, the conditioning tensor is formed by channel-wise concatenation:

$4 \times 64 \times 64 \times 48.$8

Since each latent has shape $4 \times 64 \times 64 \times 48.$9, the condition tensor has shape

$\mu(x)$0

At training and inference, the rectified flow network receives the concatenation

$\mu(x)$1

which the paper explicitly states has shape

$\mu(x)$2

This is an early-fusion conditioning mechanism by channel concatenation rather than cross-attention or classifier-free guidance (Eidex et al., 29 Sep 2025).

The latent rectified-flow path is defined using a clean target latent $\mu(x)$3, Gaussian noise $\mu(x)$4, and a monotone schedule $\mu(x)$5 with $\mu(x)$6, $\mu(x)$7:

$\mu(x)$8

Differentiating this path yields the analytical target velocity field

$\mu(x)$9

The network learns a conditional velocity field $\sigma(x)$0 under the loss

$\sigma(x)$1

The paper writes the expectation in abbreviated form, but the surrounding description makes clear that training samples a target latent, a noise latent, and a timestep, then minimizes the $\sigma(x)$2 distance between predicted and analytical velocity (Eidex et al., 29 Sep 2025).

Generation is performed by integrating the learned ODE

$\sigma(x)$3

with the fixed-step deterministic update

$\sigma(x)$4

The default reported sampling length is $\sigma(x)$5 (Eidex et al., 29 Sep 2025).

This places T1C-RFlow squarely in the ODE-based latent transport family. A plausible implication is that its practical speed advantage arises from combining latent compression with a direct velocity-field regression objective, rather than from architectural simplification alone. That reading is consistent with MAISI-v2, which also attributes accelerated 3D synthesis to replacing latent DDPM denoising with rectified-flow transport (Zhao et al., 7 Aug 2025).

4. Network architecture and training configuration

The generative backbone is reported as a 3D diffusion U-Net trained under the rectified flow objective (Eidex et al., 29 Sep 2025). The stated architectural details are concise but explicit: the network has a symmetrical encoder and decoder, channel sizes

$\sigma(x)$6

and 2 residual blocks per layer (Eidex et al., 29 Sep 2025). Figure-level descriptions in the paper indicate a denoising U-Net with residual blocks, skip connections, and timestep embedding input (Eidex et al., 29 Sep 2025).

Several implementation details are not specified in the paper. It does not explicitly report the residual block design, normalization type, activation function, attention placement, exact timestep embedding formulation, downsampling and upsampling operators, or whether sinusoidal or learned time embeddings are used (Eidex et al., 29 Sep 2025). This incompleteness is relevant for reproduction because the method’s performance advantage is established empirically, but some architectural degrees of freedom remain undocumented.

Training uses AdamW with learning rate $\sigma(x)$7, $\sigma(x)$8, $\sigma(x)$9, weight decay $$z = \mu(x) + \sigma(x)\epsilon, \quad \epsilon \sim \mathcal{N}(0,1). \tag{1}$$0, batch size 4, and 100 epochs on a single NVIDIA A6000 ADA (48 GB) (Eidex et al., 29 Sep 2025). The rectified-flow training setup uses 1000 training timesteps and a logit-normal sampling distribution based on latent size $$z = \mu(x) + \sigma(x)\epsilon, \quad \epsilon \sim \mathcal{N}(0,1). \tag{1}$$1 with 3 spatial dimensions (Eidex et al., 29 Sep 2025). The paper does not provide the explicit logit-normal formula for this scheduler (Eidex et al., 29 Sep 2025).

The benchmark suite is deliberately controlled. All compared methods are trained in the same latent space, and all latent outputs are decoded by the same VAE decoder (Eidex et al., 29 Sep 2025). The baselines are:

• pix2pix
• latent DDPM
• DiT-3D

The DDPM baseline uses a standard diffusion formulation with 1000 denoising steps, while DiT-3D is adapted from a 3D shape-generation implementation to work on medical images and to use a rectified flow scheduler (Eidex et al., 29 Sep 2025). This means the comparison against DiT-3D is not purely a scheduler comparison; it also reflects the inductive bias difference between a dense volumetric U-Net and a tokenized transformer backbone (Eidex et al., 29 Sep 2025).

5. Empirical performance and efficiency

The study uses the BraTS 2024 challenge data across three tumor cohorts:

• Glioma (GLI): 1480 patients
• Meningioma (MEN): 1141 patients
• Metastases (MET): 1475 patients

for a total of 4096 cases, split into Training: 2860, Validation: 612, and Test: 614, while maintaining cohort proportions (Eidex et al., 29 Sep 2025). The test set contains GLI: 239, MEN: 162, and MET: 213 (Eidex et al., 29 Sep 2025).

Whole-brain evaluation is reported using NMSE, PSNR, NCC, and SSIM on decoded image-space volumes normalized in $$z = \mu(x) + \sigma(x)\epsilon, \quad \epsilon \sim \mathcal{N}(0,1). \tag{1}$$2, with SSIM constants

$$z = \mu(x) + \sigma(x)\epsilon, \quad \epsilon \sim \mathcal{N}(0,1). \tag{1}$$3

On the overall test set, T1C-RFlow achieved:

• NMSE: $$z = \mu(x) + \sigma(x)\epsilon, \quad \epsilon \sim \mathcal{N}(0,1). \tag{1}$$4
• PSNR: $$z = \mu(x) + \sigma(x)\epsilon, \quad \epsilon \sim \mathcal{N}(0,1). \tag{1}$$5 dB
• NCC: $$z = \mu(x) + \sigma(x)\epsilon, \quad \epsilon \sim \mathcal{N}(0,1). \tag{1}$$6
• SSIM: $$z = \mu(x) + \sigma(x)\epsilon, \quad \epsilon \sim \mathcal{N}(0,1). \tag{1}$$7

compared with:

Method	NMSE	PSNR	NCC	SSIM
T1C-RFlow	$$z = \mu(x) + \sigma(x)\epsilon, \quad \epsilon \sim \mathcal{N}(0,1). \tag{1}$$8	$$z = \mu(x) + \sigma(x)\epsilon, \quad \epsilon \sim \mathcal{N}(0,1). \tag{1}$$9	$256 \times 256 \times 192,$0	$256 \times 256 \times 192,$1
DDPM	$256 \times 256 \times 192,$2	$256 \times 256 \times 192,$3	$256 \times 256 \times 192,$4	$256 \times 256 \times 192,$5
pix2pix	$256 \times 256 \times 192,$6	$256 \times 256 \times 192,$7	$256 \times 256 \times 192,$8	$256 \times 256 \times 192,$9
DiT-3D	$[-1,1].$0	$[-1,1].$1	$[-1,1].$2	$[-1,1].$3

The paper states that average NMSE improved by 25% over the next-best method, DDPM, and that most improvements were statistically significant, with the noted exception of SSIM versus pix2pix in whole-brain results (Eidex et al., 29 Sep 2025).

By cohort, T1C-RFlow achieved the following headline values:

• GLI: NMSE $[-1,1].$4, SSIM $[-1,1].$5
• MEN: NMSE $[-1,1].$6, SSIM $[-1,1].$7
• MET: NMSE $[-1,1].$8, SSIM $[-1,1].$9

with the metastases cohort described as consistently harder for all methods, which the authors suggest may be due to lower quality T1C images in that dataset (Eidex et al., 29 Sep 2025).

For tumor-region evaluation, a subset of 545 patients with segmentation maps was used, defining the tumor region by a bounding box around the segmentation map with 5 voxels of padding (Eidex et al., 29 Sep 2025). In that region, T1C-RFlow also performed best overall, with:

• NMSE: $0.63 \times 10^{-2}$0
• PSNR: $0.63 \times 10^{-2}$1
• NCC: $0.63 \times 10^{-2}$2
• SSIM: $0.63 \times 10^{-2}$3

The paper specifically emphasizes stronger reconstruction of the contrast-enhancing tumor region and better preservation of fine anatomical detail relative to the baselines (Eidex et al., 29 Sep 2025).

Efficiency is one of the method’s most concrete advantages. On the A6000 ADA GPU, the reported times are:

• VAE encode: 1.2 s
• T1C-RFlow denoising: 6.9 s
• VAE decode: 1.6 s
• Total: 9.7 s/volume

This is compared with:

• DDPM (latent, 1000 steps): 37.7 s
• DDPM (patch-based image space): 4.3 hr
• DiT-3D: 11.9 s
• pix2pix latent prediction: 74.0 ms

The key interpretation in the paper is that T1C-RFlow is much faster than latent DDPM and dramatically faster than patch-based image-space DDPM, while producing higher image quality than the one-step pix2pix baseline (Eidex et al., 29 Sep 2025). This mirrors the broader acceleration pattern reported for rectified-flow-based medical synthesis in MAISI-v2, where replacing latent DDPM with rectified flow yielded substantially better speed-quality tradeoffs (Zhao et al., 7 Aug 2025).

6. Interpretive context, ablations, and limitations

The main ablation studies the contribution of the two conditioning modalities. Using both T1w and T2-FLAIR produced the best performance:

• T1w + T2-FLAIR: NMSE $0.63 \times 10^{-2}$4, SSIM $0.63 \times 10^{-2}$5
• T1w only: NMSE $0.63 \times 10^{-2}$6, SSIM $0.63 \times 10^{-2}$7
• T2-FLAIR only: NMSE $0.63 \times 10^{-2}$8, SSIM $0.63 \times 10^{-2}$9

with reported significance $35.3 \pm 2.0$0 for the multimodal improvement (Eidex et al., 29 Sep 2025). This supports the paper’s interpretation that T1w provides stronger direct structural and intensity correspondence to T1C, while FLAIR contributes complementary lesion information (Eidex et al., 29 Sep 2025).

The paper also offers an implicit architectural argument through benchmark comparison. Because all methods share the same latent space and decoder, the superiority of T1C-RFlow over latent DDPM suggests that the rectified-flow transport objective is advantageous in this setup, while the superiority over DiT-3D suggests that a volumetric U-Net may better preserve dense spatial structure than a flattened transformer tokenization scheme for this task (Eidex et al., 29 Sep 2025). This suggests that in medical volumetric synthesis, scheduler choice and architectural inductive bias interact rather than contributing independently.

Several limitations are explicitly acknowledged. The training data are limited to brain tumor cohorts from BraTS 2024, so performance on other neurologic diseases, institutions, scanners, and acquisition protocols remains unvalidated (Eidex et al., 29 Sep 2025). The model does not use segmentation masks or tumor priors during training, which the authors note may limit performance in large or highly heterogeneous tumors (Eidex et al., 29 Sep 2025). The method is also dependent on the latent space inherited from MAISI’s pretrained VAE, which was not designed specifically for T1C synthesis or tumor-aware conditioning (Eidex et al., 29 Sep 2025).

The qualitative discussion notes several observed reconstruction limitations: slight visual differences in contrast-enhancing regions, possible mismatches in overall brightness between T1C and synthetic T1C, more difficulty in low-quality ground-truth T1C cases, and lower performance on metastases and complex gliomas (Eidex et al., 29 Sep 2025). The paper also cautions that synthetic contrast images may look plausible while not perfectly reflecting actual pathology or enhancement, so the method is framed as a promising research direction rather than a clinically unrestricted substitute (Eidex et al., 29 Sep 2025).

A common misconception is that T1C-RFlow is simply a faster DDPM. The paper’s formulation is more specific: it trains a deterministic conditional velocity field in latent space and samples by fixed-step ODE integration, rather than by reverse diffusion denoising (Eidex et al., 29 Sep 2025). Another possible misconception is to view it as a generic 3D latent rectified-flow framework. More precisely, it is a task-specific whole-volume 3D synthetic contrast MRI system whose conditioning, preprocessing, and evaluation are tightly aligned to paired brain tumor MRI (Eidex et al., 29 Sep 2025).

In the wider rectified-flow literature, T1C-RFlow can be situated alongside other latent 3D transport models, but its domain-specificity matters. MAISI-v2 is a direct methodological reference for 3D latent rectified flow in medical imaging (Zhao et al., 7 Aug 2025), while CTFlow shows a related latent flow-matching strategy for whole-volume text-conditioned CT synthesis using a video-inspired autoregressive design (Wang et al., 18 Aug 2025). By contrast, T1C-RFlow remains a paired multimodal MRI synthesis model rather than a text-conditioned or mask-conditioned foundation model (Eidex et al., 29 Sep 2025, Zhao et al., 7 Aug 2025, Wang et al., 18 Aug 2025).

T1C-RFlow is therefore best understood as a specialized 3D latent rectified-flow system for synthetic post-contrast MRI generation: it compresses T1w, T2-FLAIR, and T1C into a compact volumetric latent space; conditions a 3D U-Net on T1w and FLAIR latents; learns a deterministic velocity field from Gaussian noise to T1C latent; and reconstructs a full synthetic T1C volume with practical whole-volume runtime (Eidex et al., 29 Sep 2025). Its significance lies in showing that high-quality whole-volume 3D synthetic contrast MRI can be made computationally feasible while outperforming matched latent-space DDPM, pix2pix, and DiT-3D baselines on BraTS 2024 brain tumor cohorts (Eidex et al., 29 Sep 2025).