Integrating Anatomical Priors into a Causal Diffusion Model

Abstract

3D brain MRI studies often examine subtle morphometric differences between cohorts that are hard to detect visually. Given the high cost of MRI acquisition, these studies could greatly benefit from image syntheses, particularly counterfactual image generation, as has been the case for applications in computer vision. However, counterfactual models struggle to produce anatomically plausible MRIs due to a lack of explicit inductive biases to preserve fine-grained anatomical details. This shortcoming arises from the training of models that optimize overall image appearance (e.g., via cross-entropy) rather than preserving subtle, yet medically relevant, local variations across subjects. To preserve subtle variations, we propose to explicitly integrate anatomical constraints at the voxel level as priors into a generative diffusion framework. Termed Probabilistic Causal Graph Model (PCGM), the approach captures anatomical constraints via a probabilistic graph module and translates those constraints into spatial binary masks of regions where subtle variations occur. The masks (encoded by a 3D ControlNet) constrain a novel counterfactual denoising UNet, whose encodings are then transferred into high-quality brain MRIs via our 3D diffusion decoder. Extensive experiments across multiple datasets demonstrate that PCGM generates structural brain MRIs of higher quality than several baseline approaches. Furthermore, we show, for the first time, that brain measurements extracted from counterfactuals (generated by PCGM) replicate the subtle effects of a disease on cortical brain regions previously reported in the neuroscience literature. This achievement is an important milestone in the use of synthetic MRIs in studies investigating subtle morphological differences. The codes are available at https://github.com/AndyCA111/PCGM.

I. Introduction

THE generation of high-fidelity structural brain MRIs is increasingly important in medical imaging research and clinical practice, as structural brain MRIs are indispensable for investigating neurodevelopment [1], monitoring disease progression [2], and developing AI-assisted diagnostic tools [3]. However, the acquisition of 3D MRI scans is limited by factors such as scanner availability, lengthy scan times, and high costs, resulting in relatively small and fragmented datasets [4], [5]. These brain MRI studies could greatly benefit from synthetically generated MRIs as high-quality synthetic data that can augment limited datasets and support AI-driven diagnosis and research [6]–[10].

While progress in 2D image generation, especially based on diffusion models [11], has been substantial [12]–[15], extending these models to generate anatomically plausible 3D MRIs remains challenging [16], [17]. In addition to having to account for the high voxel dimensionality of MRIs (>5M voxels) coupled with confining training to relatively small datasets (< 100K), existing models prioritize reconstruction of global appearances (by optimizing cross-entropy) rather than focusing on preserving fine-grained morphology on a local level that is important for studying many neuropsychiatric conditions [16]. For instance, mild cognitive impairment [18], human immunodeficiency virus (HIV) [19], and alcohol use disorder (AUD) [20] are associated with subtle morphological changes in several cortical regions that are not visible to the naked eye. These subtle changes are not well captured by state-of-the-art (SOTA) models [21], highlighting the need for models that are tailored to the specific needs of brain MRI studies.

This need becomes even more critical in the context of counterfactual generation, which aims to address the fundamental question of how a person’s brain would change under a given condition (such as transforming the MRI of a healthy control into that of the same person diagnosed with AUD) [22]. Learning to capture these intra-subject changes frequently requires training on longitudinal data, which are generally of an even smaller sample size than the cross-sectional data typically used for training unconditional generative models. One possible solution is to train models on MRIs from multiple datasets [16], [23]. However, the resulting sample size would still be less than 1K for most diseases, i.e., too small to robustly train data-driven methods. An alternative to data pooling could be causal generative models [21], [24]–[26], which first extract key brain measurements from the MRIs and then model their dependencies with respect to metadata using a causal graph. However, these methods so far have only been designed to capture coarse, visible effects (e.g., ventricular enlargement in Alzheimer’s disease) [27]. To generate counterfactual structural MRIs that account for subtle changes in the brain, we propose a diffusion-based counterfactual model that explicitly integrates anatomical knowledge on a voxel-level into the generation process.

Called the Probabilistic Causal Graph Model (PCGM; see Fig. 1), the approach first learns to encode interactions among subject-level factors (e.g., sex, age) and brain regional measurements using a probabilistic graph module (PGM). The ROI measurements (e.g., volumes of cortical regions) generated by a PGM are then turned into binary masks. The resulting ROI masks are encoded by a 3D ControlNet (our 3D extension of [28]), whose outputs, together with the altered metadata, provide conditioning for our Counterfactual Denoising UNet [29]. Instead of directly decoding the latent features produced by that UNet with a standard VAE decoder (as done by most Latent Diffusion Models (LDM) architectures [12], [30]), we pretrain a dedicated 3D diffusion decoder to reconstruct the final 3D brain MRI, which ensures that the output image is high quality and anatomically plausible.

Fig. 1. Generating Counterfactuals via the Probabilistic Causal Graph Model (PCGM).

1) For each brain region of interest (ROI) $\mathit{k}$, the Probabilistic Graph Module (PGM) learns the structural equations linking the parent variables ${\mathbf{p}\mathbf{a}}_{\mathit{k}}$ (e.g., the metadata age, sex, diagnosis (Dx)) to the ROI volume ${\mathit{v}}_{\mathit{k}}$ derived from the automatic segmentation of the real MRI. During counterfactual inference, the model infers the subject-specific exogenous noise ${\mathit{u}}_{\mathit{k}}$ from ${\mathit{v}}_{\mathit{k}}$ and ${\mathbf{p}\mathbf{a}}_{\mathit{k}}$ (Abduction). Next, the parent variables are set to their counterfactual values ${\widehat{\mathbf{p}\mathbf{a}}}_{\mathit{k}}$ (Action). The final step of inference computes the counterfactual ${\widehat{\mathit{v}}}_{\mathit{k}}$ based on ${\widehat{\mathbf{p}\mathbf{a}}}_{\mathit{k}}$ and ${\mathit{u}}_{\mathit{k}}$ (Prediction). 2) Based on the probabilities of the ROI and neighboring regions (e.g. CSF) along the boundary, the Counterfactual Mask Generator (CMG) modifies the original ROI mask $\mathit{M}$ so that its volume matches ${\widehat{\mathit{v}}}_{\mathit{k}}$, yielding a counterfactual mask $\widehat{\mathit{M}}$ that is anatomically plausible. 3) Conditioned on the counterfactual metadata and original MRI, the Mask Guided Diffusion (MGD) generates the counterfactual MRI by first encoding $\widehat{\mathit{M}}$ via 3D ControlNet and then using the output to confine the generative process of the Counterfactual Diffusion Module (CDM).

We first train our model on 3954 T1w MRIs of controls from ADNI [31] and NCANDA [32]. Evaluation based on a matched, hold-out set of 400 subjects from both data sets and 41 individuals with HIV [33] reveal that our model consistently produces MRIs with higher image quality and stronger anatomical plausibility than all baseline models. On a separate in-house dataset consisting of 199 controls and 222 participants diagnosed with AUD, only the counterfactual MRIs generated by PCGM yield cortical brain measurements that replicate the subtle effects of AUD on the brain published on the same data set by [20]. To our knowledge, PCGM is the first approach to achieve this significant milestone in generating MRIs useful for neuroscience studies.

In summary, our contributions are as follows:

1. We present a novel diffusion-based generative model (calledPCGM) that is able to create anatomically plausible, fine-grained counterfactuals of 3D MRIs.

2. Subtle disease effects are modeled by a causal graph constructed from established neuroscience findings [20] and then translated into counterfactual spatial masks, which guide the diffusion process and thereby constrain structural changes to specific brain regions while preserving global anatomical consistency.

3. For computational efficiency and to ensure anatomical plausibility, we introduce the first Causal Encoder tailored for 3D brain MRI and pair it with the first 3D CNN-based diffusion decoder to recover high-fidelity brain MRIs.

4. Our counterfactuals are the first to replicate published group-level findings regarding brain structural differences between health controls and disease cohorts that are generally too subtle to identify in individuals.

II. Related Works

A. MRI Synthesis

Traditional methods for MRI synthesis have relied on deforming real MRIs rather than directly generating MRI intensities [34]. These methods map real MRIs to a template, modify the deformation field or the template itself, and then map the results back to create a synthesized MRI [34]–[37]. More recently, deep learning has enabled direct intensity-based synthesis by encoding the intensity distributions of MRIs [38]. Approaches within this framework include variational autoencoders (VAEs) [39] and generative adversarial networks (GANs) [4], with GANs achieving notable success.

The two types of GAN-based approaches are image-to-image transformations and unconditional generation. Image-to-image transformations create new MRIs from existing ones and have been applied to cross-modality synthesis [40], counterfactual generation [41], and tumor simulation [42]. However, these models often require large, well-curated datasets, and their ability to increase data diversity is limited [43], [44]. To produce entirely new samples, unconditional generation encodes the underlying distribution of the dataset and then transforms random noise into synthetic images [45], [46]. While recent advances by methods (such as α-WGAN [47] and 4D-DANI-Net [48]) have improved the quality of the generated MRIs, GANs still face challenges with model collapse, high memory requirements, and unstable training, limiting their ability to generate realistic, high-quality 3D MRIs [49].

An alternative approach is the denoising diffusion probabilistic model (DDPM) [11], [50], which synthesizes images by gradually transforming a Gaussian distribution into a target distribution through a Markov chain process. To improve computational efficiency, recent models rely on non-Markovian processes so that they can be used for medical image analysis, including anomaly detection [51], segmentation [52], and MRI acceleration [38]. Extending DDPMs to 3D MRI synthesis typically involves adapting 2D operations to 3D [53], which can still be computationally prohibitive and may not reach the same quality as GAN-based MRI synthesis [54]. Additionally, extending diffusion models to longitudinal MRI synthesis remains challenging due to high computational demands [55].

MedGen3D [56] addresses these limitations by synthesizing MRIs slice-by-slice, conditioning each slice on prior ones to reduce resource requirements. However, this approach can result in artifacts, such as inconsistent intensities between slices [54]. Recently, BrainSynth [49] was proposed to generate high-resolution, subject-agnostic 3D brain volumes, achieving anatomically accurate structures compared to previous methods. Nevertheless, a human expert was able to reliably distinguish synthetic from real MRIs as the synthetic MRIs contained subtle artifacts (such as always showing a vessel at exactly the same location in the brain).

B. Counterfactual MRI Generation

Counterfactual MRI generation aims to produce MRIs with anatomically plausible variations [24]. For example, models like CounterSynth [57] use a conditional generative framework to modify existing MRIs based on specific labels. Instead of generating a new MRI from scratch, it applies realistic, smooth deformations to the input image to simulate the desired condition. Moving beyond geometric deformations, recent approaches [8], [25] have embedded language understanding to encode input prompts. By directly modifying the metadata within these prompts, they guide an LDM to synthesize 2D and 3D brain images that reflect the desired counterfactual conditions. In a related direction, recent work [58] explores counterfactual brain MRI synthesis by explicitly modeling temporal differences between MRI scans using diffusion models. Alternatively, BrLP [23] integrates subject metadata to enhance individualization and incorporate prior knowledge of disease dynamics via an auxiliary model. BrLP then employs a Latent Average Stabilization (LAS) algorithm to enforce spatiotemporal consistency and quantify uncertainty in the predicted progression. However, all these methods typically rely on global conditioning (e.g., text prompts or scalar metadata), which restricts their capacity to explicitly model and control the subtle, localized structural variations essential for capturing fine-grained disease effects. Some GAN-based approaches attempt counterfactual synthesis via image-to-image transformations [59], yet they similarly rely on available training pairs, limiting the amount of variation in the generated samples. Recently, De Sousa Ribeiro et al. [24] proposed a high-fidelity counterfactual model for lung CTs and brain MRIs. Due to the complexity of 3D counterfactuals, their work focused on 2D slices and on clearly visible changes in brain structure related to aging, such as ventricular enlargement. Meanwhile, studies on latent causal modeling [21], [26] of 3D MRI counterfactuals leverage causal graphs to model disease-related effects, but fail to faithfully reproduce subtle, spatially localized disease-induced anatomical changes in the generated images. In contrast, our 3D counterfactual model targets nuanced structural changes that are often observed in psychiatric studies, thereby advancing the capacity for subtle, anatomically plausible modifications of MRIs.

III. Methodology

We now describe our approach for generating accurate counterfactuals of MRIs (PCGM) in further detail (Fig. 1). Given a T1w brain MRI, the approach first uses SynthSeg⁺ [60] to extract a segmentation and for each region of interest (ROI) a volume score, probability map, and a quality score. The approach then excludes further analysis for MRIs whose quality score falls below a reliable threshold [16], which mitigates error propagation from upstream tasks. Next, the volume scores together with the original and modified metadata (such as age and diagnoses) are fed into the PGM in order to update the scores according to the modifications. Given the ‘intervened’ scores, the Counterfactual Mask Generator (CMG) produces a new binary mask for each ROI. Finally, the modified masks guide the generation of the counterfactual MRI by the Mask Guided Diffusion (MGD) module. We now describe these three modules in further detail and end with how to use PCGM to generate counterfactual MRIs.

A. Probabilistic Graph Module (PGM)

PGM models causal relationships between metadata (e.g., age, sex, and diagnosis) and regional brain measurements using a deep structural causal model (DSCM) [61]. In this work, the causal graph is constructed based on established neuroscience findings, such as those reported in [20]. Formally, the causal graph is a directed acyclic graph (DAG), whose nodes $v_i$ correspond to random variables representing patient attributes and region-of-interest (ROI) volume scores. An edge from node $v_j$ to $v_k$ indicates that $v_j$ is a direct causal parent of $v_k$, such as the diagnosis of AUD $\left(v_j\right)$ and the volume of the frontal lobe ($v_k$ ) according to [20]. For a given ROI $k$, we denote by ${\mathbf{p}\mathbf{a}}_k$ the set of parent variables (which in our case are meta data) of $v_k$ (i.e., the volume of the ROI), and by $u_k$ an exogenous noise variable that captures unobserved factors influencing $v_k$. As in [62], each endogenous variable $v_k$ is modeled by a structural equation

$$v_k:=f_k\left(u_k,\mathbf{p}{\mathbf{a}}_k\right),$$ (1)

where $f_k$ represents a causal mechanism parameterized as a conditional normalizing flow [63]. We choose this model as it enables encoding nonlinear causal dependencies while allowing tractable inversion, an important property for generating counterfactuals.

Specifically, generating counterfactuals follows the standard three-step process of abduction, action, and prediction (see also The pseudo-code provided in Algorithm 1). Given the observation $V$, abduction recovers the latent noise variables $U$ via the inverse transformation

$$u_k=f_k^{-1}\left(v_k;\mathbf{p}{\mathbf{a}}_k\right),$$ (2)

which isolates the individual-specific latent factors associated with each variable.

Leaving the structural equations unchanged, action applies the intervention to all parent variables of $v_k$, i.e.,

$$do\left(\left\{v_j=c_j\mid v_j\in p{a}_k\right\}\right),$$

to replace the original parent set ${\mathbf{p}\mathbf{a}}_k$ with counterfactual values ${\widehat{\mathbf{p}\mathbf{a}}}_k$.

Based on the abducted exogenous noise from the abduction step and the modified parent set, the final prediction step propagates the intervention through the structural equation of $v_k$ to compute the counterfactual outcome. The counterfactual value of $v_k$ is given by

$${\widehat{v}}_k:=f_k\left(f_k^{-1}\left(v_k;\mathbf{p}{\mathbf{a}}_k\right),{\widehat{\mathbf{p}\mathbf{a}}}_k\right)=f_k\left(u_k,{\widehat{\mathbf{p}\mathbf{a}}}_k\right),$$ (3)

which preserves the inferred exogenous noise $u_k$ while modifying only the causal inputs affected by the intervention.

B. Counterfactual Mask Generator (CMG)

Based on the counterfactual ROI volume scores generated by PGM, our approach now modifies the corresponding mask of each region (Fig. 1). Here, we describe how we modified the masks of cortical regions as subtle differences in those regions are important findings of many psychiatric studies. For example, differences in cortical volume for those diagnosed with AUD (vs. controls) are reported in [20], whose findings we aim to replicate later. However, the approach described below (and summarized in Algorithm 2) can be easily extended to other brain regions impacted by other diseases.

To model the subtle impact of psychiatric diseases on $M$ cortical ROIs, one needs to know that small changes to an ROI also change the neighboring Cerebrospinal fluid (CSF) but not the white matter [64]. In other words, changing the volume of an ROI needs to result in a change of the boundary between the ROI and CSF, but not the white matter. Thus, simply eroding or dilating masks in accordance with the counterfactual volume would imply changing both CSF and white matter and thus be unrealistic.

For an arbitrary cortical ROI $k\in \{1,\dots M\}$, we instead first identify the boundary between CSF and the ROI based on the segmentation provided by SynthSeg⁺. Around this boundary, we define a voxel-level probability map $P_k$ (also generated by SynthSeg⁺). Thus $P_k(l=i\mid x)$ is the probability that label $i\in \left\{\mathrm{w}\mathrm{h}\mathrm{i}\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{a}\mathrm{t}\mathrm{t}\mathrm{e}\mathrm{r},\left.\mathrm{C}\mathrm{S}\mathrm{F},{\mathrm{R}\mathrm{O}\mathrm{I}}_k\right\}\right.$ is assigned to voxel $x$.

Now let’s assume that the mask of the ROI $k$ needs to be increased, i.e., $v_k$ (in voxels) is smaller than ${\hat{v}}_k$ determined by the PGM. To generate the updated mask, let ${ℳ}_k\subset \mathrm{\Omega }$ denote the original binary mask of ROI $k$, where $\mathrm{\Omega }$ is the voxel grid of the MRI volume. Then the original ROI volume is $v_k:=\left|{ℳ}_k\right|$, i.e., the number of voxels labeled as ROI $k$. After a counterfactual intervention, the PGM outputs a target ROI volume $v_k>{\hat{v}}_k$ so that the required volume increase is defined as $d:=v_k-{\hat{v}}_k$.

Let $P_k(l=i\mid x)$ denote the voxel-wise class probability map produced by the segmentation network for ROI $k$, where $i\in \left\{{\mathrm{R}\mathrm{O}\mathrm{I}}_k,\mathrm{C}\mathrm{S}\mathrm{F}\right\}$ and $x\in \mathrm{\Omega }$. We further define the boundary between the ROI and the CSF boundary as

$${ℬ}_k:=\left\{x\in \mathrm{\Omega }\mid x\notin {ℳ}_k\wedge x\text{is}\text{adjacent}\text{to}{ℳ}_k\right\}.$$ (4)

To increase the ROI mask by exactly $d$ voxels, we rank all boundary voxels $x\in {ℬ}_k$ according to the score

$$s_k\left(x\right):=P_k\left({\mathrm{R}\mathrm{O}\mathrm{I}}_k\mid x\right)-P_k(\mathrm{C}\mathrm{S}\mathrm{F}\mid x),$$ (5)

which measures the relative preference of assigning voxel $x$ to ROI $k$ versus CSF. The counterfactual mask is then obtained by

$${\widehat{ℳ}}_k={ℳ}_k\cup \underset{x\in {ℬ}_k}{\mathrm{T}\mathrm{o}\mathrm{p}-\mathrm{d}}{s}_k(x),$$ (6)

where Top-d selects the $d$ boundary voxels with the largest scores. Crucially, by leveraging continuous probability maps rather than relying solely on discrete binary masks, the probabilistic ranking ensures that morphological changes are concentrated in regions of high boundary uncertainty and thus preserves anatomical plausibility.

In the case where the mask of ROI $k$ needs to be decreased, we cannot simply lower the ROI probabilities, as boundary voxels may otherwise be reassigned to white matter or neighboring ROIs instead of CSF. To ensure anatomically consistent shrinkage, we restrict the operation to boundary voxels within the original ROI and rank them according to their preference for reassignment to CSF. Specifically, voxels with score $s_k^{\prime }\left(x\right)=P_k(\mathrm{C}\mathrm{S}\mathrm{F}\mid x)-P_k\left({\mathrm{R}\mathrm{O}\mathrm{I}}_k\mid x\right)$ are removed first, ensuring that the reduction primarily occurs along regions of high boundary uncertainty and preserves plausible tissue transitions.

Note, the masks are topologically plausible as our method only makes minor modifications to the mask, i.e., it only modifies the labels of voxels located along the boundary of an ROI, where the segmentation probability is most uncertain about label assignment. These adjustments are therefore spatially localized and guided by the spatially smooth probability maps produced by the segmenter. While, in theory, isolated “islands” could be introduced, in practice this does not occur because the probability maps inherently enforce local continuity, ensuring that the resulting masks remain topologically plausible. Furthermore, the mask is only used for guiding the diffusion model so that small islands most likely will have little impact on the generated MRIs. Finally, for larger volumetric changes (such as ventricle enlargement across a broad age span), the mask is not really needed as the changes are visually obvious, so that the diffusion model can directly learn to encode this change from data without relying on a learned causal prior.

C. Mask Guided Diffusion (MGD)

Guided by the counterfactual masks produced by the CMG, our Mask Guided Diffusion (MGD) module produces counterfactual MRIs based on three key components: (1) a causal encoder that embeds MRIs into a latent space; (2) a novel counterfactual denoising UNet that conditions the latent encoding of MRIs with respect to counterfactual metadata and mask; and (3) a 3D diffusion decoder that transforms the MRI encodings into MRIs of the resolution of the input. Each of these components is now described in further detail:

1). Causal Encoder:

Recognizing the importance of capturing subtle details in generating MRIs, we rely on a continuous VAE by adapting the causal architecture [65] (often used on videos [66]) to 3D MRIs. Specifically, in each batch, our model views each slice of an MRI as a static frame and learns to encode those 2D frames while simultaneously learning cross-slice (or frame) consistency to properly account for constraints within the entire 3D volume. To minimize biases in the encoding towards the acquisition plane, we view each 3D MRI as a volume with 3 directions and then randomly select the acquisition plane (axial, coronal, or sagittal) in that volume. We do so by simply selecting the corresponding direction as the third dimension and viewing the other two dimensions as the ones defining each slice. This ensures the model learns isotropic 3D consistency rather than being biased towards a single acquisition plane.

2). Counterfactual Denoising UNet:

As in MedSyn [67], we rely on a fully 3D CNN encoder-decoder UNet backbone augmented with self-attention layers. The UNet encoder is followed by four attention blocks, each consisting of three attention layers: (1) a 3D volumetric attention layer, which extends MedSyn’s 2D spatial attention to operate directly on volumetric patches so that it can better capture anatomical context in 3D; (2) a cross-attention mechanism that couples counterfactual metadata with MRI features (replacing the text-based conditioning in MedSyn); and (3) a temporal attention aligned with the diffusion timestep to model the dynamics of the denoising process.

In addition to metadata-based conditioning, we further incorporate the counterfactual mask to directly guide the diffusion process on a voxel-level. Specifically, we first encode the 3D mask via 3D ControlNet, which consists of replacing conv (designed for 2D images) with conv3D in ControlNet [68]. Using the same model architecture as the UNet encoder, we combine the MRI mask features extracted by the encoder layer of 3D ControlNet with MRI features extracted by the corresponding UNet layer through the skip connections and with the output of the attention block of the final layer. Guided by the diffusion noise schedule of the diffusion module, this design progressively incorporates the mask as the image denoises, ensuring the output adheres to the voxel-level condition defined by the mask at each denoising step.

3). 3D Diffusion Decoder:

The diffusion decoder proposed in [69] reconstructed high-fidelity 2D images by leveraging a diffusion model. Unlike the feedforward upsampling decoders used in VAEs [70], this diffusion decoder employs an iterative denoising process that progressively refines noisy samples into realistic images conditioned on latent representations. Inspired by their success, we design the first 3D CNN-based diffusion decoder that transforms the counterfactual latent representation $z_c$ (generated by the Counterfactual Denoising UNet) into high-fidelity counterfactual MRIs. Unlike in [69], we first upsample $z_c$ to $z_c^{\prime }$ so that it matches the spatial resolution of the target MRI $x_0$. Conditioned on $z_c^{\prime }$, the diffusion decoder then denoises a sequence of noisy samples in order to approximate the data distribution $p\left(x_0\mid z_c^{\prime }\right)$. Furthermore, the diffusion decoder acts as a generative regularizer against potential upstream errors. By first lifting the latent representation to high spatial resolution and then reconstructing the MRI via an iterative diffusion process, the final output is an anatomically plausible MRI.

D. Counterfactual Generation

To generate a counterfactual, we first perform the intervention on the metadata and apply the PGM to obtain the corresponding values of the leaf nodes (i.e., volumes of the ROIs). For each ROI, the CMG modifies its mask according to the modified volume scores. Next, DDIM inversion [71] is applied to the 3D causal encoding of the original MRI, which produces the reverse-generation sequence that aligns with the original metadata. By selecting an intermediate latent state from this sequence as the initialization point for denoising, the model enables counterfactual generation of the MRI under given altered metadata conditions. Finally, conditioned on both the counterfactual mask and the modified metadata, we apply the DDIM inversion and regeneration process to synthesize counterfactual MRIs that reflect the intervention while preserving overall anatomical consistency.

IV. Experiments

A. Experimental Setup

To document the strengths and weaknesses of our approach, we systematically evaluate our method in three stages. First, we focus on assessing the quality of MRIs generated just by the unconditional diffusion model of our method (i.e., by omitting the encoding of the original MRI, metadata and the mask; the blue components in Fig.1). Next, we add the encoding of the original MRI and meta-data to the model (but still omit the mask generated by the CMG; i.e., CDM in Fig.1) to create longitudinal counterfactuals (i.e., counterfactuals with respect age) and assess the accuracy of the generated counterfactuals with respect to the ventricles, i.e., a structure that visually increases in size with age. Finally, we test the complete PCGM approach (i.e., all components shown in Fig.1) in replicating the subtle effects of alcohol use disorder (AUD) on cortical structures as reported in [20]. To ease readability, we now first describe the experimental setup and findings of the first two tasks. The resulting model will then be the base of PCGM, which will be tested in the third experiment on a separate dataset.

1). Datasets:

The first two tasks are based on 1273 T1w MRIs from all 380 controls of the Alzheimer’s Disease Neuroimaging Initiative (ADNI, baseline age: 75.5 ± 6.1, female ratio: 50.72%, Data Releases: ADNI 1, 2, 3 and GO) [76] and 3081 T1w MRI from 767 healthy participants of the National Consortium on Alcohol and Neurodevelopment in Adolescence (NCANDA, baseline age: 16.1 ± 2.5, female ratio: 51.53%, Data Releases: NCANDA _PUBLIC 6Y STRUCTURAL_V01) [32] that passed through our processing pipeline [54]. All MRIs were affinely registered to the SRI24 [77] atlas to normalize for differences in head position and brain size. Following the training strategy of other generative models [11], [12], [78]–[81], we used a train-test split to maximize the number of training samples and relied on a fixed number of training iterations rather than validation-based stopping criteria. Specifically, we split the joint data set into 667 subjects (consisting of 3954 MRIs) for training and the remaining 400 subjects (132 from ADNI, 268 from NCANDA) for testing so that the two subsets were matched with respect to sex and age.

While the first task tests the generative approach on the baseline MRIs of all 400 subjects, the test set for the second task is further reduced to the 7 longitudinal MRIs from the NCANDA data set with at least 5 visits and the 23 longitudinal MRIs from ADNI. The test set of the second task is complemented with an out-of-sample data set of longitudinal MRIs (consisting of two visits) of 41 participants with HIV (age: 53.3 ± 7.8, female ratio: 36.5%) of the SRI-Stanford study (PI: Sullivan, Pfefferaum) [33]. All T1-weighted MRIs were preprocessed following [54], including denoising, skull stripping, registration, and intensity normalization. In addition, each MRI was segmented using SynthSeg⁺ [60].

2). Implementation Details:

All experiments were run on a single NVIDIA A100 GPU (80GB). For the first two tasks, we trained the foundational components of our model, i.e., the Causal Encoder, CDM, and the 3D Diffusion Decoder (blue and orange components in Fig. 1). The Causal Encoder of the MGD was initialized from a pre-trained OpenSora Causal-VAE [65] and fine-tuned for 40,000 iterations using a batch size of 1, a learning rate of 1e⁻⁵, and cropped MRIs to dimension 101×104×104. Next, we trained the counterfactual denoising UNet conditioned on z-scored metadata (i.e., age and sex) and the 3D Diffusion Decoder separately for 40K iterations with a learning rate of 8e⁻⁶. This implementation of PCGM required (i) less than 40 GB of GPU memory during training, (ii) the full model trains in 72 hours on a single A100 with PGM, CMG, 3D ControlNet take ~ 24 hours separately, and (iii) whole counterfactual inference of PCGM takes about 200 seconds per 3D scan. Despite integrating multiple components, the overall cost remains comparable to existing 3D diffusion-based baselines.

To further improve the ’alignment’ between (altered) metadata and generated MRIs, we relied on classifier-free guidance [82]. Finally, we generated 400 MRIs for Task 1 from random noise without any metadata conditioning. For Task 2, we generated counterfactuals for each test subject by obtaining an intermediate latent sequence through DDIM inversion of the baseline MRI. We then adjusted the age of the model to the age of the subject at subsequent visits and performed DDIM generation to produce counterfactual MRIs. For each MRI, we measured the ventricular volume using SynthSeg⁺. We focused on the ventricles as these are visibly increasing in size as individuals get older (i.e., we do not require the mask encoding brain regions).

B. Task 1: General Brain Synthesis

This task evaluates the MGD module in an unconditional setting (ablating metadata and masks) to verify the fundamental high-fidelity synthesis capability of our 3D Diffusion Decoder. Specifically, the 400 MRIs produced by MGD were compared against those generated by three state-of-the-art GAN approaches (i.e., VAE-GAN [72], α-WGAN [73], and HA-GAN [74]) and three diffusion models (i.e., M-LDM [75], MedSyn [67], and BrainSynth [49]). Each method was trained and evaluated using the same experimental setup as our method.

1). Qualitative Results:

As shown in Fig. 2, the brain MRIs generated by the four diffusion models are of superior visual quality compared to GAN-based approaches. Of the diffusion models, the MRIs of M-LDM and MedSyn are still quite fuzzy, i.e., gray matter boundaries are not clearly defined. BrainSynth and our approach produce visually very nice MRIs. However, the MRI generated by our approach is the only one showing clear gray matter boundaries within the cerebellum (last row in Fig. 2).

Fig. 2. Real and synthetic MRIs created by generative approaches.

Given the real MRI, the figure displays the most similar synthetic MRI generated by each method. Each MRI is displayed from the axial (first row) and sagittal view (third row). Compared to baseline approaches, the image contrast and visibility of anatomical structures in the MRI generated by our method most closely match the real MRI, especially for the cerebellum (fourth row).

2). Quantitative Results:

This observation is also supported by the quantitative evaluation summarized in Table I. Specifically, the 400 MRIs produced by each approach were assessed using the traditional imaging metrics Frechet Inception Distance (FID) [83] and Maximum Mean Discrepancy (MMD), which were calculated in both feature and image spaces. To assess the MRIs in feature space, we employed the pretrained 3D medical networks 3D ResNet-101 and ResNet-50 as in [74]. In addition, we recorded their MS-SSIM [84] score and computed the % difference with respect to the MS-SSIM recorded on the 400 real MRIs that were omitted from the training set. Table I reveals that our approach achieves the top or second-best score in all 6 categories. VAE-GAN achieves the top score for the MMD score computed in the image space as its MRIs are overly smooth and have a fuzzy appearance, which reduces pixel-level discrepancies. BrainSynth and our method achieve the best MMD scores based on the ResNet-50 and ResNet-101 encodings. However, with respect to the two metrics on the imaging space (i.e., voxel space), our method clearly outperforms BrainSynth indicating that subtleties of MRIs are probably not well captured by the metrics based on the Res-Net encodings, which were originally derived for natural images. Overall, this comparison highlights that the generative model of our counterfactual approach synthesizes MRIs of superior image quality than state-of-the-art methods.

TABLE I. Comparison between generative models.

The absolute relative difference in MS-SSIM between synthetic and real MRIs (MS-SSIM: 0.767), and the FID and the MMD scores in both image and feature spaces (using 3D ResNet 101(R101) and ResNet 50(R50)) produced by 7 generative approaches. The top scores are in bold and the second-best scores are underlined. Our method produces the best scores in 4 categories and the second-best score in the remaining two, underlying its overall superiority over the other state-of-the-art methods.

Model	ResNet-R101		ResNet-R50		Image MMD(↓)	MS-SSIM(↓)
	FID(↓)	MMD(↓)	FID(↓)	MMD(↓)
VAE-GAN [72]	0.032±0.004	0.020±0.004	0.400±0.032	0.210±0.019	142069±12873	5.96±0.64%
α-WGAN [73]	0.032±0.003	0.020±0.004	0.496±0.033	0.258±0.022	214578±21348	3.28±0.49%
HA-GAN [74]	0.036±0.005	0.020±0.005	0.088±0.09	0.056±0.006	767583±89234	13.25±1.76%
M-LDM [75]	0.320±0.029	0.160±0.021	1.910±0.147	0.960±0.080	3432589±29546	35.21±3.23%
MedSyn [67]	0.014±0.001	0.012±0.001	0.048±0.006	0.036±0.004	245896±21046	1.86±0.021%
BrainSynth [49]	0.005±0.000	0.007±0.000	0.022±0.002	0.022±0.003	300841±25761	2.99±0.214%
Ours	0.001±0.000	0.006±0.000	0.011±0.001	0.030±0.002	208150±12903	1.06±0.080%

Since traditional image-level metrics may not accurately capture anatomical plausibility, we followed the evaluation pipeline proposed in [16]. Specifically, we applied FreeSurfer [85] to each real and synthetic MRI to record the volume of 34 cortical brain regions as defined by the Desikan-Killiany atlas (Aparc) and Freesurfer’s image quality control (QC) score. Only models whose QC scores were at least as high as those recorded on the real MRIs were then included in the comparison, which were MedSyn, BrainSynth, and our method. For each cortical region and method, we then computed the absolute Cohen’s d score $\left(\right|d\left|\right)$ between the volumetric distributions of the synthetic vs. real MRIs. According to [49], $\left|d\right|<0.2$ is seen as a small effect (i.e., good alignment with the real data), while $0.2<\left|d\right|<0.5$ indicates medium effects, and $\left|d\right|>0.5$ suggests a large effect implying greater deviation from the real data.

According to Fig. 3, the worst performing approach among the three is MedSyn, whose $\left|d\right|$ is always higher than that of our method with the exception of parahippocampus (MedSyn: 0.38, Our: 0.43) and caudal anterior cingulate (MedSyn: 0.26, Our: 0.46). This behavior can be attributed to MedSyn’s architectural design, which reduces the dimensionality of 3D MRIs by directly downsampling them into low-resolution MRI volumes. Such aggressive compression severely limits the information captured by the resulting low-level MRI, thereby constraining the model’s ability to capture fine-grained anatomical structures and contextual dependencies. In contrast, our method constructs a high-fidelity latent space by leveraging the causal encoder that preserves rich anatomical and textural information, leading to substantially better reconstruction quality and cross-modality generalization.

Fig. 3. Anatomical Plausibility.

Displayed are the natural logarithm of the absolute Cohen's d $\left(\right|\mathit{d}\left|\right)$ for 32 regions and three methods. $\left|\mathit{d}\right|<0.2$ is viewed as a small effect, $0.2<\left|\mathit{d}\right|<0.5$ indicates a medium effect, and $\left|\mathit{d}\right|>0.5$ corresponds to a large effect. Our method records the smallest d-score for the majority of regions, indicating the highest overall anatomical plausibility among the 3 methods. Note, the plot connects the scores between ROIs simply to ease comparison.

While BrainSynth is generally better than MedSyn, it is somewhat unstable as it produces the worst overall $\left|d\right|$ with 1.54 in the frontal pole and exceeds the critical 0.5 threshold for 24% of the regions. In comparison, our approach exceeds that threshold only for one region (i.e., lateral occipital lobe: $\left|d\right|=0.53$), is well aligned with volume scores from the real MRI for 62.8 % of the regions, and produces the lowest $\left|d\right|$ across all three methods in 67.6 % of the regions. In summary, the anatomical plausibility of MRIs produced by our approach is generally high and superior to these state-of-the-art methods.

3). User Study:

We further assessed the ability of our model to generate 3D MRIs of high realism by repeating the user study of the second-best approach BrainSynth [49] with the same experts, number of image pairs, and evaluation metric. Specifically, we randomly selected 50 real MRIs from the test set. For each MRI we then identified the most similar synthetic MRI generated by our method. These 100 MRIs (50 real and 50 synthetic) were then randomly mixed and independently evaluated by the same three experts as in prior work [49]. Each expert has over 20 years of experience in reading MRIs. They were asked to label each MRI as either real or synthetic. The overall average classification accuracy across the three experts was 46.0% (see Table II). This indicates that the experts were not able to distinguish real from synthetic MRIs, which was not the case for BrainSynth [49] (overall accuracy was 70.7%).

TABLE II.

Accuracy of identifying real and synthetic MRIs by experts.

	Real	Synthetic	Overall accuracy
Expert 1	46.0%	54.0%	50.0%
Expert 2	50.0%	44.0%	47.0%
Expert 3	42.0%	40.0%	41.0%
Average	46.0%	46.0%	46.0%

C. Task 2: Aging Counterfactual Generation

We now review the ability of our simple counterfactual approach (i.e., ablating the PGM and CMG by confining the model to the blue and orange components in Fig. 1) to capture changes in regions with clearly defined boundaries, i.e., the ventricles. We refer to this model as Counterfactual Diffusion Module (CDM). For comparison, we repeat the analysis for MedSyn (using the same experimental setup as for CDM), TUMSyn [8], TADM [58], BrLP [86] and CounterSynth [87]. For TUMSyn, we used its officially released, pretrained weights. Those weights were generated from 31,407 3D images across 7 modalities collected from 13 studies, which included 500 T1w MRIS from ADNI (a subset of our training set), 2864 from ABCD (age range: 9–19 years) [88], 1000 from UKBioBank (age range: 44–82 years) [89], 1100 from HCPY (22–35 years) [90]. Counterfactual brains were generated by modifying the age specification in the text prompt of TUMSyn. Like for the other approaches, we record the ventricular volume of the longitudinal MRIs generated by TUMSyn.

We quantitatively compare each synthetic longitudinal MRI to the corresponding real sequence by computing the Pearson correlation coefficient and average normalized mean square error (NMSE) of the ventricular volume at the subject level. We then perform the paired t-tests on the subject-level NMSE scores between our method and other baseline methods. The findings are summarized in Table III, which reveals that our method achieves the best average Pearson coefficient of 0.59 compared to 0.38 for the best baseline approach MedSyn. It also achieves a significantly smaller NMSE value (p-values < 0.001 compared to scores of all methods) demonstrating that our method more accurately captures the aging process of the ventricles.

TABLE III.

Results on Task 2. Top scores are in bold and the second-best scores are underline. Our PCGM method is significantly better than all baselines with respect to NMSE and pearson score. The d.

Method	NMSE(↓)	Pearson(↑)
CDM (ours)	0.015	0.59
MedSyn	0.034	0.38
TUMSyn	0.042	0.31
TADM	0.082	0.25
CounterSynth	0.063	0.27
BrLP	0.039	0.35

Fig. 4 confirms those findings qualitatively. First, the trajectory of the ventricular volume based on our synthetically generated MRIs closely matches the ones extracted from the real data. In contrast, the ventricular volumes extracted from MRIs generated by MedSyn (the second best approach according to Table III) deviate quite a lot, especially on the ADNI and HIV data, as the volumes hardly change within a longitudinal sequence. For the trajectories of the subject highlighted in yellow in the plot based on ADNI data, the bottom of Fig. 4 shows the counterfactuals for all approaches and the difference between them and the real longitudinal MRI for the ventricular region. Again, our approach produces the longitudinal MRI that most closely resembles the real sequence.

Fig. 4. Age trajectory modeling.

Top: Each trajectory in the plot represents the volume of the ventricle of one subject measured at different ages based on the real MRI and those produced by the top two approaches according to Table III. The subjects were participants of NCANDA (ages 14 – 26 years), ADNI (ages 60 – 90 years), or diagnosed with HIV (ages 33 – 74 years). Compared to MedSyn, the trajectories extracted from the counterfactual MRIs produced by our proposed CDM align the best with those of the real MRIs. Bottom: The real and corresponding synthetic longitudinal MRI of the one subject, whose trajectories are highlighted in yellow in the plot above. The right shows the difference between real and synthetic MRIs of the ventricular region (outlined in green on the left). Among all six methods, CDM also visually produces the counterfactuals most closely matching the real ones.

D. Task 3: Disease Modeling

The third task tests the abilities of our proposed counterfactual approach PCGM and ablated CDM to replicate the findings with respect to AUD on the brain originally reported in [20]. The dataset in [20] consists of 826 T1w MRIs acquired of 222 participants diagnosed with AUD (baseline age: 48.05 ± 10.33; female ratio: 31.13%) and 199 age-matched healthy controls (age: 47.21 ± 12.64; female ratio: 42.89%). We applied SynthSeg+ to each MRI and then, as in [91], regressed out the supratentorial volume from each of the cortical volume measurements of the 6 cortical regions (Frontal, Parietal, Insula, Cingulate, Occipital and Temporal). For each ROI, we computed its average value across all visits for each subject. Across subjects, we then identified significant differences (p-value < 0.00833, i.e., p-value of 0.05 after Bonferroni correction for six regions) between control and AUD.

Next, we trained and tested PCGM to create the counterfactuals for this task. Specifically, we kept the encoder, diffusion model, and decoder that were trained for Tasks 1&2 (i.e., on a different data set). Furthermore, we used the pretrained U-Net of the CDM to initialize the weights of the 3D ControlNet and then trained 3D ControlNet on the training data of Tasks 1 & 2. The remaining components of our approach were trained and tested on the data specific to Task 3 via 5-fold cross-validation. Note, there is no overlap between this dataset and the ones used in Tasks 1 and 2, ensuring that no information leakage occurs between the training of the PGM and the generative model.

During 5-fold cross-validation, we trained the PGM module to create a causal graph relating scalar variables age, sex, and diagnosis (control or AUD) to the volumes of cortical regions frontal lobe, parietal lobe, insula, cingulate and temporal lobe. Training of the PGM model ran for 50,000 iterations with a batch size of 64 and a learning rate of 1e⁻⁵. For each test subject, we then computed its counterfactual by computing the cortical volume under diagnostic interventions, i.e., by changing the diagnosis. Together with the segmentation and probability map, these changes were then the input to the CMG, which produced a modified mask for each cortical region. The modified mask and the real MRI were then the input to the MGD, which produced the counterfactual. From the counterfactuals, we extracted the cortical volumes, regressed out the supratentorial volume, and, for each region, identified significant differences between control and AUD.

For comparison, we repeated this experiment for the counterfactuals only using the CDM (of Task 2, i.e., producing counterfactuals without mask), TUMSyn, and AUD-DAE. Regarding AUD-DAE, we re-implemented the approach proposed in [92] (called AD-DAE) as the official source code was not available. For TUMSyn, we set the disease label as a global condition. Furthermore, TUMSyn required paired brain scans from the same patient to learn how metadata influences image generation. We therefore created 1,662 intra-subject pairs from all the 211 subjects that had multiple MRIs (a total of 614 scans). We then trained the approach for 40 epochs.

As in the original publication, using the real MRIs revealed significant differences between the control and AUD group for the frontal lobe (p<0.0001), insula (p=0.0008), parietal lobe (p=0.0002), cingulate (p=0.0004), and temporal lobe (p<0.0001) but not for the occipital lobe (p=0.9848). Those findings were replicated when using the volumetric measurements extracted from the counterfactuals generated by our approach (Table IV). This was not the case for CDM, whose MRIs did not reveal significant differences in the cingulate and temporal lobes. In other words, PGM and CMG are necessary to capture the fine-grained, morphological changes linked to AUD. Even when just omitting voxel-level guidance provided by the CMG results in the same outcome: PGM-based generators fail to capture subtle regional changes, as we showed in [21], [26].

TABLE IV. Replicating AUD findings.

In line with [20], cortical measurements extracted from the counterfactual MRIs of our method (PCGM) successfully reproduces the significant group differences (p-value < 0.00833, i.e., p-value of 0.05 after Bonferroni correction) between control and subjects diagnosed with alcohol use disorder (AUD) for five of the six brain regions (whether real or synthetic). In contrast, no significant differences are correctly reported within the same group (i.e., between real and synthetic controls or between real and synthetic AUDs), indicating that our counterfactuals preserve group identity while capturing meaningful disease-related differences [20]. This is not the case for CDM (i.e., PCGM without the mask), TumSyn, and AUD-DAE, which fail to reproduce the findings of [20]. This indicates that simply conditioning on label signals is insufficient for the model to capture the complex structural changes associated with disease.

	Region	Counterfactual Only		Original MRI vs. Counterfactual
		Control vs. AUD	Control vs. AUD	AUD vs. Control	Control vs. Control	AUD vs. AUD
PCGM	Frontal	<0.0001	<0.0001	<0.0001	0.4242	0.1928
	Insula	0.0013	<0.0001	0.0078	0.3312	0.4976
	Parietal	0.0015	<0.0001	<0.0001	0.7331	0.9256
	Cingulate	0.0022	0.0023	0.0064	0.3018	0.3377
	Temporal	<0.0001	<0.0001	<0.0001	0.1038	0.5042
	Occipital	0.8242	0.5428	0.9891	0.9778	0.5341
	# Correct	6	6	6	6	6
CDM	Frontal	0.0022	0.1231	0.3315	0.4566	0.1979
	Insula	0.0122	0.3813	0.1291	0.1083	0.0568
	Parietal	0.0012	0.1757	0.2977	0.1557	0.3338
	Cingulate	0.0059	0.4667	0.3648	0.1077	0.2828
	Temporal	0.0093	0.2118	0.8977	0.0243	0.0338
	Occipital	0.5241	0.4318	0.3277	0.0891	0.1233
	# Correct	4	1	1	6	6
TUMSyn	Frontal	0.0033	0.9837	0.6342	0.0007	0.0009
	Insula	0.0028	0.9321	0.8632	0.0017	0.0019
	Parietal	0.0542	0.9318	0.7302	0.0005	0.0024
	Cingulate	0.0132	0.8136	0.9218	0.0008	<0.0001
	Temporal	0.0242	0.4367	0.3917	<0.0001	0.0009
	Occipital	0.5518	0.8128	0.7477	0.7439	0.8255
	# Correct	3	1	1	1	1
AUD-DAE	Frontal	0.0898	0.7689	0.8211	0.0025	0.0055
	Insula	0.0913	0.5896	0.4534	0.0059	0.0063
	Parietal	0.1223	0.6523	0.3425	0.0015	0.0049
	Cingulate	0.1478	0.7724	0.5247	0.0038	0.0026
	Temporal	0.0865	0.7877	0.2534	0.0086	0.0045
	Occipital	0.7823	0.4512	0.3123	0.5690	0.4432
	# Correct	1	1	1	1	1

Also, the other baseline approaches failed to replicate the AUD-specific findings: No significant group differences were measured based on the MRIs generated by AUD-DAE, and only the frontal lobes and insula were significantly different in MRIs generated by TUMSyn. Even more importantly, when repeating the analysis on just the controls by comparing their real values to the ones produced by their counterfactual AUD scores, only the measurements based on PCGM confirmed the findings. This is also the case when confining analysis to the real AUD cases. Finally, when comparing the volume scores of real to counterfactual controls (i.e., from real AUD), no significant differences were correctly reported for ours and CDM, but significant differences were detected for TUMSyn. The same was true when comparing real to counterfactual AUDs (i.e., generated from real controls). In summary, only our method is able to produce counterfactuals that align with the original findings reported in [91].

Note, the cortical volumes between the original and counterfactual MRI (produced by PCGM) differed by up to 20%. This change in volume can accurately be modeled by PCGM according to Fig. 5. This figure was produced by manually setting the change in volume for one region (x-Axis), producing the mask and corresponding counterfactual based on that volume score, and recording the difference between the original volume and the one extracted from the counterfactual MRI. The results reveal a clear trend: while the model maintains high fidelity for moderate changes, it begins to underestimate the target volume as the magnitude of change approaches extreme values (e.g., 100%). This saturation effect occurs because such drastic changes push the anatomy far outside the distribution of realistic brain structures seen during training. Consequently, while the benefit of the mask diminishes for these extreme, out-of-distribution changes, PCGM proves highly effective within the subtle, fine-grained range required for modeling AUD.

Fig. 5.

Comparison between expected volumetric changes (Δ Ground Truth Volume) and the one produced by the PCGM-generated counterfactual measurements (Δ Measured Volume) across 5 the cortical regions affected by AUD. As the magnitude of the expected change increases (e.g., approaching a large expansion or contraction), the predicted counterfactual changes tend to underestimate the change.

V. Conclusion

This work introduces Probabilistic Causal Graph Model (PCGM), a novel causal diffusion model for generating counterfactual MRI of high anatomical plausibility. PCGM consists of the Probabilistic Graph Module (PGM) for capturing known causal relationships between metadata and ROIs, the Counterfactual Mask Generator (CMG) for modifying the mask of each ROI to match the volume given by PGM, and the Mask Guided Diffusion (MGD) for high-fidelity 3D MRI synthesis based on the counterfactual denoising UNet. Even with limited training data, this approach accurately captures both broad and subtle changes in MRIs linked to aging and alcohol use disorder (AUD) as revealed by our experiments. With respect to AUD, the counterfactual MRIs generated by our approach were able to replicate published findings on subtle cortical changes, which is an important milestone for advancing disease modeling and synthetic data generation for neuroscience research.