TADM-3D: 3D Temporally-Aware Diffusion Model

• The paper introduces a novel 3D diffusion framework that predicts MRI residuals based on time gaps and patient metadata.
• It employs back-in-time regularisation and a frozen Brain-Age Estimator to enforce temporal consistency in neuroanatomical forecasting.
• Evaluations on OASIS-3 and NACC show significant improvements in regional error metrics for predicting neurodegenerative progression.

Searching arXiv for the primary TADM-3D paper and closely related temporally aware 3D/dynamic diffusion work. TADM-3D, short for Temporally-Aware Diffusion Model for Brain Progression Modelling with Bidirectional Temporal Regularisation, is a 3D diffusion-based longitudinal MRI forecasting model that predicts residual brain changes rather than full images, conditions generation on time gap and patient metadata, and enforces temporal realism through a frozen Brain-Age Estimator (BAE) and Back-In-Time Regularisation (BITR) (Litrico et al., 3 Sep 2025). Its primary target is subject-specific modelling of neuroanatomical progression in longitudinal brain MRI, especially in neurodegenerative disease settings such as Alzheimer’s disease, where forecasting future pathology is clinically distinct from image interpolation or generic age-conditioned synthesis.

1. Clinical task and methodological lineage

TADM-3D is formulated on longitudinal MRI pairs from the same subject, with a baseline scan $I_{T_a}$ and a follow-up scan $I_{T_b}$. The task is to predict the future scan from the earlier one, conditioned on the elapsed time and patient information. The method is explicitly positioned against two limitations: approaches that do not explicitly model the relationship between structure change and time gap, and interpolation methods that generate intermediate images between two known scans rather than future pathological progression (Litrico et al., 3 Sep 2025).

A central premise is that brain changes are strongly time-dependent but not fully determined by absolute age alone. The same time gap can occur at very different ages, and age-balanced data are rarely available. TADM-3D therefore treats temporal awareness as the ability to model change over an interval, rather than memorizing age-specific appearance. This is why the framework conditions on age difference instead of only on target age.

The model extends the earlier TADM framework, which introduced a Temporally-Aware Diffusion Model for neurodegenerative progression on brain MRI and was presented primarily as a 2D method, while explicitly noting that it can be extended to 3D (Litrico et al., 2024). The 3D version retains the residual-diffusion formulation and BAE-guided temporal supervision of the earlier method, but addresses the specific limitation that many existing approaches rely on 2D slice-wise generation and therefore disregard full 3D anatomical context, which the later paper identifies as essential for accurate longitudinal prediction (Litrico et al., 3 Sep 2025).

2. Residual diffusion formulation on volumetric MRI

The core generative idea in TADM-3D is to predict a residual image rather than to synthesize a full follow-up MRI directly. The residual is defined as

$I_{\Delta_{a,b}} = I_{T_b} - I_{T_a},$

where $\Delta_{a,b} = T_b - T_a$ is the time interval between the two scans. The predicted follow-up is reconstructed as

$$\widehat{I}_{T_b} = I_{T_a} + \widehat{I}_{\Delta_{a,b}}.$$

This residual formulation is presented as simplifying the generation task because the network only needs to model temporal changes rather than the entire image distribution. The paper argues that this reduces artefacts and helps the diffusion model focus on disease-related progression (Litrico et al., 3 Sep 2025).

The diffusion backbone is a Denoising Diffusion Probabilistic Model (DDPM) operating on full 3D MRI volumes. The forward process progressively corrupts the input with Gaussian noise, and the reverse process learns Gaussian denoising transitions. In TADM-3D, the object of diffusion is the residual volume, not the full follow-up scan. Architecturally, the backbone is a U-Net adapted to 3D volumes, and the paper identifies this volumetric design as a main contribution relative to the earlier slice-based version. The model also includes an encoder $\Phi$, described as 3D U-Net-based and trained end-to-end with the diffusion model, to extract the baseline representation used for conditioning.

The significance of the volumetric formulation is anatomical coherence. A 3D model can capture inter-slice dependencies, 3D shape consistency, and spatially coherent pathology progression across all three axes. This is especially relevant in Alzheimer’s disease, where structural changes are distributed across regions rather than confined to independent slices.

3. Conditioning strategy and Brain-Age Estimator guidance

TADM-3D conditions generation on three sources of information:

1. the baseline scan representation $z_a = \Phi(I_{T_a})$,
2. the age difference $\Delta_{a,b}$,
3. patient-specific metadata, including baseline age $A$ and cognitive status $D$.

The DDPM is invoked in the form

$I_{T_b}$0

where $I_{T_b}$1 denotes the noisy residual at diffusion step $I_{T_b}$2. The age gap is encoded using positional encoding before being integrated into the model (Litrico et al., 3 Sep 2025).

The emphasis on age-gap conditioning rather than direct age conditioning is one of the method’s defining claims. The paper argues that the same interval, such as 5 years, should correspond to similar kinds of structural change whether it occurs from age 60 to 65 or 80 to 85. Conditioning on age gap therefore better aligns generation with longitudinal dynamics and reduces the need for perfectly age-balanced training data. Baseline age and cognitive status provide additional context: baseline age grounds the trajectory’s starting point, and cognitive status helps distinguish healthy aging from disease-related progression.

A distinctive component is the use of a frozen Brain-Age Estimator. Given baseline $I_{T_b}$3 and generated follow-up $I_{T_b}$4, the estimated age difference is

$I_{T_b}$5

where $I_{T_b}$6 is the encoder and $I_{T_b}$7 is the BAE. The corresponding auxiliary loss is

$I_{T_b}$8

This term is combined with the diffusion-model loss:

$I_{T_b}$9

The paper characterizes the BAE as an auxiliary supervision signal that penalizes temporally implausible generations. A plausible implication is that the BAE functions as a temporal consistency critic: it does not merely ask whether a generated MRI looks anatomically plausible, but whether it looks as though it lies at the correct temporal distance from baseline.

4. Back-In-Time Regularisation and bidirectional training

The second major novelty in TADM-3D is Back-In-Time Regularisation (BITR). Under standard forward prediction, the model learns

$I_{\Delta_{a,b}} = I_{T_b} - I_{T_a},$0

with residual target $I_{\Delta_{a,b}} = I_{T_b} - I_{T_a},$1. Under BITR, the model is also trained to predict in the reverse direction,

$I_{\Delta_{a,b}} = I_{T_b} - I_{T_a},$2

During training, with probability $I_{\Delta_{a,b}} = I_{T_b} - I_{T_a},$3, the roles of baseline and follow-up are swapped. The paper describes this as swapping the scans and flipping the sign of the temporal variables: flip $I_{\Delta_{a,b}} = I_{T_b} - I_{T_a},$4, flip $I_{\Delta_{a,b}} = I_{T_b} - I_{T_a},$5, and flip $I_{\Delta_{a,b}} = I_{T_b} - I_{T_a},$6 (Litrico et al., 3 Sep 2025).

The stated motivation is not clinical use of backward prediction. The authors explicitly note that predicting past scans has limited clinical applications. Instead, BITR is used as a regularizer: a temporally aware progression model should learn the inverse relationship between two time points as well as the forward relationship. The claimed effect is improved forward prediction and better temporal consistency.

The training procedure is summarized in the paper as a nine-step pipeline:

1. sample a longitudinal MRI pair $I_{\Delta_{a,b}} = I_{T_b} - I_{T_a},$7,
2. compute residual $I_{\Delta_{a,b}} = I_{T_b} - I_{T_a},$8,
3. encode baseline to obtain $I_{\Delta_{a,b}} = I_{T_b} - I_{T_a},$9,
4. optionally swap the pair with probability $\Delta_{a,b} = T_b - T_a$0 for BITR,
5. add noise to the residual and predict it with the DDPM,
6. reconstruct the predicted follow-up,
7. encode the prediction and the baseline using the frozen BAE,
8. compute the diffusion loss and the BAE loss,
9. optimize the total objective $\Delta_{a,b} = T_b - T_a$1.

In this formulation, temporal awareness is enforced twice: once through explicit conditioning on $\Delta_{a,b} = T_b - T_a$2, and again through a bidirectional constraint on how progression is represented during training.

5. Data, evaluation protocol, and reported performance

TADM-3D is trained and evaluated on OASIS-3 and externally validated on NACC. MRI volumes are linearly registered to MNI152 and skull stripped using FSL. Optimization uses AdamW, learning rate $\Delta_{a,b} = T_b - T_a$3, weight decay $\Delta_{a,b} = T_b - T_a$4, batch size 16, and a cosine learning-rate schedule (Litrico et al., 3 Sep 2025).

Dataset	Composition	Role
OASIS-3	2,535 T1-weighted scans; 634 subjects; age range 42–95; CN, MCI, AD	Training, validation, test
NACC	2,257 T1-weighted MRIs; 962 subjects; maximum follow-up interval of 13 years; average follow-up interval of 3.8 years	External evaluation

For OASIS-3, the split is 70% training, 10% validation, and 20% test. The paper states that OASIS-3 spans roughly 15 years longitudinally. NACC is used only for evaluation to test generalization; approximately 75% CN at last visit, with the remainder MCI or AD.

Evaluation covers both image fidelity and anatomical progression. The image-based metrics are MSE and SSIM. Region-volume fidelity is measured using SynthSeg 2.0, segmenting the hippocampus, amygdala, lateral ventricles, thalamus, and CSF, and reporting Mean Absolute Error (MAE) of predicted region volumes as a percentage of total brain volume.

On the internal OASIS-3 test set, the paper reports:

Metric	Value
MSE	$\Delta_{a,b} = T_b - T_a$5
SSIM	$\Delta_{a,b} = T_b - T_a$6
Hippocampus MAE	$\Delta_{a,b} = T_b - T_a$7
Amygdala MAE	$\Delta_{a,b} = T_b - T_a$8
Lateral ventricle MAE	$\Delta_{a,b} = T_b - T_a$9
Thalamus MAE	$$\widehat{I}_{T_b} = I_{T_a} + \widehat{I}_{\Delta_{a,b}}.$$0
CSF MAE	$$\widehat{I}_{T_b} = I_{T_a} + \widehat{I}_{\Delta_{a,b}}.$$1

The paper further summarizes these gains as roughly 40% reduction in hippocampal error, 12% reduction in amygdala error, 13% reduction in ventricle error, 30% reduction in thalamus error, and 27% reduction in CSF error relative to prior methods.

On the external NACC test set, the reported aggregate performance is MSE $$\widehat{I}_{T_b} = I_{T_a} + \widehat{I}_{\Delta_{a,b}}.$$2 and SSIM $$\widehat{I}_{T_b} = I_{T_a} + \widehat{I}_{\Delta_{a,b}}.$$3. The paper states that TADM-3D achieves the best performance on MSE and 4 of 5 regional metrics, while BrLP slightly outperforms it on SSIM and lateral ventricle MAE in the external setting. The baseline set includes DaniNet, CounterSynth, BrLP, and references the earlier sequence-aware diffusion line such as SADM.

6. Ablations, limitations, and relation to broader temporally-aware 3D diffusion research

The ablation studies isolate the contribution of the main components. Removing patient metadata causes only a slight degradation, which the paper interprets as evidence that metadata helps but is not the dominant factor. Removing age-gap conditioning causes a much larger degradation, confirming that explicit temporal conditioning is central to the model. Removing BAE worsens performance, and removing BITR also produces a significant drop. The paper further reports that the 2D variant, TADM-2.5D, performs substantially worse than native 3D TADM-3D, supporting the claim that full volumetric context matters for longitudinal brain modelling (Litrico et al., 3 Sep 2025).

A further experiment deliberately sets cognitive status incorrectly at inference time, and the output errors increase, especially in AD-sensitive regions like the hippocampus. This suggests that the model is responsive to clinically meaningful conditioning rather than merely reproducing a healthy-aging trajectory.

Several misconceptions are explicitly addressed by the method’s framing. First, TADM-3D is not an interpolation model. The paper contrasts it with interpolation approaches such as DDM and DiffuseMorph, arguing that interpolation is useful for smooth transitions but not for predicting future disease progression. Second, TADM-3D does not require multiple input scans at inference, unlike SADM. Third, although the model is bidirectional during training, the paper emphasizes that back-in-time prediction is not clinically useful by itself; its role is regularization.

The limitations are equally explicit. The authors state that the model struggles with long-term forecasting over very large time gaps, where temporal consistency can degrade. They also note that the current formulation does not incorporate additional potentially important clinical variables such as genetics, comorbidities, and medications. A plausible implication is that the current temporal signal is strong but still incomplete with respect to heterogeneous disease drivers.

In the broader literature, TADM-3D sits within a wider family of temporally-aware diffusion approaches in 3D or 4D settings, although those methods target different objects of generation. The earlier TADM paper established the residual-diffusion and age-gap-conditioning paradigm in a 2D slice-based MRI setting and reported an average 24% reduction in region size error and a 4% improvement in similarity metrics on OASIS-3 (Litrico et al., 2024). Outside brain MRI, Diffusion$$\widehat{I}_{T_b} = I_{T_a} + \widehat{I}_{\Delta_{a,b}}.$$4 generates dynamic 3D content by composing scores from pretrained video diffusion and multi-view diffusion models into dense multi-view multi-frame image matrices for 4D reconstruction (Yang et al., 2024). GeoTDM extends diffusion from static 3D geometries to full 3D geometric trajectories over time, combining SE(3)-equivariant spatial graph convolution with temporal self-attention (Han et al., 2024). VideoTex uses a temporally-aware video diffusion model, geometry-aware conditions, and UV-space refinement to produce temporally stable 3D texture synthesis on meshes (Kang et al., 26 Jun 2025). These works do not solve the same clinical problem as TADM-3D, but together they show that “temporally-aware diffusion” in three-dimensional settings can refer to volumetric medical forecasting, 4D reconstruction, geometric trajectory generation, or texture synthesis, depending on what the model treats as the primary dynamical object.