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HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative Modelling
António Cardoso, Pedro Sousa, Tania Pereira, Hélder P. Oliveira
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Summary
HUydra is a novel generative framework for lung CT synthesis that decomposes the full Hounsfield Unit (HU) range into tissue-specific intervals. By training generative models on individual HU windows and merging them via a learned reconstruction network, the approach improves visual fidelity, anatomical consistency, and computational efficiency compared to traditional full-range 2D baselines. A multi-head VQVAE variant achieved the best performance, validated through quantitative metrics and a Visual Turing Test with clinicians.
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HUydra → synthesizes → Lung CT
confidence 100% · Introduction of a novel HU-interval decomposition strategy for full lung CT scan generation
HUydra → usesdataset → LIDC-IDRI
confidence 100% · Both training and validation are performed on the publicly available LIDC-IDRI dataset
multi-head VQVAE → componentof → HUydra
confidence 95% · Proposal and comparison of three architectural variants for a HU window-aware generative design, with the multi-head VQVAE being the one to achieve a better performance.
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Abstract
Abstract:Currently, a central challenge and bottleneck in the deployment and validation of computer-aided diagnosis (CAD) models within the field of medical imaging is data scarcity. For lung cancer, one of the most prevalent types worldwide, limited datasets can delay diagnosis and have an impact on patient outcome. Generative AI offers a promising solution for this issue, but dealing with the complex distribution of full Hounsfield Unit (HU) range lung CT scans is challenging and remains as a highly computationally demanding task. This paper introduces a novel decomposition strategy that synthesizes CT images one HU interval at a time, rather than modelling the entire HU domain at once. This framework focuses on training generative architectures on individual tissue-focused HU windows, then merges their output into a full-range scan via a learned reconstruction network that effectively reverses the HU-windowing process. We further propose multi-head and multi-decoder models to better capture textures while preserving anatomical consistency, with a multi-head VQVAE achieving the best performance for the generative task. Quantitative evaluation shows this approach significantly outperforms conventional 2D full-range baselines, achieving a 6.2% improvement in FID and superior MMD, Precision, and Recall across all HU intervals. The best performance is achieved by a multi-head VQVAE variant, demonstrating that it is possible to enhance visual fidelity and variability while also reducing model complexity and computational cost. This work establishes a new paradigm for structure-aware medical image synthesis, aligning generative modelling with clinical interpretation.
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- Source: https://arxiv.org/abs/2603.23041v1
- Canonical: https://arxiv.org/abs/2603.23041v1
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HUYDRA: FULL-RANGE LUNG CT SYNTHESIS VIA MULTIPLE HU INTERVAL GENERATIVE MODELLING A PREPRINT António Cardoso INESC TEC, Portugal Faculty of Engineering, University of Porto, Portugal Faculty of Sciences, University of Porto, Portugal antonio.l.cardoso@inesctec.pt Pedro Sousa INESC TEC, Portugal pedro.fernandes.sousa@inesctec.pt Tania Pereira INESC TEC, Portugal Faculty of Engineering, University of Porto, Portugal tania.pereira@inesctec.pt Hélder P. Oliveira INESC TEC, Portugal Faculty of Sciences, University of Porto, Portugal helder.f.oliveira@inesctec.pt ABSTRACT Currently, a central challenge and bottleneck in the deployment and validation of computer-aided diagnosis (CAD) models within the field of medical imaging is data scarcity. For lung cancer, one of the most prevalent types worldwide, limited datasets can delay diagnosis and have an impact on patient outcome. Generative AI offers a promising solution for this issue, but dealing with the complex distribution of full Hounsfield Unit (HU) range lung CT scans is challenging and remains as a highly computationally demanding task. This paper introduces a novel decomposition strategy that synthesizes CT images one HU interval at a time, rather than modelling the entire HU domain at once. This framework focuses on training generative architectures on individual tissue-focused HU windows, then merges their output into a full-range scan via a learned reconstruction network that effectively reverses the HU-windowing process. We further propose multi-head and multi-decoder models to better capture textures while preserving anatomical consistency, with a multi-head VQVAE achieving the best performance for the generative task. Quantitative evaluation shows this approach significantly outperforms conventional 2D full-range baselines, achieving a 6.2% improvement in FID and superior MMD, Precision, and Recall across all HU intervals. The best performance is achieved by a multi-head VQVAE variant, demonstrating that it is possible to enhance visual fidelity and variability while also reducing model complexity and computational cost. This work establishes a new paradigm for structure-aware medical image synthesis, aligning generative modelling with clinical interpretation. 1 Introduction 1.1 CT Scans and Hounsfield Units Lung cancer is one of the deadliest cancers worldwide, accounting for the highest rate of cancer-related deaths (approximately 18.7%) both in men and women, in 2022 [1]. Computerized Tomography (CT) chest scans have been adopted as the main tool for diagnosing lung cancer, and other lung diseases, as they provide the ability to visualise pulmonary anatomy and assess the presence of tumours, their exact location, size and stage with accurate diagnostic images, playing a key roll for patient diagnosis and treatment planning [2, 3]. arXiv:2603.23041v1 [cs.CV] 24 Mar 2026 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT CT scan machines employ X-ray detectors and beams that rotate around a patient’s body to capture 2D or 3D cross- sectional images of the region of interest for the specific diagnosis. During image reconstruction, each tissue’s X-ray absorption coefficient are quantified into Hounsfield units (HU), computed from a linear transformation of the baseline attenuation coefficient of the X-ray beam [4], ranging from−1000to3000. The greater the tissue density, the higher the absorption coefficient is, and, therefore, the higher the HU value will be. Table 1 frames the HU values of some tissues and materials found in CT scans. Table 1: Hounsfield units for different tissues and materials [5] TissueHounsfield Unit (HU) Air−1000 Lung[−700,−600] Fat[−120,−90] Water0 Abscess/pus0 or 20, 40 or 45 Blood[30, 45] Muscle[35, 55] Bone[700, 3000] 1.2 Generative Approaches for Medical Imaging The use of Artificial Intelligence (AI), in particular Deep Learning, has been extensively explored for applications in Computer Assisted Diagnosis (CAD) systems, such as nodule segmentation and classification in lung cancer screening. However, data availability limitations impose challenges for model training [6], while the curation process of such data collections also raises new challenges due to time and costs, as well as data validation from medical teams [7], to ensure any trained model has processes clinical trustworthy data. To address this challenge, Image Generative AI models have surfaced as a promising solution [7], capable of producing synthetic data with realistic and structural and anatomical characteristics derived from training data. In recent years, many Generative AI has been applied to the context of medical images, such as in image enhancement for noise reduction [2], super-resolution [8] and image-to-image modality translation [9]. As of late, many generative methods employ techniques such as Generative Adversarial Networks (GANs), Diffusion Models (DMs) and corresponding score-based implementations, and, latent generative models, for example Vector- Quantized Variational Autoencoders (VQVAEs). 1.2.1 Generative Adversarial Networks GANs formulate generative modelling as a two-player minimax game between a generator networkGand a discriminator networkD[10]. The generator maps samples from a prior distributionz ∼ p z to the data space,G(z), while the discriminator distinguishes between real samplesx∼ p data and generated ones ̃x∼ p G . The general GAN framework is summarized on the diagram in Figure 1. The standard GAN optimization objective is formulated by Equation 1. min G max D E x∼p data [logD(x)] + E z∼p z [log(1− D(G(z)))](1) Ideally, the adversarial game formulation converges when thep G matchesp data . However, while effective, GANs often suffer from unstable training and mode collapse due to vanishing gradients whenDstrongly outperformsG. To address these issues, Wasserstein GANs (WGANs) [11] reformulate the objective by minimizing the Earth Mover distance (Wasserstein distance) betweenp data andp G , and restricting the family of functions ofDto the set of 1-Lipschitz functions,D. The Lipschitz constraint is crucial, because it stabilizes training by encouraging the discriminator’s gradients to have unit norm, leading to more robust convergence. Instead of enforcing the constraint through weight clipping, (author?)[12]proposed the WGAN with Gradient Penalty (WGAN-GP), which adds a soft penalty on the gradient norm to the optimization objective, framed in Equation 2, where ̄x are samples interpolated between real and generated data. min G max D E x∼p data [D(x)]− E z∼p z [D(G(z)))] + λ GP · E ̄x∼p ̄x (||∇ ̄x D( ̄x)|| 2 − 1) 2 (2) 2 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT z G D [0, 1] Dataset x x ~ Figure 1: General GAN framework, where the DiscriminatorDpredicts the probability of authenticity for both real images from the dataset or synthetic ones, generated from the output of the Generator G given a latent vector z. p 0 p T Forward Diffusion Process Reverse Diffusion Process Figure 2: Effect of forward and reverse diffusion processes on a chest CT scan slice. 1.2.2 Score-based Diffusion Models Denoising Diffusion Probabilistic Models (DDPMs) [13] operate by first defining a forward process that gradually perturbs data from the original distributionp 0 (x), with Gaussian noise over a fixed number ofTtimesteps, until it approaches a pure Gaussian prior distributionp T (x). Afterwards, it is possible to learn the reverse process, which iteratively denoises the samples step by step, allowing for the reconstructions of realistic data from pure noise. The effects of the forward and reverse processes are shown in Figure 2. This discrete formulation can be generalized to a continuous-time approach, where score-based generative modelling defines the reverse process as the solution of a Stochastic Differential Equation (SDE). Lettingx(t) t∈[0,T ] represent a continuous diffusion process, the corresponding stochastic forward and reverse processes are defined by Equation 3 and 4, respectively. dx = f (x,t)dt + g(t)dw(3) dx = [f (x,t)− g 2 (t)∇ x logp t (x)]dt + g(t)d ̄w(4) Next, setting the drift coefficientf (·,t)and the diffusion coefficientg(t)as in Equation 5 describes a variance preserving SDE that equivalently models DDPM’s discrete diffusion process [14], where β(t) describes a linear noise schedule. f (x,t) =− 1 2 β(t)x, g(t) = p β(t), β(t) = (β max − β min ) t T + β min (5) Finally, through the optimization of a time-informed neural network to estimate the score-function of each timestep marginal distribution,∇ x logp t (x), it is possible to sample data fromp 0 (x)by executing the reverse diffusion process from Gaussian noise. The score-predicting model’s architectures are usually time-informed U-Nets, composed by an 3 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT downsampling, encoding component, an upsampling, decoding component, and skip connections for the use of shared information from earlier layers, alongside embedding-producing shallow multi-layer perceptrons to integrate timestep information for score prediction. The optimization of a timestep-informed score-based modelsis performed over the minimization of MSE to the score-function through denoising score matching [15], as displayed in Equation 6, whereλ is an appropriate positive weighting function [16] and t is uniformly sampled over [0,T ]. min E t λ(t)E x(0) E x(t)|x(0) ||s(x(t),t)−∇ x(t) logp 0t (x(t)|x(0))|| 2 2 (6) 1.2.3 Vector-Quantized Variational Autoencoders Two-stage approaches family of generative models attempt at learning encoded representations of the data distribution, and later optimize a generative model to learn the encoded representation distribution. Some works have shown state-of-the-art results using these approaches, such as Latent Diffusion Models [17], Variational Diffusion Models [18], as well as VQVAEs [19] and VQGANs [20]. Learning meaningful and compact latent representations, capturing the essential semantic structures of the data, is needed to, consequently, operate more tractably, efficiently and stably in a reduced-dimensional latent space during the generative modelling stage. While most encoding methods provide continuous features for generative modelling, VQVAEs focus on the extraction of discrete representations [19]. On the first stage of training, the VQVAE learns an encoder modelEand decoder modelD, such that, together, they learn to represent images using codes from a learned discrete codebookZ = z c C c=1 , wherez k ∈ R n z . More specifically, an imagex∈ R H×W×C is approximated byˆx = D(z q ), where the quantized latent representationz q is obtained from the encoder outputˆz = E(x)∈ R H×W×n z through element-wise nearest-neighbour quantization, as in Equation 7. z q = q(ˆz) = arg min z c ∈Z ||ˆz ij − z c ||(7) Thus, the reconstruction is given by ˆx = D(z q ) = D(q(E(x))). Since the quantization operation in Equation 7 is non-differentiable, a straight-through gradient estimator [21] is used to copy gradients from the decoder back to the encoder, allowing the training of both the codebook and the model. The overall training loss function is shown in Equation 8, where the first term denotes the reconstruction loss,sg[·]is the stop-gradient operation, and the last term is the commitment loss [19] that encourages the encoder outputs to remain close to their corresponding codebook entries, with λ c being a weighting factor. L(E,D,Z,x) =||x− ˆx|| 2 2 +||sg[E(x)]− z q || 2 2 + λ c ||sg[z q ]− E(x)|| 2 2 (8) On the second training stage, given the trained encoderEand decoderD, feed-forwarded images can be represented as sequences of codebook indices corresponding to their quantized latent encoding, i.e., the quantized latent representation of an imagez q ∈ R H×W×n z is mapped to a sequences∈0, 1,...C− 1 H×W , where each elements ij indexes the its nearest codebook vectorz c . By converting the indices insback to their respective codebook entries, the image can be reconstructed as ˆx = D(z s ij ). To model the data distribution, a transformer model is trained auto-regressively on the index sequences, predicting each tokens i conditioned on all previous oness <i , to compute the likelihood of the full representation asp(s) = Q i p(s i |s <i ) . Thus, the model maximizes the log-likelihood of the discrete latent representations, defining the transformer loss function as in Equation 9. L Transformer = E x∼p(x) [− logp(s)](9) A VQVAE generates new samples by generating sequences of codebook indexes, which are then converted to their vector representation and re-ordered back to grid structure, and, finally, fed through the decoder network to obtain the new, synthetic images. The overall VQVAE framework is displayed in the diagram of Figure 3. 1.3 Motivation & Contributions In clinical practice, radiologists often adjust HU windows to better visualise specific tissues. Therefore, this windowing method can effectively perform a form of semantic segmentation for different anatomical structures in a totally analytical manner. Despite this being a routine practice, current generative approaches mostly ignore this form of decomposition, 4 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT z q D E x Dataset qxz Codebook Z 1 2 C Transformer arg min p(s i | s <i ) Figure 3: General VQVAE framework. A given imagexpasses through the Encoder networkEto produce a continuous latent representationz. Next, given the codebookZwithCvectors, the quantization operatorqproduces a discrete latent representation z q . Finally the decoder network D predicts a reconstruction of the original image ˆx by decoding z q . The transformer module auto-regressively generates sequences of discrete values that try to match those produced by z q , allowing the synthesis of new images. and attempt to deal with full-range CT scans as a single continuous distribution, seeing as this is the modality most useful in any real world application. In this work, we propose a two-step generative framework to decompose full CT generation into structure-specific subtasks. Rather than using traditionally full-domain scans, this allows for the joint modelling of various individual HU intervals, each one ideally corresponding to a distinct tissue. Their outputs are then fused through a simple reconstruction network, effectively imitating the reverse process of HU windowing with minimal information loss. Both training and validation are performed on the publicly available LIDC-IDRI dataset [22,23] and resorting to both quantitative key metrics and qualitative expert evaluation. This study therefore exploits a disconnect between existing generative literature and clinical interpretation of lung CT scans. The advantages brought about by this method are fourfold: by using multiple generators, each focused on a narrower intensity distribution, it is possible to reduce model complexity and optimise computational efficiency - especially relevant in resource-strained scenarios / environments. Moreover, this allows for better interpretability and more control over the results, seeing as clinicians are given access not only to the final full-range CT scans but also all the HU windows it is comprised of. In summary, the contributions of this research are as follows: •Introduction of a novel HU-interval decomposition strategy for full lung CT scan generation, with the aim of aligning generative modelling and clinical practice and enabling a targeted, tissue-specific manner of generation. • Proposal and comparison of three architectural variants for a HU window-aware generative design, with the multi-head VQVAE being the one to achieve a better performance. •Enhancement of generative explainability through the use of a transparent stepwise process which enables clinicians to interpret and validate the synthetic output at a macro and component levels. •Expansion upon the concept of HU windowing by providing a learned reconstruction method to reverse it with minimal loss of information. •Demonstration of significant improvements in both perceptual quality and diversity over traditional AI-based full-range baselines, while also priming for a decrease in computational demands and training costs. •Conduction of a Visual Turing Test (VTT) with practising clinicians with satisfactory results, thus providing real clinical validation by proving the results’ anatomical realism and diagnostic relevance. • Creation of an open framework that may possibly be extended to other medical imaging modalities where intensity-based decomposition is possible and meaningful. The remainder of the manuscript is organised as follows: section 2 introduces the related work and literature state-of-the- art on the matter; section 3 presents our designed architecture and pipeline for decomposed full lung CT scan generation; 5 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT section 4 we discuss the extensive experimentation regiment conducted in order to evaluate method performance quantitatively and qualitatively; and section 5 finally concludes the paper with a brief overview on contributions and future potential. 2 Related Work The field of medical image synthesis has evolved significantly over the years. Early analytical physics-based approaches relied mostly on mathematical phantoms [24,25] (e.g. the Shepp-Logan phantom) or finite-element simulations [26] which would produce images to be used in calibration and algorithm validation for the most part. These approaches saw variability being handled through the use of linear combinations for principal components, in what were called statistical shape and active appearance modelling [27,28]. Furthermore, atlas-based synthesis [29] was a staple of multimodality, seeing as generation was done via registration to a template. This method, specifically allowed for improved interpretability and control over anatomical features, as well as facilitating downstream tasks, such as segmentation. However, analytical methods were inherently unable to fully capture and mimic the complexity of real samples, being limited by faulty physic assumptions and low-dimensional representations, even despite their reliance on experts defining priors. The rise of machine and deep learning shifted this paradigm from using simplified physics approximations to iterative data-driven modelling [30,31]. This revolutionised not only the generative scene, but perhaps more importantly contributed greatly towards the optimisation and automation of downstream tasks such as pathology prediction [32]. Variational autoencoders (VAEs) were some of the first on the scene to be applied to not only representation learning of healthy lung CT scan [33,34,35,36] but also for the purpose of enhancing lung nodule variability [37,38,39]. It should also be denoted how, in the same sense, convolutional neural networks (CNNs) also demonstrated the potential to produce full high-resolution CT scans in a number of different works and tasks, including pure synthesis [40], imaging modality translation [41], etc. Some major examples of such an application include the works of Chen et al. [42] who employed a VAE to create synthetic lung CT patches as a way of constructing a continuous texture latent space and more recently Singla et al. [43], whose use of VQVAEs for this data further prove the still-existing capabilities of autoencoders in the generative scene. Together, CNNs and VAEs can be considered the first deep learning applications to CT data augmentation and, therefore, the ones to lay the foundation for lung anatomy representation learning, despite their tendency to produce blurry and/or detail-lacking samples. This shift in data augmentation was further pushed by GANs, whose ability to produce samples with strong perceptual quality and realistic textures far surpassed that of autoencoders and CNNs [44,45]. The adoption of this new adversarial golden standard quickly proved to cause a significant leap, marked by an explosion in the number of tasks for which generative models could be adapted to within the medical imaging field [46,47], and more specifically regarding lung CT data [48,49]. Consequently, there are a variety of works which have employed GANs trained on lung CT scan data for tasks such as denoising [50,51] and more importantly data augmentation. For instance, both Chuquicusma et al. [52] and Jin et al. [53] demonstrated how a GAN-based model can produce fake lung nodules realistic enough to deceive radiologists into thinking they are real; Han et al. [54] and Mendes et al. [55] developed a conditional GAN framework for the creation of full 2D lung CT slices using semantic anatomical maps; Salehinejad et al. [56] utilised a deep convolutional GAN to generate high-resolution samples with synthetic interstitial pathological visual markers. The COVID-19 pandemic in 2020 also significantly increased the need for synthetic data for the sake of expediting the screening and diagnosis processes, thus prompting numerous GAN-based augmentation efforts [57,58,59,60]. This was due to the GAN framework’s versatility, seeing as its main strength is how it can combine its adversarial training nature with any other generative model, including VAEs. This is not, however, without drawbacks, as GANs are very data-sensitive [61] and prone to a phenomenon known as mode collapse [62]. Mostly though, early GAN approaches also lacked precise control over structural coherence and especially the fine detail intricacies of lung CT scans. As such, the newest state-of-the-art benchmarks in output quality and variability have been set by DDPMs, which traded the single-pass generation process used by GANs for an iterative denoising process with far superior results both in the understanding of underlying distributions and in the training stability [63,64]. A foundational and major advancement in 3D medical imaging generation was established by Khader et al. [65], who proved the success in applying this architecture for volumetric data and bypassed significant memory and complexity challenges to obtain wondrous results. Within the field of lung CT scan production specifically, diffusion models have been widely adopted: Jiang et al. [66] optimised an efficient diffusion model for thoracic CT scans by balancing perceptual quality and reduced computational expenses; Pan et al. [67] focused on displaying the scalability of transformer-based diffusion models for 2D synthesis, having achieved high fidelity slice-wise generation; Jiang et al. [68] utilised a Fast-DDPM for image-image translation, effectively proving that diffusion models can be a viable option for time-sensitive applications and real time inference; Chen et al. [69] who also addressed modality translation from cone-beam CT (CBCT) scans to regular CT images, eliminating the need for accurate dose calculation when performing CBCT radiotherapy; Daum 6 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT et al. [70] extended diffusion into the clinically relevant field of privacy protection by developing a differentiable 3D latent diffusion framework for secure medical image generation. Beyond unconditional synthesis and modality translation, diffusion models have also shown strong performance in conditional / pathology-aware generation as seen in the works by Kaur et al. [60] on COVID-19 chest X-ray generation, Zhang et al. [71] on multi scale conditioning and Zhao et al. [72] on visual modelling of CT scan disease progression. One other notable work in this same line is that of Olivera et al. [73] which succeeds at producing high-fidelity 3D chest CT volumes with explicit control over both global anatomy and local nodule features, thus marking a significant step forward towards clinically-relevant conditionally-aware 3D imaging synthesis. Finally, although these methods eliminate the threats of mode collapse, unstable training and imprecise control over fine-grained anatomical details, they suffer mostly from slower inference, which is, as shown by some of the works cited, a downside current research is actively working towards resolving. However, more than being solely dependant on architecture and pipeline choice, advancing the field of medical imaging synthesis requires moving towards clinical alignment and reflecting the workflow and priorities of radiological practice. One such example is provided by Tang et al. [74], who use disentangled representation learning to decompose pathological manifestation in chest X-rays from underlying anatomy. Similarly, Cao et al. [75] developed an anatomy- aware texture generation framework to effectively handle and control the synthesis of illness-caused anomalies separately from the image’s anatomical structure. And so, even though this pursuit for interpretability and control has manifested in a number of different works, none make an attempt at the task of generation while building upon HU-based preprocessing, which as shown by Hu et al. [76] is a foundational cornerstone of radiology workflow. Despite these advances, a common methodological limitation persists: most works handle lung CT data as if its intensity distribution is homogeneous, and can be modelled in its entirety without the need to address specific components separately. This, however, is contrary to radiology practice, where HU windowing is usually used to isolate and evidence specific intensity ranges / tissue types [76]. This oversight, creates a discrepancy between the synthesis process and radiologist’s interpretation of the data, which may result in harder acceptance of the technology and its output. It is also true that using single network frameworks to learn complex distributions of data that can be decomposed could be considered an inefficient use of resources, especially in environments where these are spread thin. Only one other prior work has explicitly decomposed the generation of this data type according to this clinically grounded HU windowing practice, although, in their work, Krishna et al. [77] depend on the existence of segmentation maps as a way to guide the generative process, which are not easily available and require the execution of unnecessary prior downstream tasks. To the best of our knowledge, this paper is the first to address these gaps by introducing a truly unbound generative HU-interval decomposition strategy which aligns generation with clinical workflow, while also improving upon the efficiency and output fidelity of lung CT synthesis. 3 Methodology 3.1 Full-range CT Reconstruction from HU Intervals LetX : V → H ⊂ Rdenote a CT scan as a function over the voxel domainV ⊂ Z 3 , where each voxel position corresponds to a HU value within the full HU rangeHof the scan. Then, consider a set of non-overlapping HU intervals, whose union does not necessarily cover the entire HU range of X . I =I 1 ,I 2 ,...,I K , I k = [hu min , hu max ], I i ∩ I j = ∅(10) For each intervalI k ∈ I,X k is defined as the result from a clipping transformation that retains the HU value ofX withinI k while setting values lower thanhu min tohu min and values greater thanhu max tohu max . Afterwards, both the original scan and the interval-clipped scans are min-max scaled to the unit range[0, 1]. Thus, the setX 1 ,X 2 ,...,X k represents multiple complementary views of the same CT scan, each capturing a limited portion of its original HU distribution. X k (v) = clip(X(v), hu min , hu max )− hu min hu max − hu min ,clip(h,a,b) = a,if h < a h, if h∈ [a,b] b,if h > b. (11) The first key objective of this study is to demonstrate that it is possible to reconstruct the full-range scanXfrom the collection of interval-clipped scansX k K k=1 using a learned reconstruction modelR. 7 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT Firstly, it should be noted that it is not possible to reconstructXfromX k using a fixed, linear or affine combination. In particular, there exists no coefficientsα k and bias β that satisfy X(v) = K X k=1 α k X k (v) + β, ∀v ∈V.(12) This impossibility arises because eachX k encodes a mapping from HU values to normalized intensities that are locally linear withinI k but globally inconsistent across the whole HU range. Furthermore, a voxel’s contribution to the reconstruction depends on which HU interval it originally belonged to, which varies across the image. To formalize this, it is possible to define binary masks that identify the active interval for each voxel as M k (v) = ( 1, if X k (v)∈ I k 0, otherwise. (13) The scaled full-range scan can then be expressed as a piecewise mapping X(v) = K X k=1 M k (φ k (v))· σ(φ k (v)),(14) where each composite functionσ(φ k (·))reprojects a HU intensity ofX k to the respective intensity inX. One can unfold the composition and describeφ k (·)as a transformation from the HU ofX k to its original value inI k , andσ(·) as a linear scaling function within the full-range ofX. However, if the union of HU intervals does not cover the whole CT scan HU range, then those HU values must still be deductible fromX k . In this context, a reconstruction modelR, defined by a deep neural network, can be trained to estimate reconstruction of XfromX k by implicitly learning to approximate the non-linear mask functionsM k (·), corresponding reprojection functionsφ k (·), as well as to model the reconstruction of HU values uncovered byI. This work explores the use of Multi-layer Perceptrons (MLPs) and CNNs of different feature sizes and depths to model the reconstruction of full-range CT scans given a collection of HU-clipped views of those same scans. The MLP models receive a vectorx v = [X 1 (v),X 2 (v),...,X K (v)] T ∈ [0, 1] K , representing theKscaled HU- window values at voxelv, and output a single scalar ˆ X(v)∈ [0, 1] . As depicted in Figure 4a, the MLP architectures consist of an input layer of sizeKfollowed by a variable number of full-connected (FC) layers, each also with feature size K. All hidden layers employ the ReLU activation function to introduce non-linearity, while the final output layer uses a Sigmoid activation to constrain the reconstructed voxel intensity to the[0, 1]range. By processing all voxels of the given images, the full-range CT reconstruction estimation is obtained. On the other hand, in contrast to the voxel-wise MLP networks, the CNN models operate at the image level. GivenK input imagesX 1 ,X 2 ,...,X K , each representing a scaled HU interval of a CT scan, the CNN receives aK-channel input tensor and predicts a single-channel output image ˆ X , corresponding to the scaled, reconstructed full-range CT. The architecture is composed of a sequence of convolutional layers, each followed by a ReLU activation function. All convolutional layers preserve both spatial resolution and the number of channels, matching the dimensionality of the input, except for the final convolutional layer, which reduces the feature dimension to a single channel. The final output layer employs a Sigmoid activation to ensure that the reconstructed HU values remain within the scaled range[0, 1]. A diagram of the CNN architectures is also displayed in Figure 4b. 3.2 Multiple HU Interval Generation The second core goal of this study lies in the synthesis of multiple HU interval representations that enable the generation of high-quality, realistic, full-range CT samples. Instead of training a model to directly generate full-range CT scans, the proposed methods learn to generate several HU interval representations, each reflecting a specific sub-range of tissue or material contrasts, such that their combination through a reconstruction model produces a realistic, full-range CT sample. Hence, the presented work aims at learning a generative model that produces a sequence sample ̃ X 1 , ̃ X 2 ,..., ̃ X K such that their reconstruction samples ̃ X =R( ̃ X k )create a full-range CT scan sample distributionp ̃ X similar to the original onep X . This objective was explored using three generative paradigms, WGAN-GP, score-based DMs, and VQVAEs, each adapted to handle multi-interval generation through different architectural variants. 8 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT Reconstruction MLP FC ReLU FC ReLU FC Sigmoid Variable Number of Blocks (a) Reconstruction CNN Conv ReLU Conv ReLU Conv Sigmoid Variable Number of Blocks (b) Figure 4: Illustration of the proposed CT reconstruction networks. (a) An MLP-based model that receives, for each voxel, a vector of clipped-scaled HU values sampled from the corresponding voxel location across multiple input slices, and predicts the scaled full-range HU value using a sequence of fully connected–ReLU blocks followed by a sigmoid output layer. (b) A CNN-based model that takes a K-channel image in which each channel encodes a clipped-scaled HU slice, and reconstructs the corresponding scaled full-range CT image through a series of convolution–ReLU blocks and a final convolutional layer with sigmoid activation. z G D Critic Score Dataset Reconstruction Model ❄ X k ~ X ~ X Figure 5: Multi-channel WGAN-GP framework. 3.2.1 Multi-channel Approaches The multi-channel modelling approach represents the most direct extension of traditional generative architectures to the multi-interval CT reconstruction setting. Its core idea lies in adapting single-channel generative frameworks to produce K-channel outputs, where each channel corresponds to a specific HU interval sample. This approach requires minimal modification to the original model architectures, therefore preserving inductive biases and optimization properties of the adapted framework. Since this modification can be applied seamlessly across diverse generative families, this multi-channel formulation can be regarded as a model-agnostic strategy for multiple HU interval generation. In the WGAN-GP configuration, as pictured in Figure 5, the generator networkGis adapted to produce a K-channel output, which is then passed through the reconstruction modelRto obtain the final single-channel sample. The reconstructed images are inputted to the critic network D, which compares it against real full-range CT images. 9 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT Dataset Noise Scheduler Time-informed U-Net X k X k (t) Predicted Score Figure 6: Multi-channel score-based diffusion model framework. Reconstruction Model Dataset ❄ X k X k X z q D E qz Codebook Z 1 2 C Transformer arg min p(s i | s <i ) Figure 7: Multi-channel VQVAE framework. For score-based DMs, the same principle applies, but the underlying architecture differs from the GAN framework. Here, a standard U-Net is employed to receive K-channel images and predict K-channel score values, displayed in Figure 6, thus directly modelling the denoising process in the multi-interval domain. Since the diffusion models in this work do not operate on direct image-prediction, the reconstruction modelRis not directly used during training. After sampling, theK-channel HU intervals samples are processed by the reconstruction modelRto obtain the full-range CT sample. Finally, in the VQVAE framework, the encoder-decoder architecture is modified to operate overK-channel inputs and outputs, similarly to the previous generative approaches. The encoderEcompresses the multi-interval input into a shared latent codebook representation, while the decoderDreconstructs the originalK-channel image from the quantized latent embeddings. The multi-channel framework for VQVAE is framed in Figure 7. This adaptation pushes the encoder to model shared representations of the various HU intervals on each codebook entry. After training, the transformer model produces the quantized latent sequence, which decoded byDproduces the HU samples. Lastly, these are given to the reconstruction modelR to produce the full-range CT synthetic image. 3.2.2 Multi-decoder and Multi-head Approaches While the multi-channel strategy provides a simple and model-agnostic way of extending single-channel generative models to the multi-interval setting, it does not explicitly separate the modelling of individual HU intervals. In particular, all interval representations share the same encoding and decoding pathways, which may limit the model’s ability to learn distinct statistical characteristics and textural details of specific HU ranges. To address this limitation, two alternative methods, multi-decoder and multi-head networks, were designed to provide finer modelling over interval-specific features. It is relevant to highlight that these approaches were implemented exclusively for the VQVAE generative framework, given that its two-stage structure divides the latent representation modelling and generative phases, offering greater flexibility for architectural modification in the encoding-decoding process. On one hand, the multi-decoder configuration is characterized by using a single encoder to process a concatenated, K-channel input representing the multiple HU clipped views, producing a unified latent representation that captures common structural information across HU intervals, as well as adjusting codebook entries to represent multiple textures for different HU content in the same quantized vector. Then, this representation is decoded independently byKdistinct decoder branches, each responsible for reconstructing one specific interval image. The outputs of these decoders are concatenated channel-wise and subsequently passed through the reconstruction modelRto obtain the final full-range CT sample. The described architecture is displayed in Figure 8. This approach encourages learning a shared latent representation, while allowing each decoder to specialize in each domain. 10 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT D Reconstruction Model Dataset ❄ X k X k X z q D E qz Codebook Z 1 2 C Transformer arg min p(s i | s <i ) D k Figure 8: Multi-decoder VQVAE framework. D k D k Reconstruction Model Dataset ❄ X k X k X z q qz Codebook Z 1 2 C Transformer arg min p(s i | s <i ) D k D E k E k E k E Figure 9: Multi-head VQVAE framework. On the other hand, the multi-head method introduces interval-specific modelling at both the encoding and decoding stages. It employsKseparate encoder heads, each dedicated to processing one HU interval input, followed by a shared encoder-decoder backbone that performs mid-fusion of each intervals extracted features from their respective encoder head. Similarly to the other approaches, this one also pushes the codebook to produce entries representative of the various HU views values. The shared decoder path of the backbone is then followed byKseparate decoder heads that reconstruct the corresponding interval outputs. The resultingKsingle-channel outputs are again concatenated and fed through the reconstruction modelRto yield the full-range CT sample. An illustration of the multi-head architecture is framed in Figure 9. Collectively, these VQVAE variant methods explore the trade-off between shared and specialized representations for multiple HU interval modelling in the same network. 3.2.3 Loss Function Formulations For both the WGAN-GP and score-based DM configurations, the loss functions remain consistent with their respective single-channel counterparts. However, the VQVAE loss used in this work extends the original definitions. Please note that the pre-trained reconstruction modelRis not updated or fine-tuned during any of the generative models training process. For the following formulations, let B stand for the batch size from which the given loss is being computed. WGAN-GP Loss.For WGAN-GP, the adversarial objective preserves its original formulation, where the Generator G and Critic D losses are described as in Equation 15 and 16, respectively. L G = 1 B B X b=1 h − D(R(G(z (b) ) i , z ∼N (0,I)(15) L D = 1 B B X b=1 h D(R(G(z (b) )))− D(X (b) ) + λ GP · (||∇ ̄ X (b) D( ̄ X (b) )|| 2 − 1) i , z ∼N (0,I)(16) Score-based DMs Loss.The denoising score-matching objective for diffusion models is computed over all K channels simultaneously, following the original score-predicting scheme. Note that when the perturbation kernel is Gaussian with variance σ(t) 2 , the score∇ x(t) logp 0t (x(t)|x(0)) has a defined closed form: X(t) = X(0) + σ(t)· ε, ε∼N (0,I) ⇒ ∇ X(t) logp 0t (X(t)|X(0)) = X(t)− X(0) σ(t) 2 =− ε σ(t) .(17) 11 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT Hence, the loss is defined as in Equation 18. L DM = 1 B B X b=1 h ||s(X(t (b) ),t (b) ) + ε (b) /σ(t (b) )|| 2 2 i , ε∼N (0,I)(18) VQVAE Loss.For all VQVAE methods considered in this work, the same loss function is used to train the autoencoder of the first training stage of the generative framework. The complete loss function is composed of three main loss terms: pre-reconstruction loss, post-reconstruction loss, and quantization loss. The first term is designed to optimize the synthesis of each individual HU interval before reconstruction to a full-range CT sample. For each intervalk, the VQVAE decoder output ̃ X k is compared with its corresponding ground-truthX k using a weighted combination of three complementary losses. The mean squared error (L MSE ) computes pixel-wise reconstruction. Then, the complementary of the structural similarity index (L SSIM ) accounts for structural consistency. The last term employs a perceptual loss (L RIN ) over feature vectors of ̃ X k andX k , extracted from a pre-trained ResNet-50 on the RadImageNet (RIN) dataset [78]. These losses are aggregated per interval and subsequently combined across all HU channels using a set of dynamic HU weights, in order to balance the influence of the losses across channels. More specifically, intervals containing a higher proportion of non-zero values receive larger weights, while sparse channels retain a minimum weight. The HU weights w k of the HU interval imagesX k from a CT scan image are computed as in Equation 19, which also guarantees that the sum of all weights amounts to one. w k = softmax n max #[X k > 0] |X k | ,w min , k ∈1, 2,...,K o (19) Then, the pre-reconstruction lossL Pre-Rec is defined as in Equation 20, whereλ Pre-MSE ,λ SSIM , andλ Pre-RIN are positive loss weights for each respective atomic loss term in the pre-reconstruction loss definition,L MSE ,L SSIM , and L RIN . L Pre-Rec = 1 B B X b=1 K X k=1 w (b) k · h λ Pre-MSE ·L MSE (X (b) k , ˆ X (b) k )+ λ SSIM ·L SSIM (X (b) k , ˆ X (b) k ) + λ Pre-RIN ·L RIN (X (b) k , ˆ X (b) k ) i (20) Afterwards, the second term ensures that the reconstruction from the generated HU interval samples outputted from the reconstruction modelRyields realistic and coherent full-range CT sample. The post-reconstruction loss (L Post-Rec ), described in Equation 21 is composed by the sum ofL MSE andL RIN on a full-range CT imageXand its full-range reconstructed version from the encoding-decoding process ˆ X =R( ˆ X k ) . The inclusion of this post-reconstruction term encourages independently learned HU interval representations contribute synergistically to an high-fidelity CT reconstruction. The termsλ Post-MSE , andλ Post-RIN are weight coefficients for the contribution ofL MSE andL RIN in the final total loss. L Post-Rec = 1 B B X b=1 h λ Post-MSE ·L MSE (X (b) , ˆ X (b) ) + λ Post-RIN ·L RIN (X (b) , ˆ X (b) ) i (21) Lastly, the quantization loss (L V Q ) composes the last term of the VQVAE loss formulation, corresponding to the standard commitment and codebook update objectives in the generative framework, as seen in Equation 22. This term stabilizes the discrete latent space by minimizing the discrepancy between continuous encoder embeddings and their quantized versions. The termλ V Q regularizes the weight of the quantization loss for the global VQVAE loss function. L V Q = λ V Q · 1 B B X b=1 h ||sg[E(X (b) )]− z (b) q || 2 2 +||sg[z (b) q ]− E(X (b) )|| 2 2 i (22) Collecting the terms above, the total loss function for the VQVAE networks used in this study is defined as: L V QV AE =L Pre-Rec +L Post-Rec +L V Q .(23) 12 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT Full-range[-950, -700][-500, -200][30, 70][100, 1000] Figure 10: Example of a full-range CT sample and its respective HU-clipped views for the HU intervals[−950,−700], [−500,−200], [30, 70] and [100, 1000]. Table 2: Configuration of the experimented reconstruction models Reconstruction ModelModel TypeParametersDescription MLP 0 MLP5Zero hidden layers MLP 4 MLP25One hidden layer with feature size 4 MLP 4×4 MLP45Two hidden layers, all with feature size 4 MLP 4×4×4 MLP65Three hidden layers, all with feature size 4 CNN 3 CNN37One convolution with kernel size 3 CNN 7 CNN197One convolution with kernel size 7 CNN 11 CNN485One convolution with kernel size 11 CNN 3×3 CNN185Two convolutions with kernel size 3 CNN 3×3×3 CNN333Three convolutions with kernel size 3 3.3 Dataset and Preprocessing The dataset employed in this study was derived from the publicly accessible Lung Image Database Consortium (LIDC- IDRI) collection [22,23]. This database is composed of 1,018 thoracic CT scans acquired for lung cancer screening, each represented as a 3D volume of sizeS× 512× 512, whereSdenotes the number of axial slices per scan. The dataset utilized adheres to the ethical approvals, ensured on the corresponding cited description paper. For this work, 80% of the volumes were allocated to the training set, while the remaining 20% where reserved for testing, ensuring that no slices from the same patient appear across both sets. Moreover, only slices corresponding to indices 30 through 90 of each CT volume were retained for analysis. Each CT slice undergoes a preprocessing step consistent with the data preparation described in the beginning of Section 3.1. More specifically, a new preliminary step is performed, where the original CT slice is first clipped to the range [−1000, 1000], and, afterwards, min-max scaled to[0, 1], setting the full-range baseline representation. Next, for each HU interval inI =[−950,−700], [−500,−200], [30, 70], [100, 1000], the HU interval representations were created using the same clipping and scaling procedure. Figure 10 displays an example of a full-range CT scan slice and its corresponding HU-windowed representations. The set of HU intervals previously defined was used throughout the entirety of the experiments of this work. The HU ranges were chosen considering the values in Table 1, and such that there is high independence between each HU views’ textural details. The final dataset contains around 50 thousand data points consisted of a full-range CT scan slice and respective HU-clipped interval views, amounting to a total of nearly 250 thousand images in this work. 3.4 Experimental Setup Firstly, in the first set of experiments, it was evaluated the feasibility of reconstructing full-range CT scans from their respective HU-restricted representations using Deep Learning models. The network architectures employed for this objective are summarized in Table 2. All reconstruction models were trained and tested under the same conditions to ensure fair results comparison. Each model was optimized using a mean squared error (MSE) loss and trained with the Adam optimizer (β 1 = 0.9, β 2 = 0.999) with a learning rate of5× 10 −5 , over 50 epochs with a batch of size 16. These hyperparameter values were chosen from empirical experimentation. The models performance was assessed using MSE, MS-SSIM, FID, 13 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT Table 3: Configuration of the experimented CT and HU generative models Model TypeApproachParameters (Millions)Reconstruction Model WGAN-GP Baseline6.4- Multi-channel6.8 MLP 0 CNN 3×3×3 Score-based DM Baseline72.3- Multi-channel72.3 MLP 0 CNN 3×3×3 VQVAE Baseline48.3- Multi-channel48.3 MLP 0 CNN 3×3×3 Multi-decoder68.9 MLP 0 CNN 3×3×3 Multi-head49.3 MLP 0 CNN 3×3×3 MMD, Precision and Recall metrics, computed across 10 independent test runs, each involving the reconstruction of 256 full-range CT scans slices from their corresponding HU-clipped views. Next, for the second set of experiments, it was investigated whether the proposed methods for generating full-range CT scans via the reconstruction of synthetically generated HU-interval representations yield superior results compared to models trained to produce full-range images directly. Table 3 details the generative model types (WGAN-GP, Score-based DMs or VQVAEs), architectural variants and reconstruction models employed in each experimental configuration. The Baseline approaches correspond to single-channel generative models trained directly on full-range CT images, serving as reference for evaluating the performance achieved by the proposed multi-interval generation methods. In the case of experiments using WGAN-GP models, the latent representations are 16-dimensional vectors sampled from Gaussian distribution,λ GP is set to 10, and the both the generator and critic networks use the Adam optimizer with beta parametersβ 1 = 0andβ 2 = 0.9with learning rate of10 −4 . The training stage was executed for 20 epochs with batch size 16. Afterwards, for the experiments with Score-based DMs, the linear noise scheduler usedβ min = 0.1andβ max = 20 and 1000 timesteps for sampling, and the networks were optimized with Adam (β 1 = 0.9andβ 2 = 0.999) and learning rate of 5× 10 −5 for 20 epochs with batch size 16. After, for all experiments that employed VQVAEs, the corresponding codebooks were constituted by 512 vectors of dimensionality 16, and the commitment loss weightλ c was set to0.5. Additionally, the multi-decoder approach utilizes, on each decoding branch, the exact same decoder architecture of the multi-channel network, except for the number of output channels. Identically, the multi-head model uses the exact same encoder-decoder backbone architecture of the multi-channel approach, and only one encoder/decoder layer per input/output head, with the same characteristics of the corresponding blocks in the multi-channel network. Finally, the weights in the VQVAE loss formulation to optimize the autoencoder network were set asλ Pre-MSE = 1.0, λ SSIM = 0.1,λ Pre-RIN = 1.0,λ Post-MSE = 0.1,λ Post-RIN = 0.25, andλ V Q = 1.0. Moreover, the HU minimum weight in Equation 19 was set asw min = 0.15. The first stage of training was conducted for 20 epochs with batch size 16, using the AdamW optimizer with beta parametersβ 1 = 0.9andβ 2 = 0.95and learning rate of10 −4 . Secondly, the transformer network was optimized with same AdamW optimizer and beta values, although with learning rate of 2× 10 −4 , over 50 epochs with simulated batch size of 64 with accumulated gradients of micro batch size 16. It is highlighted that all hyperparameter values were obtained through empirical experimentation, where various configurations were tested across multiple runs to optimize model performance. Regarding performance evaluation of the all generative models, 5 distinct runs of testing were conducted to compute the average value of FID, MMD, Precision and Recall between 256 generated samples from each model and 256 sampled real CT images, for both full-range views and HU-interval ones. The MS-SSIM metric was also used in this evaluation procedure to extract a variety metric within the synthetic collection of images in each test run, by computing the average MS-SSIM value between each possible pair of images from the sample set. Moreover, it was employed an indirect task-based evaluation strategy to assess the fidelity and utility of the generated images from the multi-head VQVAE with CNN 3×3×3 pipeline. Specifically, using the lung-area segmentation model 14 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT Table 4: MSE, FID, MMD, Precision, Recall and MS-SSIM metrics for each full-rage CT reconstruction model. Reconstruction Model MSE (×10 −4 )↓FID↓MMD (×10 −2 )↓Precision↑Recall↑MS-SSIM↑ MLP 0 4.6844.93.290.9690.9890.962 MLP 4 4.7444.63.210.9740.9880.962 MLP 4×4 4.7444.63.210.9740.9880.962 MLP 4×4×4 4.4641.92.930.9770.9950.964 CNN 3 4.6240.42.660.9890.9930.962 CNN 7 4.5440.12.680.9880.9930.962 CNN 1 14.5340.72.790.9870.9910.962 CNN 3×3 3.4534.82.150.9950.9960.979 CNN 3×3×3 2.4926.01.560.9991.0000.985 from [79], the synthetic full-range CT samples are provided as input to the network and, given that the anatomical structure of the lung regions are well defined, the segmentation output provides an objective proxy for assessing whether the generated images preserve meaningful anatomical features. It is worth noting that this is a qualitative assessment, as there are no ground-truth data from the unconditionally generated images to produce quantitative values. 3.5 Performance Evaluation Metrics To comprehensively assess the quality of reconstructed and generated CT slices, a combination of pixel-wise, distribu- tional, and structural metrics is employed. Reconstruction voxel error is quantified using the MSE between generated and ground-truth CT slices for the recon- struction models experiments, providing a direct measure of voxel-level intensity deviation. Next, Fréchet Inception Distance (FID) is reported to assess the alignment between real and generated data samples. In the case of this work, the features were extracted from the final average pooling layer of the ImageNet pre-trained InceptionV3 network, yielding 2048-dimensional vectors. Lower FID values indicate that the generated distribution more closely approximates the real data distribution in both mean and covariance, therefore reflecting higher perceptual fidelity and realism. Unlike FID, Maximum Mean Discrepancy (MMD) is a non-parametric measure of distributional divergence which does not assume Gaussian distribution of the feature space, making it complementary for assessing higher-order discrepancies. The MMD value is computed using the same InceptionV3 embeddings from FID, where smaller MMD values indicate greater similarity between the two distributions. Precision and Recall were adapted to assess the performance of generative image models by the proposed methodology of [80], which defines the fidelity and diversity of generated samples by comparing the manifold coverage of generated and real data distributions in a high-dimensional features space. For this study, the aforementioned embedding space used to obtain FID values was used as feature space, and the Precision and Recall values were obtained by implementing the algorithm provided by the cited work, where larger values indicate better performance. Precision measures the proportion of generated samples that lie within the support of the real data manifold, indicating the realism of the generated images, while Recall quantifies the fraction of real samples that are covered by the synthetic manifold, reflecting the generative diversity. Lastly, Multi-Scale Structural Similarity Index Measure (MS-SSIM) measures the structural similarity between two images across multiple spatial resolutions, combining luminance, contrast and structural comparisons at progressively coarser scales, yielding values in[0, 1], with higher values indicating greater structural similarity. Furthermore, low MS-SSIM quantifies structural dissimilarity across multiple spatial scales and if computed pairwise among samples serves as a quantitative proxy for structural variability within a sample distribution. 4 Results and Discussion 4.1 Full-range CT Reconstruction The performance of the proposed methods for full-range CT reconstruction from HU windows of those same scans is evaluated using MSE, FID, MMD, Precision, Recall and MS-SSIM. The quantitative results are summarized in Table 4, where bold-accentuated values indicate the best value obtained for the given performance metric. Additionally, visual examples of reconstructed test set slices from different MLP and CNN models are shown in Figure 11. 15 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT Original MLP 0 MLP 4×4×4 CNN 3 CNN 3×3×3 Example 1 Example 2 Example 3 Figure 11: Three full-range CT images reconstructed from four distinct models. The first column presents the original content of the full-range CT slices. The following columns frame the outputs of the reconstruction models MLP 0 , MLP 4×4×4 , CNN 3 , and CNN 3×3×3 , respectively, given the HU-clipped images of the original slice. It is verified that variations of the MLP architecture show similar results across all metrics, with MSE values ranging from 4.46×10 −4 to 4.74×10 −4 , FID values between 41.9 and 44.9, and MMD values from 2.93×10 −2 to 3.29×10 −2 , while the CNN variants with increasing convolutional kernel size and depth display greater incremental improvements. Among all configurations, CNN 3×3×3 obtained the best overall performance, reporting the lowest MSE of 2.49×10 −4 , FID of 26.0, and MMD of 1.56×10 −2 , while also achieving the best Precision and Recall values of 0.999 and 1.000 respectively, and the highest structural similarity with an MS-SSIM of 0.985. Moreover, reconstructed images from convolutional models exhibit smoother transitions between tissues of different HU intensities, although the images produced by MLP-based reconstruction models are identically detailed, where subtle differences are noticeable in some cherry-picked / specific regions. These qualitative differences between MLP and CNN reconstruction models can be attributed to their distinct inductive biases. While MLP architectures process voxels independently and therefore tend to preserve sharper local intensity transitions, convolutional models employ weight sharing and local receptive fields, which promote spatial coherence and smoother tissue boundaries, similar to what is present in real medical images. 4.2 CT and HU Interval Generation Next, the assessment of the HU generative models is executed not only for the entire HU range with the reconstructed CT image from the HU samples, but also across each HU interval image domain. Such stratified evaluation allows for a finer assessment of each model’s ability to reproduce tissue-specific image characteristics. The results are reported separately for each metric in the following sections. Apart from Table 9, for all the remaining results tables, light green and light red cells indicate better and worse performance compared to the corresponding baseline, respectively, while accentuated shades highlight the best and worst metric values within each generative model type. Furthermore, values in bold point to the approach that achieved the best result across all experiments. 16 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT Full-range[-950, -700][-500, -200][30, 70][100, 1000] Multi-channel VQVAE with CNN 3×3×3 Multi-decoder VQVAE with CNN 3×3×3 Multi-head VQVAE with CNN 3×3×3 Figure 12: Full-range CT and HU-windowed samples obtained from the proposed VQVAE methods and CNN 3×3×3 reconstruction model. 4.2.1 Qualitative Examples of Synthetic Lung CT and HU Samples This section presents examples of synthetic lung CT images generated by the VQVAE variants of the proposed method to qualitatively provide an illustrative overview of the visual characteristics achievable by the generative framework. Figure 12 illustrates synthetic samples from the aforementioned generative pipelines. The shown examples exhibit anatomically plausible lung structures with spatial coherence across HU windows, since lung parenchyma, surrounding soft tissue and skeleton structures are consistently preserved, and the reconstructed full-range images maintain clear correspondence with the windowed representations. These observations suggest effective learning of the anatomical and textural details for each HU interval domain and ability to produce structurally aligned images during sampling. On the other hand, minor grid-like texture patterns can be observed in some regions of the generated images, such as in the samples of the[30, 70]HU interval. These artifacts are commonly caused by the use of perceptual loss terms [81]. Importantly, however, such patterns do not alter the overall spatial coherence of the lung structures or alignment across HU windows, primarily affecting only local textural appearance. While these qualitative analysis highlight preliminary sample quality, the following sections present comprehensive quantitative results across models and metrics. 4.2.2 Assessment by FID Firstly, Table 5 reports the FID values computed per HU interval to assess the visual realism of the generated CT samples from all experiments. The baseline configurations highlight the performance difference across the generative model families, where the score- based DM and VQVAE models achieved considerably lower FID values (66.8 and 71.6 in full-range reconstruction, respectively) than the WGAN-GP’s (141.8). Moreover, the score-based DM obtained the lowest FID values for all HU intervals used in the work, ranging from 56.3 to 85.6 across the tested ranges. When analysing the multi-channel configurations, the results demonstrate that the approach improves the generative fidelity of HU windows images in the VQVAEs experiments, with the MLP 0 configuration achieving values as low as 52.9 in the[−500,−200]interval, while maintaining comparable performance to the baseline in the full-range reconstructed domain (76.3 and 75.7 for MLP 0 and CNN 3×3×3 variants respectively, compared to the baseline’s 71.6). 17 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT Table 5: FID computed per HU interval for each generative model configuration. Model Type Approach Reconstruction Model FID per HU Interval Full-range[−950,−700][−500,−200][30, 70][100, 1000] WGAN-GP Baseline-141.8117.5131.5157.2177.5 Multi-channel MLP 0 211.3196.1137.7134.7219.4 CNN 3×3×3 184.9145.0121.9138.2205.9 Score-based DM Baseline-66.881.356.385.681.2 Multi-channel MLP 0 84.9106.5134.9134.5192.3 CNN 3×3×3 85.9114.0140.4139.7194.7 VQVAE Baseline-71.695.565.2116.6105.5 Multi-channel MLP 0 76.375.852.983.774.6 CNN 3×3×3 75.777.666.179.275.3 Multi-decoder MLP 0 70.5100.070.586.776.3 CNN 3×3×3 67.981.469.277.477.2 Multi-head MLP 0 68.196.363.673.771.3 CNN 3×3×3 67.177.059.473.171.5 BaselineBestBetterWorseWorstGlobal Best In contrast, for WGAN-GP and DM models, the multi-channel configuration did not provide consistent gains, and in some cases led to performance degradation, with WGAN-GP reaching 211.3 and 184.9 in full-range reconstruction for MLP 0 and CNN 3×3×3 reconstruction network configurations respectively. The multi-decoder VQVAE configurations yielded noticeable improvements in the[30, 70]and[100, 1000]HU ranges, achieving 77.4 and 77.2 respectively with the CNN-based reconstruction model, while slightly under-performing in the remaining intervals. Despite not achieving uniformly lower FID values across all HU domains, the multi-decoder approach maintains baseline-level performance in full-range reconstruction (70.5 and 67.9 for MLP 0 and CNN 3×3×3 variants) while providing HU-specific samples whose feature distributions more closely match those of the original data. The multi-head configurations follow a similar trend but demonstrate superior overall performance, achieving the lowest FID values across most HU intervals, including the full-range domain with values of 68.1 and 67.1 using MLP 0 and CNN 3×3×3 respectively. It is also noted that the multi-head VQVAE with the CNN 3×3×3 reconstruction model was the only generative pipeline to obtain better results than the baseline approach in all HU ranges, as well as the experiment with lowest FID globally with a value of 67.1 in full-range reconstruction. Lastly, when comparing the results between the same generative methods with different CT reconstruction networks, the majority of the approaches employing the convolutional network outperformed the ones using MLP models. 4.2.3 Assessment by MMD Afterwards, Table 6 displays MMD values, comparing the discrepancy between the distributions of real and generated samples across HU intervals, for each generative pipeline configuration. The baseline configurations reveal substantial performance differences across generative model architectures, with the score-based DM achieving the lowest MMD values of 4.81×10 −2 in full-range reconstruction and ranging from 2.69 ×10 −2 to 5.31×10 −2 across all HU intervals, followed by VQVAE (6.31×10 −2 in full-range) and WGAN-GP (17.00 ×10 −2 ), similarly to what was registered in the respective FID scores. Examining the multi-channel experiments, the results indicate that this approach yielded improvements for VQVAE models across most HU intervals, achieving values as low as 2.92×10 −2 and 2.03×10 −2 for the MLP 0 configuration in the[−500,−200]and[100, 1000]intervals respectively, while maintaining competitive performance in full-range reconstruction with 6.56×10 −2 compared to the baseline’s 6.31×10 −2 . For WGAN-GP models, the multi-channel configuration showed mostly negative results, with full-range values increasing to 28.06×10 −2 and 23.14×10 −2 , although some improvements were observed in certain HU intervals such as[−500,−200]and[30, 70]. The score- based DM multi-channel pipeline exhibited worse performance for all HU ranges compared to its baseline model, with full-range values of 9.84×10 −2 and 7.95×10 −2 for MLP 0 and CNN 3×3×3 variants respectively. On the other hand, the multi-decoder VQVAE configurations demonstrated significant improvements for all HU ranges, achieving 4.89 ×10 −2 , 2.97×10 −2 , and 2.47×10 −2 for the[−950,−700],[30, 70], and[100, 1000]intervals respectively with the MLP 0 model, except in[−500,−200]where it displayed lower but close MMD values of 4.85×10 −2 . However, the multi-head VQVAE experiments demonstrated consistent increased performance for all HU domains in the CNN 3×3×3 18 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT Table 6: MMD computed per HU interval for each generative model configuration. Model Type Approach Reconstruction Model MMD (×10 −2 ) per HU Interval Full-range[−950,−700][−500,−200][30, 70][100, 1000] WGAN-GP Baseline-17.008.9314.5115.7816.24 Multi-channel MLP 0 28.0619.9615.089.0020.56 CNN 3×3×3 23.1411.8413.199.9418.69 Score-based DM Baseline-4.815.312.693.424.07 Multi-channel MLP 0 9.849.6917.7212.9820.53 CNN 3×3×3 7.959.5517.5413.2620.76 VQVAE Baseline-6.318.914.547.288.24 Multi-channel MLP 0 6.565.512.923.842.03 CNN 3×3×3 6.764.904.273.353.54 Multi-decoder MLP 0 5.506.844.933.972.14 CNN 3×3×3 5.204.894.852.972.47 Multi-head MLP 0 4.626.564.792.832.12 CNN 3×3×3 5.174.613.072.212.09 BaselineBestBetterWorseWorstGlobal Best Table 7: Precision computed per HU interval for each generative model configuration. Model Type Approach Reconstruction Model Precision per HU Interval Full-range[−950,−700][−500,−200][30, 70][100, 1000] WGAN-GP Baseline-0.0220.1210.1320.2620.056 Multi-channel MLP 0 0.0010.0040.1220.2690.034 CNN 3×3×3 0.0010.0620.2130.2100.029 Score-based DM Baseline-0.7470.6420.7800.6800.739 Multi-channel MLP 0 0.3110.2180.0660.3130.182 CNN 3×3×3 0.2080.2080.0680.2340.183 VQVAE Baseline-0.6390.4520.6340.5120.719 Multi-channel MLP 0 0.3820.6530.7890.6660.648 CNN 3×3×3 0.4160.6290.6080.6520.706 Multi-decoder MLP 0 0.4480.3480.5590.5450.689 CNN 3×3×3 0.5640.5410.5840.6510.652 Multi-head MLP 0 0.4540.3480.7000.7240.713 CNN 3×3×3 0.5760.6170.7020.7050.708 BaselineBestBetterWorseWorstGlobal Best variant, with full-range value of 5.17×10 −2 , while also detaining the lowest MMD values of 4.61×10 −2 and 2.21 ×10 −2 for the[−950,−700]and[30, 70]intervals respectively. Even so, the multi-head variant employing the MLP 0 reconstruction network obtained the lowest full-range MMD of all experiments with value 4.62×10 −2 . Comparing experiments that use different reconstruction networks, the convolutional models yield better results than their MLP counterparts across most configurations and HU intervals. 4.2.4 Assessment by Precision Table 7 frames the Precision values obtained for each experiment, reflecting each model’s fidelity of generated samples relative to the real data distribution. The baseline experiments demonstrate considerable variation in Precision across generative model families, with the score-based DM achieving the highest values in most HU intervals, followed by VQVAE and WGAN-GP. The score-based DM baseline obtained Precision values over 0.642 across all tested intervals, indicating strong alignment of generated samples with the original data manifold. When observing the multi-channel configurations, the results show that his approach failed to improve Precision values for WGAN-GP and score-based DM models compared to their respective baselines across most HU intervals. For 19 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT Table 8: Recall computed per HU interval for each generative model configuration. Model Type Approach Reconstruction Model Recall per HU Interval Full-range[−950,−700][−500,−200][30, 70][100, 1000] WGAN-GP Baseline-0.0160.0600.0480.0230.006 Multi-channel MLP 0 0.0030.0050.0450.0790.002 CNN 3×3×3 0.0000.0380.1190.0780.008 Score-based DM Baseline-0.2630.2820.4830.4270.464 Multi-channel MLP 0 0.1000.0730.0270.0440.007 CNN 3×3×3 0.1270.0600.0240.0340.004 VQVAE Baseline-0.1790.1090.4070.2350.301 Multi-channel MLP 0 0.1600.2630.4700.3070.509 CNN 3×3×3 0.2050.2020.4350.3770.507 Multi-decoder MLP 0 0.3540.1880.3660.3340.538 CNN 3×3×3 0.2170.2020.3820.4590.486 Multi-head MLP 0 0.3340.2430.3350.4240.474 CNN 3×3×3 0.2660.2390.4360.4320.482 BaselineBestBetterWorseWorstGlobal Best WGAN-GP, the multi-channel configuration with the convolutional reconstruction model showed great degradation in full-range Precision (0.001) compared to the baseline (0.022), although improvements were observed in specific intervals such as[−950,−700]and[−500,−200]. The score-based DM multi-channel approach similarly showed reduced Precision in the complete HU range, declining from 0.747 to 0.208 for the configuration paired with the convolutional reconstruction network. The VQVAE multi-channel, multi-decoder, and multi-head experiments all demonstrated reduced Precision values in full-range reconstruction relative to the baseline, with values ranging from 0.382 to 0.576 compared to the baseline value of 0.639. However, these methods achieved Precision values in specific HU intervals that exceed, or in certain cases closely approximate, those of the VQVAE baseline experiment. Notably, the multi-channel configuration with an MLP reconstruction network achieved 0.653 in the[−950,−700]interval and 0.789 in the[−500,−200]interval, the highest Precision values obtained across all experiments. The multi-head configuration together with CNN 3×3×3 demonstrated the most consistent Precision performance across all HU domains, with all values ranging from 0.576 to 0.708. 4.2.5 Assessment by Recall Recall is used to assess the diversity of generated samples, indicating how well each model covers the original data distribution. Table 8 lists Recall scores per HU interval for each generative experiment. The results from the baseline methods show that there is some difference between Recall performances across generative model types, with the score-based DM baseline achieving the highest values across all HU intervals, ranging from 0.263 to 0.483. The VQVAE baseline obtained Recall values between 0.109 and 0.407, while WGAN-GP demonstrated the lowest performance with values no exceeding 0.060 in any interval. When examining the multi-channel configurations, the results indicate that this approach did not surpass baseline performance for WGAN-GP and score-based DM models in most HU intervals. Despite showing some improvements in some HU intervals, the WGAN-GP multi-channel configurations showed very poor Recall values across all HU domains. The score-based DM multi-channel approaches displayed worse performance for all HU ranges, with the pipeline using the MLP reconstruction model achieving a Recall of 0.100 on full-range CT samples, and the convolutional version yielding 0.127. In contrast, the VQVAE multi-channel, multi-decoder, and multi-head configurations displayed substantial improvements in Recall values compared to the baseline across both full-range and HU-restricted domains. The multi-channel approach with MLP reconstruction network outputted the overall best Recall values for the[−950,−700]and[−500,−200] intervals, albeit achieving the worst VQVAE Recall value for full-range CT samples, similar to the baseline’s value. The multi-decoder approach coupled with MLP 0 obtained the highest full-range Recall among all experiments with 0.354, nearly doubling the baseline performance of 0.179. Furthermore, the multi-decoder approaches also achieved the best global Recall results for the[30, 70]and[100, 1000]ranges. Finally, the multi-head configurations maintained elevated Recall across all intervals, namely the one employing the CNN 3×3×3 reconstruction model which was one of 20 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT Table 9: MS-SSIM computed per HU interval, over all possible pairs of images of the synthetic sample set, for each generative model configuration. Model Type Approach Reconstruction Model MS-SSIM per HU Interval Full-range[−950,−700][−500,−200][30, 70][100, 1000] WGAN-GP Baseline-0.3920.3710.3840.3710.617 Multi-channel MLP 0 0.3820.3350.3570.4020.642 CNN 3×3×3 0.3730.3570.3730.4040.653 Score-based DM Baseline-0.3430.2910.3560.3390.659 Multi-channel MLP 0 0.3520.2930.3550.3400.642 CNN 3×3×3 0.3310.2960.3580.3440.642 VQVAE Baseline-0.3950.3700.4050.4320.756 Multi-channel MLP 0 0.3590.3360.3630.3370.646 CNN 3×3×3 0.3650.3290.3680.3710.754 Multi-decoder MLP 0 0.3390.3090.3430.3110.694 CNN 3×3×3 0.3650.3410.3680.3540.701 Multi-head MLP 0 0.3650.3110.3730.3630.698 CNN 3×3×3 0.3620.3290.3610.3540.714 Test Dataset0.3370.3210.3480.3270.644 Full-range [-950, -700] [-500, -200] [30, 70] WGAP-GP Multi-Channel with CNN 3×3×3 Score-based DM Multi-Channel with CNN 3×3×3 VQVAE Multi-Channel with CNN 3×3×3 [100, 1000] Figure 13: Sample examples with respective full-range and HU-windowed representations from the multi-channel approaches and CNN 3×3×3 reconstruction model. the experiments that outperformed the baseline across all HU ranges, alongside the multi-channel variant also paired with the convolutional reconstruction network. 4.2.6 Assessment of Sample Variety via MS-SSIM Finally, the intra-sample variety of generated images using MS-SSIM is examined. Table 9 shows MS-SSIM values across HU intervals, where lower scores indicate higher diversity among generated samples. For each generative model type and HU range, the lowest MS-SSIM value is underlined, and the global lowest values for each HU range are accentuated in bold. Moreover, some samples of different generative approaches are pictured in Figure 13, displaying some of the sample variety produced by the models. 21 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT Firstly, it is noted that the MS-SSIM was computed for the test set to obtain baseline sample variety scores for all HU ranges. The test set baseline achieved MS-SSIM values of 0.337 for full-range, 0.321 for the[−950,−700]interval, 0.348 for the [−500,−200] interval, 0.327 for the [30, 70] interval, and, lastly, 0.644 for the [100, 1000] interval. Considering the baseline experiments, MS-SSIM values range from 0.343 to 0.395, with the score-based DM baseline achieving the lowest value, followed by WGAN-GP and VQVAE. Looking into the multi-channel configurations for WGAN-GP and score-based DM models, reductions in MS-SSIM were observed compared to their respective baselines, although the differences remained small. The WGAN-GP multi-channel experiments achieved MS-SSIM values of 0.382 and 0.373 for the generative pipelines using the MLP 0 and CNN 3×3×3 respectively, while the score-based DM multi-channel approaches obtained 0.352 and 0.331. On the other hand, all VQVAE multi-channel, multi-decoder and multi-head configurations demonstrated lower MS-SSIM values than the baseline across most HU intervals. The multi-decoder configuration with MLP 0 yielded the lowest MS-SSIM values among VQVAE methods for almost all HU ranges, yielding a MS-SSIM value of 0.339 for the full-range CT samples. Specially, it is important to note that the MS-SSIM values obtained across all experimental configurations remained close to those of the test dataset, with full-range values spanning a relatively narrow range from 0.331 to 0.395. This pattern was also noted across all HU interval results, which further confirms the ability of the generative models to generate common tissue structures found in the images of each HU domain. The variation of MS-SSIM values across HU intervals aligns with known anatomical properties. For example, lung-tissue ranges exhibit lower MS-SSIM values around 0.33, reflecting higher structural variability across samples, while the[100,−1000]interval presents a significantly higher value of approximately 0.64, consistent with the rigid and homogeneous nature of bone structures. 4.3 Segmentation Task Qualitative Assessment Figure 14 illustrate generated full-range CT samples produced by the multi-head VQVAE generative model coupled with the CNN 3×3×3 reconstruction model, as well as their corresponding lung segmentation masks obtained using the segmentation model mentioned in Section 3.4. Despite the fact that analysis extracted from the Figure can only be qualitative, they provide indirect, yet informative, means of assessing whether the structural content of the synthetic samples is compatible with the expected input distributional properties of the downstream task model. Overall, the segmentation model is able to generate well-defined and anatomically coherent lung masks from the synthetic images, with the predicted segmentation masks consistently capturing the global shape of the lungs, preserving the separation of the left and right lobes, and adapting to variations in lung morphology across sampled images. The fact that a network trained on real CT data can successfully process and segment the generated samples indicates that the proposed generative pipeline produces images that lie within the effective input distribution expected by the segmentation model. This observation supports both the fidelity of the generated images and their utility for downstream tasks, as the synthetic data can be meaningfully interpreted by a separately trained model. Although Figure 14 demonstrates that the images are correctly processed by the segmentation pipeline, which points to good indirect performance from the proposed method of this work, some segmentation imperfections are visible, particularly in regions proximal to the mediastinum and pericardial cavity. These areas exhibit occasional inaccuracies or partial segmentation errors, reflecting a common challenge in both medical image segmentation and generative modelling, where complex and low-contrast anatomical boundaries are difficult to represent accurately. While these localized errors suggest that further improvements may be required to better capture fine-grained anatomical boundaries, pointing to potential directions for future work, it may also be a product of error propagation from the use of the segmentation DL model. The analysis of the heatmaps presented in figure 15 is crucial to understand the unconditional nature of the proposed generation method. Specifically, the discrepancy peaks being located at the lower lung region and near the hear indicate how having no control over the height valueZof the produced sample can affect overall results. In other words, since the real sample heatmap on the left includes all the slices forZ ∈ [30, 90]and there is no insight to be had into theZ values of the fake slices, we can assume such discrepancies stem from structural size differences across different height values. In the real dataset, this value will make the real lung and heart either less (peripheral slices) or more prominent (middle slices), but as there is no control over this variable, produced samples aim for a range of differentZvalues, which for the shown population seem to be more intermediate than peripheral. 4.4 Performance Across Generative Architectures Beyond metric-specific comparisons, other consistent patterns emerge when analysing the architectural design choices across the evaluated generative pipelines. 22 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT Sample Segmentation Sample Segmentation Figure 14: Synthetic full-range CT images sampled from the multi-head VQVAE and CNN 3×3×3 reconstruction model and respective segmentation masks outputted from the segmentation model from [79]. Multi-channel approaches are almost identical copies of their respective baseline architectures, with only the input and/or output layers of the networks changing dimensions, which introduces a negligible amount of learnable parameters to the generative pipeline. However, the data size increments proportionally to the number of HU intervals being used. This may lead to expect a performance drop for all multi-channel approaches compared to their respective baselines, since the the model capacity stays identical while the size the data distribution to be learned increases in complexity. This phenomenon was confirmed for the WGAN-GP and Score-based DMs approaches, where the multi-channel variations underperformed against their baselines for most of the HU windows, including full-range, across the various metrics. In contrast, the multi-channel VQVAE approaches consistently displayed better performance compared to its baseline across FID, MMD and Recall metrics and HU intervals. The VQVAE approaches likely benefit from the multi-channel formulation due to the discrete nature of their latent representation and the presence of a learned codebook. By quantizing latent features into a finite set of embeddings, the VQVAE effectively partitions the representation space into semantically meaningful regions, where, in this setting, different HU channels can be mapped to complementary subsets of the codebook, enabling specialization without enforcing direct competition within a shared continuous latent space. Across the evaluated metrics, the differences between multi-channel, multi-decoder, and multi-head VQVAE methods can be understood primarily as trade-offs between HU-specific specialization and global representational coherence. Despite forcing the encoding of the spatial coherence and elements of the various HU windows into a joint representation latent space, the multi-channel methodology also introduces challenges at the decoder level that can adversely affect both training stability and reconstruction quality. In particular, while spatial alignment across channels is generally well preserved, channel-specific textural details may be over-smoothed as gradients associated with disparate texture statistics interact through the shared decoder weights. In contrast, the multi-decoder approach targeted these limita- tions by decoupling the reconstruction of individual channels through multiple decoder branches, thereby reducing gradient interference and enabling channel-specific modelling and specialization in reconstructing the characteristics of corresponding HU intervals while preserving the shared spatial structure encoded by the latent representation. For the full-range CT images, the multi-decoder approaches achieved overall superior performance across all metrics compared to the multi-channel counterparts across the evaluated metrics. However, when performance is examined 23 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT Figure 15: Visual representation of the computed intensity heatmaps for both the full LIDC-IDRI dataset (left) and a population of 100 synthetic samples (center). The difference in sample number (1018 vs. 100) explains the texture difference between the real and fake heatmaps (blurry vs blocky). The rightmost image displays the difference between the two heatmaps and a color scale, revealing the maximum discrepancy between intensity distributions at any given pixel is valued at 30 out of 255. within individual HU domains, the relative ranking of the two approaches becomes considerably less stable. Depending on the specific HU interval and evaluation metric considered, either the multi-decoder or the multi-channel model may exhibit better performance, with no approach consistently dominating across all HU ranges. These observations may be attributed to the composite training loss in Equation 23, as the inclusion of the post-reconstruction termL Post-Rec can bias optimization toward representations that are most effective for the employed reconstruction model, rather than uniformly optimizing fidelity within each individual HU domain that is imposed by the pre-reconstruction termL Pre-Rec . In this context, the multi-decoder networks provide greater flexibility by allowing channel-specific reconstructions to adapt independently, thereby reducing interference and enabling convergence to representations that better support the full-range mapping. Conversely, the multi-channel approaches enforce tighter coupling at the decoder level, which may promote more uniform behaviour across HU domains but can restrict the model’s ability to allocate representational capacity in a manner that is better aligned with the reconstruction model expected inputs for higher fidelity full-range CT image synthesis. The multi-head formulation represents a structured formulation between the fully shared multi-channel design and the fully separated multi-decoder approach. By introducing channel-specific encoder heads, the model can capture low-level, HU-dependent appearance characteristics before projecting them into a shared latent space that encodes the common spatial and semantic structure across HU domains. On the decoding side, this shared representation is processed by a common decoder backbone to enforce global coherence, after which channel-specific decoder heads reproduce HU-specific textural details in the final reconstructions. Empirically, this balance translated into the most consistent and reliable performance across the experiments, with the multi-head models achieving the best results for many subsets of metrics and HU windows, most notably in FID and MMD for full-range CT images, while remaining competitive in cases where it was not the top-performing method. This consistency suggests that the multi-head method strikes a favourable balance between joint representation learning and HU-specific specialization, mitigating the limitations observed in the multi-channel and multi-decoder architectures inspected earlier. 4.5 Model Complexity and Performance Trade-off In addition to absolute reconstruction quality, model complexity plays a central role in determining the practical viability of generative architectures. Therefore, the relationship between performance and parameter count is examined across the evaluated models. The reconstruction models demonstrate a clear performance-complexity relationship, were increased capacity generally leads to improved reconstruction quality. While the simplest MLP-based models achieved great performance with extremely low parameter counts, they consistently underperform to their equivalently deep convolutional alternatives, particularly in distributional metrics such as FID and MMD. These substantial gains further highlight the advantage pro- 24 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT vided by the spatial inductive bias from the CNN reconstruction models compared to the fully-connected reconstruction networks. Moreover, it is worth noting that, although deeper convolutional configurations increase parameter count, the results obtained from these models translate to near-perfect HU-to-CT translations of the images at an extremely low memory footprint and parameter count. Next, despite the WGAN-GP methods presenting the most lightweight networks, with generators and critics adding up to 6.8 million parameters, their generative fidelity remains substantially lower than that of the remaining methods. Similarly, the score-based diffusion models, with approximately 72.3 million parameters, represent the most parameter-heavy approach among the experimented, yet consistently underperform all VQVAE variants across all evaluation metrics. Together, these suggest that, for the multiple HU-window generative task, neither adversarial training nor diffusion- based sampling effectively translated increased model capacity into superior reconstruction quality or distributional alignment. Regarding VQVAE approaches, the multi-channel VQVAEs maintains identical parameter counts to its the baseline VQVAE at approximately 48.3 million but shows limited gains in generative performance, indicating that naively extending the input dimensionality does not substantially improve representational capacity and reconstruction. In contrast, the multi-decoder VQVAE significantly increases model size to 68.9 million parameters due to the replication of decoder components in the network. While this configuration yields improvements over simpler variants, the gains are not proportional to the additional complexity and memory usage, resulting in a less efficient approach. The multi-head VQVAE achieves a notably better balance between capacity and performance, where, with only a marginal increase from 48.3 million to 49.3 million parameters compared to its baseline, it consistently matches or outperforms both multi-channel and multi-decoder designs. By combining channel-specific encoder and decoder heads with a shared latent space, the multi-head VQVAE approach supports the creation of stronger joint latent representation of all HU- views and allows for the specialization of each decoding unit into HU-specific restoration while avoiding the parameter count overhead of fully independent decoders. Consequently, it achieves the most favourable performance-complexity trade-off across the evaluated approaches. 4.6 Decoupled Generation and Reconstruction An additional practical implication of the proposed pipeline lies in the explicit decoupling of the generative process for HU-windowed views from full-range CT reconstruction and downstream usage. In this formulation, the HU samples act as intermediate representation that is generated once, store persistently, and subsequently reconstructed by a reconstruction model to recover a full-range representation on demand. This design is motivated by the pronounced asymmetry between the generative and reconstruction tasks computational costs, since the generative models are computationally intensive, both in terms of training and inference, whereas the reconstruction networks are compact and efficient. By isolating the expensive synthesis step, large collections of HU views can be produced offline and archived, while reconstruction can be performed dynamically as required by a given task, visualization protocol, or any other specialized application. In contrast, the finite number of HU-clipped samples that can be generated and stored imposes concerns regarding potential limitation of the diversity of full-range outputs. However, it rests on the assumption that the primary objective is to maximize the amount of full-range CT images, ignoring the utility of the HU-filtered images produced by the generative step of the proposed pipeline. 5 Conclusion In essence, this work introduced a novel framework for full-range lung CT scan slices synthesis based on modelling disjunctive HU domains, establishing HU-decomposition generation as a viable paradigm for CT image synthesis. By reformulating CT generation as a the synthesis of multiple HU-windowed representations followed by a learned reconstruction step, the proposed methodology addresses the complexity of modelling the full CT intensity distribution. Initial results demonstrate that full-range CT images can be accurately reconstructed from a limited set of non- overlapping HU intervals using extremely lightweight neural networks, achieving excellent reconstruction accuracy, distributional fidelity and structural similarity results with negligible computation cost. After extensive experimental evaluation among the explored generative approaches, the VQVAE-based methods consistently outperformed their baseline, contrary to the WGAN-GP and score-based DM ones. In particular, the multi-head VQVAE architecture achieves the most favourable balance between performance and complexity, delivering superior FID and MMD scores for full-range reconstructions while maintaining competitive Precision and Recall across all HU intervals, as well as adequate structural variety within the generated samples. 25 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT Beyond quantitative gains, the qualitative segmentation task assessment further supports the fidelity and utility of the generated images, showing that synthetic CT scans produced by the proposed pipeline are compatible with models trained on real data, although some localized imperfections remain in anatomically complex regions, which point towards future improvements in fine-grained boundary modelling. Furthermore, the proposed framework offers the ability to disconnected the computationally expensive generative process of the pipeline from the lightweight full-range reconstruction process, enabling the HU-windowed samples to become reusable for full-range CT slices reconstruction on demand. Future work may extend this framework to three-dimensional medical scan volumes, additional HU decompositions, or other imaging modalities where intensity-based semantics are meaningful, further reinforcing the role of clinically informed design in generative medical imaging research. Acknowledgments This work is supported by the European Commission funded PHASE IV AI project (Grant Agreement No. 101095384) under the European Union’s Horizon Europe research and innovation programme. Moreover, the authors acknowledge the National Cancer Institute and the Foundation for the National Institutes of Health, and their critical role in the creation of the free publicly available LIDC/IDRI Database used in this study. References [1]Freddie Bray, M. Laversanne, H. Sung, J. Ferlay, R. L. Siegel, I. Soerjomataram, and A. Jemal. Global cancer statistics 2022: Globocan estimates of incidence and mortality worldwide for 36 cancers in 185 countries. CA: A Cancer Journal for Clinicians, 2024. [2]Luella Marcos, Paul Babyn, and Javad Alirezaie. Generative AI in Medical Imaging and Its Application in Low Dose Computed Tomography (CT) Image Denoising, pages 387–401. Springer International Publishing, Cham, 2024. [3]Jiaxing Tan, Longlong Jing, Yumei Huo, Lihong Li, Oguz Akin, and Yingli Tian. Lgan: Lung segmentation in ct scans using generative adversarial network. Computerized Medical Imaging and Graphics, 87:101817, 2021. [4] Tami D. DenOtter and Johanna Schubert. Hounsfield Unit. StatPearls Publishing, Treasure Island (FL), 2025. [5] M.H. Lev and R.G. Gonzalez. 17 - ct angiography and ct perfusion imaging. In Arthur W. Toga and John C. Mazziotta, editors, Brain Mapping: The Methods (Second Edition), pages 427–484. Academic Press, San Diego, second edition edition, 2002. [6] Choong Ho Lee and Hyung-Jin Yoon. Medical big data: promise and challenges. Kidney research and clinical practice, 36(1):3, 2017. [7]Evgin Goceri. Medical image data augmentation: techniques, comparisons and interpretations. Artificial Intelligence Review, 56(11):12561–12605, 2023. [8] Hujun Yang, Zhongyang Wang, Xinyao Liu, Chuangang Li, Junchang Xin, and Zhiqiong Wang. Deep learning in medical image super resolution: a review. Applied Intelligence, 53(18):20891–20916, 2023. [9] Zhaohu Xing, Sicheng Yang, Sixiang Chen, Tian Ye, Yijun Yang, Jing Qin, and Lei Zhu. Cross-conditioned diffusion model for medical image to image translation. In Medical Image Computing and Computer Assisted Intervention – MICCAI 2024, pages 201–211, Cham, 2024. Springer Nature Switzerland. [10] Ian J Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio. Generative adversarial nets. Advances in neural information processing systems, 27, 2014. [11]Martin Arjovsky, Soumith Chintala, and Léon Bottou. Wasserstein generative adversarial networks. In Interna- tional conference on machine learning, pages 214–223. PMLR, 2017. [12]Ishaan Gulrajani, Faruk Ahmed, Martin Arjovsky, Vincent Dumoulin, and Aaron C Courville. Improved training of wasserstein gans. Advances in neural information processing systems, 30, 2017. [13]Jonathan Ho, Ajay Jain, and Pieter Abbeel. Denoising diffusion probabilistic models. Advances in neural information processing systems, 33:6840–6851, 2020. [14]Yang Song, Jascha Sohl-Dickstein, Diederik P Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. Score- based generative modeling through stochastic differential equations. In International Conference on Learning Representations, 2021. 26 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT [15]Pascal Vincent. A connection between score matching and denoising autoencoders. Neural computation, 23(7):1661–1674, 2011. [16] Yang Song, Conor Durkan, Iain Murray, and Stefano Ermon. Maximum likelihood training of score-based diffusion models. Advances in neural information processing systems, 34:1415–1428, 2021. [17]Robin Rombach, Andreas Blattmann, Dominik Lorenz, Patrick Esser, and Björn Ommer. High-resolution image synthesis with latent diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 10684–10695, June 2022. [18] Diederik Kingma, Tim Salimans, Ben Poole, and Jonathan Ho. Variational diffusion models. Advances in neural information processing systems, 34:21696–21707, 2021. [19]Aaron Van Den Oord, Oriol Vinyals, et al. Neural discrete representation learning. Advances in neural information processing systems, 30, 2017. [20] Patrick Esser, Robin Rombach, and Bjorn Ommer. Taming transformers for high-resolution image synthesis. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 12873–12883, June 2021. [21]Yoshua Bengio, Nicholas Léonard, and Aaron Courville. Estimating or propagating gradients through stochastic neurons for conditional computation, 2013. [22]Samuel G Armato I, Geoffrey McLennan, Luc Bidaut, Michael F McNitt-Gray, Charles R Meyer, Anthony P Reeves, Binsheng Zhao, Denise R Aberle, Claudia I Henschke, Eric A Hoffman, et al. The lung image database consortium (lidc) and image database resource initiative (idri): a completed reference database of lung nodules on ct scans. Medical physics, 38(2):915–931, 2011. [23]Samuel G. Armato I, Geoffrey McLennan, Luc Bidaut, Michael F. McNitt-Gray, Charles R. Meyer, and et al. Data from lidc-idri.https://doi.org/10.7937/K9/TCIA.2015.LO9QL9SX, 2015. The Cancer Imaging Archive. [24]W. P. Segars, G. Sturgeon, S. Mendonca, Jason Grimes, and B. M. W. Tsui.4D XCAT phan- tom for multimodality imaging research.Medical Physics, 37(9):4902–4915, 2010._eprint: https://aapm.onlinelibrary.wiley.com/doi/pdf/10.1118/1.3480985 TLDR: The XCAT provides an important tool in imaging research to evaluate and improve imaging devices and techniques and may also provide the necessary foundation with which to optimize clinical CT applications in terms of image quality versus radiation dose. [25]L. A. Shepp and B. F. Logan. The Fourier reconstruction of a head section. IEEE Transactions on Nuclear Science, 21(3):21–43, June 1974. TLDR: The authors compare the Fourier algorithm and a search algorithm using a simulated phantom to speed the search algorithm by using fewer interactions leaves decreased resolution in the region just inside the skull which could mask a subdural hematoma. [26] René Werner, Jan Ehrhardt, Rainer Schmidt, and Heinz Handels. Patient-specific finite element modeling of respiratory lung motion using 4D CT image data. Medical Physics, 36(5):1500–1511, May 2009. TLDR: Outcomes show that the modeling approach is an adequate strategy in predicting lung dynamics due to lung ventilation, and the decreased prediction quality in cases of large tumors demands further study of the influence of lung tumors on global and local lung elasticity properties. [27]T. F. Cootes, C. J. Taylor, D. H. Cooper, and J. Graham. Active shape models-their training and application. Computer Vision and Image Understanding, 61(1):38–59, January 1995. TLDR: This work describes a method for building models by learning patterns of variability from a training set of correctly annotated images that can be used for image search in an iterative refinement algorithm analogous to that employed by Active Contour Models (Snakes). [28] T.F. Cootes, G.J. Edwards, and C.J. Taylor. Active appearance models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(6):681–685, June 2001. [29] Juan Eugenio Iglesias and Mert R. Sabuncu. Multi-atlas segmentation of biomedical images: a survey. Medical Image Analysis, 24(1):205–219, August 2015. TLDR: A survey of published MAS algorithms and studies that have applied these methods to various biomedical problems and a perspective on the future of MAS, which, it is believed, will be one of the dominant approaches in biomedical image segmentation. [30] Sanuwani Dayarathna, Kh Tohidul Islam, Sergio Uribe, Guang Yang, Munawar Hayat, and Zhaolin Chen. Deep learning based synthesis of MRI, CT and PET: Review and analysis. Medical Image Analysis, 92:103046, February 2024. TLDR: This survey comprehensively reviews deep learning-based medical imaging translation from 2018 to 2023 on pseudo-CT, synthetic MR, and synthetic PET, and provides an overview of synthetic contrasts in medical imaging and the most frequently employed deep learning networks for medical image synthesis. 27 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT [31]Aryan Nikul Patel and Kathiravan Srinivasan. Deep learning paradigms in lung cancer diagnosis: A methodological review, open challenges, and future directions. Physica Medica: European Journal of Medical Physics, 131, March 2025. Publisher: Elsevier TLDR: This methodological review comprehensively explores deep learning models’ application in lung cancer diagnosis, uncovering their integration across various imaging modalities and emphasizing the potential of deep learning to significantly improve the precision and efficiency of lung cancer diagnosis. [32]Wessam M. Salama, Ahmed Shokry, and Moustafa H. Aly. A generalized framework for lung cancer classification based on deep generative models. Multimedia Tools and Applications, 81(23):32705–32722, September 2022. [33]David Zimmerer, Fabian Isensee, Jens Petersen, Simon Kohl, and Klaus Maier-Hein. Unsupervised anomaly localization using variational auto-encoders, July 2019. [34]Irem Cetin, Maialen Stephens, Oscar Camara, and Miguel A. González Ballester. Attri-VAE: Attribute-based interpretable representations of medical images with variational autoencoders. Computerized Medical Imaging and Graphics, 104:102158, March 2023. TLDR: This paper proposes a VAE approach that includes an attribute regularization term to associate clinical and medical imaging attributes with different regularized dimensions in the generated latent space, enabling a better-disentangled interpretation of the attributes. [35] Maya Varma, Ashwin Kumar, Rogier van der Sluijs, Sophie Ostmeier, Louis Blankemeier, Pierre Chambon, Christian Bluethgen, Jip Prince, Curtis Langlotz, and Akshay Chaudhari. MedVAE: efficient automated interpre- tation of medical images with large-scale generalizable autoencoders, June 2025. TLDR: This work addresses the challenge of downsizing medical images in order to improve downstream computational efficiency while preserving clinically-relevant features and introduces MedVAE, a family of six large-scale 2D and 3D autoencoders capable of encoding medical images as downsized latent representations and decoding latent representations back to high-resolution images. arXiv:2502.14753 [eess]. [36]Khadija Rais, Mohamed Amroune, Abdelmadjid Benmachiche, and Mohamed Yassine Haouam. Exploring Varia- tional Autoencoders for Medical Image Generation: A Comprehensive Study, November 2024. arXiv:2411.07348 [cs] TLDR: This study reviews important architectures and methods used to develop VAEs for medical images and provides a comparison with other generative models such as GANs on issues such as image quality, and low diversity of generated samples. [37]Gang Liu, Fei Liu, Jun Gu, Xu Mao, XiaoTing Xie, and Jingyao Sang. An attention-based deep learning network for lung nodule malignancy discrimination. Frontiers in Neuroscience, 16:1106937, January 2023. [38]Yiheng Li, Christoph Y. Sadée, Francisco Carrillo-Perez, Heather M. Selby, Alexander H. Thieme, and Olivier Gevaert. A 3D lung lesion variational autoencoder. Cell Reports Methods, 4(2):100695, January 2024. TLDR: A 3D beta variational autoencoder (beta-VAE) to advance lung cancer imaging analysis, countering the constraints of conventional radiomics methods and suggesting its potential as a pretrained model for predicting patient outcomes in medical imaging. [39]Charmi Patel, Yiyang Wang, Roselyne Tchoua, Alexandru Orhean, Jacob Furst, and Daniela Raicu. Enhancing lung nodule classification with variational autoencoder-based image augmentation. April 2025. [40]Dong Nie, Roger Trullo, Jun Lian, Li Wang, Caroline Petitjean, Su Ruan, Qian Wang, and Dinggang Shen. Medical image synthesis with deep convolutional adversarial networks. IEEE Transactions on Biomedical Engineering, 65(12):2720–2730, December 2018. [41] Xiao Han. MR-based synthetic CT generation using a deep convolutional neural network method. Medical Physics, 44(4):1408–1419, 2017. _eprint: https://aapm.onlinelibrary.wiley.com/doi/pdf/10.1002/mp.12155 TLDR: A novel deep convolutional neural network (DCNN) method was developed and shown to be able to produce highly accurate sCT estimations from conventional, single-sequence MR images in near real time. [42]Xiaoran Chen, Suhang You, Kerem Can Tezcan, and Ender Konukoglu. Unsupervised lesion detection via image restoration with a normative prior, April 2020. arXiv:2005.00031 [eess]. [43]Chaitanya Singla, Rajat Bhardwaj, Nilesh Shelke, and Gurpreet Singh. Data augmentation: synthetic image generation for medical images using vector quantized variational autoencoders. In 2025 3rd International Conference on Disruptive Technologies (ICDT), pages 1502–1507, March 2025. [44]Xiaoran Chen, Nick Pawlowski, Martin Rajchl, Ben Glocker, and Ender Konukoglu. Deep generative models in the real-world: an open challenge from medical imaging, June 2018. arXiv:1806.05452 [cs]. [45]Hoo-Chang Shin, Neil Tenenholtz, Jameson Rogers, Christopher Schwarz, Matthew Senjem, Jeffrey Gunter, Katherine Andriole, and Mark Michalski. Medical image synthesis for data augmentation and anonymization using generative adversarial networks: third international workshop, SASHIMI 2018, held in conjunction with MICCAI 2018, granada, spain, september 16, 2018, proceedings. pages 1–11. September 2018. 28 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT [46]Youssef Skandarani, Pierre-Marc Jodoin, and Alain Lalande. GANs for medical image synthesis: an empirical study, July 2021. arXiv:2105.05318 [eess]. [47] Salome Kazeminia, Christoph Baur, Arjan Kuijper, Bram van Ginneken, Nassir Navab, Shadi Albarqouni, and Anirban Mukhopadhyay. GANs for medical image analysis. Artificial Intelligence in Medicine, 109:101938, September 2020. [48]Luis Gonzalez-Abril, Cecilio Angulo, Juan Antonio Ortega, José-Luis Lopez-Guerra, Luis Gonzalez-Abril, Cecilio Angulo, Juan Antonio Ortega, and José-Luis Lopez-Guerra. Statistical validation of synthetic data for lung cancer patients generated by using generative adversarial networks. Electronics, 11(20), October 2022. Company: Multidisciplinary Digital Publishing Institute Distributor: Multidisciplinary Digital Publishing Institute Institution: Multidisciplinary Digital Publishing Institute Label: Multidisciplinary Digital Publishing Institute Publisher: publisher. [49] Joshua R Astley, Jim M Wild, and Bilal A Tahir. Deep learning in structural and functional lung image analysis. The British Journal of Radiology, 95(1132):20201107, April 2022. TLDR: Concerns over inconsistent validation and evaluation strategies, intersite generalisability, transparency of methodological detail and interpretability need to be addressed before widespread adoption in clinical lung imaging workflow. [50]Qingsong Yang, Pingkun Yan, Yanbo Zhang, Hengyong Yu, Yongyi Shi, Xuanqin Mou, Mannudeep K. Kalra, Yi Zhang, Ling Sun, and Ge Wang. Low-dose CT image denoising using a generative adversarial network with wasserstein distance and perceptual loss. IEEE Transactions on Medical Imaging, 37(6):1348–1357, June 2018. TLDR: This paper introduces a new CT image denoising method based on the generative adversarial network (GAN) with Wasserstein distance and perceptual similarity that is capable of not only reducing the image noise level but also trying to keep the critical information at the same time. [51] Jelmer M. Wolterink, Tim Leiner, Max A. Viergever, and Ivana Išgum. Generative adversarial networks for noise reduction in low-dose CT. IEEE Transactions on Medical Imaging, 36(12):2536–2545, December 2017. [52]Maria J. M. Chuquicusma, Sarfaraz Hussein, Jeremy Burt, and Ulas Bagci. How to fool radiologists with generative adversarial networks? A visual turing test for lung cancer diagnosis, January 2018. arXiv:1710.09762 [cs]. [53]Dakai Jin, Ziyue Xu, Youbao Tang, Adam P. Harrison, and Daniel J. Mollura. CT-realistic lung nodule simulation from 3D conditional generative adversarial networks for robust lung segmentation, June 2018. arXiv:1806.04051 [cs]. [54]Changhee Han, Yoshiro Kitamura, Akira Kudo, Akimichi Ichinose, Leonardo Rundo, Yujiro Furukawa, Kazuki Umemoto, Yuanzhong Li, and Hideki Nakayama. Synthesizing diverse lung nodules wherever massively: 3D multi-conditional GAN-based CT image augmentation for object detection. September 2019. Pages: 737. [55]José Mendes, Tania Pereira, Francisco Silva, Julieta Frade, Joana Morgado, Cláudia Freitas, Eduardo Negrão, Beatriz Flor de Lima, Miguel Correia da Silva, António J. Madureira, Isabel Ramos, José Luís Costa, Venceslau Hespanhol, António Cunha, and Hélder P. Oliveira. Lung CT image synthesis using GANs. Expert Systems with Applications, 215:119350, April 2023. [56] Hojjat Salehinejad, Errol Colak, Tim Dowdell, Joseph Barfett, and Shahrokh Valaee. Synthesizing chest X-ray pathology for training deep convolutional neural networks. IEEE transactions on medical imaging, 38(5):1197– 1206, May 2019. [57]Zonggui Li, Junhua Zhang, Bo Li, Xiaoying Gu, and Xudong Luo. COVID-19 diagnosis on CT scan images using a generative adversarial network and concatenated feature pyramid network with an attention mechanism. Medical Physics, 48(8):4334–4349, August 2021. TLDR: The method can help clinicians build deep learning models using their private datasets to achieve automatic diagnosis of COVID-19 with a high precision and helps overcome the problem of limited training data when using deep learning methods to diagnose CO VID-19. [58]Sumeet Menon, Jayalakshmi Mangalagiri, Josh Galita, Michael Morris, Babak Saboury, Yaacov Yesha, Yelena Yesha, Phuong Nguyen, Aryya Gangopadhyay, and David Chapman. CCS-GAN: COVID-19 CT scan generation and classification with very few positive training images. Journal of Digital Imaging, 36(4):1376–1389, August 2023. TLDR: A novel algorithm is presented that is able to generate deep synthetic COVID-19 pneumonia CT scan slices using a very small sample of positive training images in tandem with a larger number of normal images to enable a DNN classifier to achieve high classification accuracy. [59] Mohamed Loey, Florentin Smarandache, Nour Eldeen M. Khalifa, Mohamed Loey, Florentin Smarandache, and Nour Eldeen M. Khalifa. Within the lack of chest COVID-19 X-ray dataset: a novel detection model based on GAN and deep transfer learning. Symmetry, 12(4), April 2020. Company: Multidisciplinary Digital Publishing Institute Distributor: Multidisciplinary Digital Publishing Institute Institution: Multidisciplinary Digital Publishing Institute Label: Multidisciplinary Digital Publishing Institute Publisher: publisher TLDR: The main idea is to 29 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT collect all the possible images for COVID-19 that exists until the writing of this research and use the GAN network to generate more images to help in the detection of this virus from the available X-rays images with the highest accuracy possible. [60]Sehajpreet Kaur, Shivansh Kumar, and Hajar Homayouni. Synthetic High-Resolution COVID-19 Chest X-Ray Generation. In ACM Other conferences, pages 151–159, Melbourne VIC Australia, January 2023. ACM. Archive Location: world. [61]Sam Ellis, Octavio E. Martinez Manzanera, Vasileios Baltatzis, Ibrahim Nawaz, Arjun Nair, Loïc Le Folgoc, Sujal Desai, Ben Glocker, and Julia A. Schnabel. Evaluation of 3D GANs for lung tissue modelling in pulmonary CT, August 2022. arXiv:2208.08184 [eess]. [62] Hoang Thanh-Tung and Truyen Tran. On catastrophic forgetting and mode collapse in generative adversarial networks, March 2020. arXiv:1807.04015 [cs] version: 8. [63]Yaqing Shi, Abudukelimu Abulizi, Hao Wang, Ke Feng, Nihemaiti Abudukelimu, Youli Su, and Halidanmu Abudukelimu. Diffusion models for medical image computing: a survey. Tsinghua Science and Technology, 30(1):357–383, January 2025. [64] Muhammad Usman Akbar, Wuhao Wang, and Anders Eklund. Beware of diffusion models for synthesizing medical images – A comparison with GANs in terms of memorizing brain MRI and chest x-ray images, July 2024. arXiv:2305.07644 [eess] TLDR: Results show that diffusion models are much more likely to memorize the training images, especially for small datasets, and researchers should be careful when using diffusion models for medical imaging, if the final goal is to share the synthetic images. [65]Firas Khader, Gustav Müller-Franzes, Soroosh Tayebi Arasteh, Tianyu Han, Christoph Haarburger, Maximilian Schulze-Hagen, Philipp Schad, Sandy Engelhardt, Bettina Baeßler, Sebastian Foersch, Johannes Stegmaier, Christiane Kuhl, Sven Nebelung, Jakob Nikolas Kather, and Daniel Truhn. Denoising diffusion probabilistic models for 3D medical image generation. Scientific Reports, 13(1):7303, May 2023. TLDR: It is shown that diffusion probabilistic models can synthesize high-quality medical data for magnetic resonance imaging (MRI) and computed tomography (CT) and can be used in self-supervised pre-training and improve the performance of breast segmentation models when data is scarce. [66]Yifan Jiang, Ahmad Shariftabrizi, and Venkata S. K. Manem. Lung-DDPM+: Efficient thoracic CT image synthesis using diffusion probabilistic model. Computers in Biology and Medicine, 199:111290, December 2025. TLDR: It is demonstrated that Lung-DDPM+ can effectively generate high-quality thoracic CT images with lung nodules, highlighting its potential for broader applications, such as general tumor synthesis and lesion generation in medical imaging. [67]Shaoyan Pan, Tonghe Wang, Richard L. J. Qiu, Marian Axente, Chih-Wei Chang, Junbo Peng, Ashish B. Patel, Joseph Shelton, Sagar A. Patel, Justin Roper, and Xiaofeng Yang. 2D medical image synthesis using transformer- based denoising diffusion probabilistic model. Physics in Medicine and Biology, 68(10):105004, May 2023. TLDR: A 2D image synthesis framework based on a diffusion model using a Swin-transformer-based network that can generate high-quality medical images of different imaging modalities with the purpose of supplementing existing training sets for AI model deployment is introduced. [68]Hongxu Jiang, Muhammad Imran, Teng Zhang, Yuyin Zhou, Muxuan Liang, Kuang Gong, and Wei Shao. Fast- DDPM: fast denoising diffusion probabilistic models for medical image-to-image generation. IEEE Journal of Biomedical and Health Informatics, 29(10):7326–7335, October 2025. TLDR: Fast-DDPM is introduced, a simple yet effective approach capable of simultaneously improving training speed, sampling speed, and generation quality in medical imaging, and outperformed DDPM and current state-of-the-art methods based on convolutional networks and generative adversarial networks in all tasks. [69]Xiaoqian Chen, Richard L.J. Qiu, Junbo Peng, Joseph W. Shelton, Chih-Wei Chang, Xiaofeng Yang, and Aparna H. Kesarwala. CBCT-based Synthetic CT Image Generation Using a Diffusion Model for CBCT-Guided Lung Radiotherapy. Medical physics, 51(11):8168–8178, November 2024. [70]Deniz Daum, Richard Osuala, Anneliese Riess, Georgios Kaissis, Julia A. Schnabel, and Maxime Di Folco. On differentially private 3D medical image synthesis with controllable latent diffusion models, July 2024. arXiv:2407.16405 [eess] TLDR: This work proposes Latent Diffusion Models that generate synthetic images conditioned on medical attributes, while ensuring patient privacy through differentially private model training, and is the first work to apply and quantify differential privacy in 3D medical image generation. [71]Sicheng Zhang, Jin Liu, Bo Hu, and Zhendong Mao. GH-DDM: the generalized hybrid denoising diffusion model for medical image generation. Multimedia Systems, 29(3):1335–1345, June 2023. TLDR: The Generalized Hybrid Denoising Diffusion Model (GH-DDM) is presented, which leverages the strong abilities of transformers into diffusion models to model long-range interactions and spatial relationships between anatomical structures, and 30 HUydra: Full-Range Lung CT Synthesis via Multiple HU Interval Generative ModellingA PREPRINT further proposes several key modifications to make the model easy to generalize to various kinds of generation tasks. [72]An Zhao, Moucheng Xu, Ahmed H. Shahin, Wim Wuyts, Mark G. Jones, Joseph Jacob, and Daniel C. Alexander. 4D VQ-GAN: synthesising medical scans at any time point for personalised disease progression modelling of idiopathic pulmonary fibrosis, February 2025. arXiv:2502.05713 [eess] TLDR: 4D Vector Quantised Generative Adversarial Networks (4D-VQ-GAN) is proposed, a model capable of generating realistic CT volumes of IPF patients at any time point and can reliably predict survival outcomes. [73]Anna Oliveras, Roger Marí, Rafael Redondo, Oriol Guardià, Ana Tost, Bhalaji Nagarajan, Carolina Migliorelli, Vicent Ribas, and Petia Radeva. LAND: Lung and Nodule Diffusion for 3D Chest CT Synthesis with Anatomical Guidance, October 2025. arXiv:2510.18446 [cs] TLDR: A new latent diffusion model is introduced to generate high-quality 3D chest CT scans conditioned on 3D anatomical masks to support the generation of diverse CT volumes with and without lung nodules of varying attributes, providing a valuable tool for training AI models or healthcare professionals. [74]Youbao Tang, Yuxing Tang, Yingying Zhu, Jing Xiao, and Ronald M. Summers. A disentangled generative model for disease decomposition in chest X-rays via normal image synthesis. Medical Image Analysis, 67:101839, January 2021. [75]Qinyi Cao, Jianan Fan, and Weidong Cai. ART-ASyn: anatomy-aware realistic texture-based anomaly synthesis framework for chest X-rays, November 2025. arXiv:2512.00310 [cs]. [76] Shiying Hu, Eric Hoffman, and Joseph Reinhardt. Automatic lung segmentation for accurate quantitation of volumetric X-ray CT images. IEEE transactions on medical imaging, 20:490–8, July 2001. [77]Arjun Krishna, Shanmukha Yenneti, Ge Wang, and Klaus Mueller. Image factory: a method for synthesizing novel CT images with anatomical guidance. Medical physics, 51(5):3464–3479, May 2024. [78]Xueyan Mei, Zelong Liu, Philip M. Robson, Brett Marinelli, Mingqian Huang, Amish Doshi, Adam Jacobi, Chendi Cao, Katherine E. Link, Thomas Yang, Ying Wang, Hayit Greenspan, Timothy Deyer, Zahi A. Fayad, and Yang Yang. Radimagenet: An open radiologic deep learning research dataset for effective transfer learning. Radiology: Artificial Intelligence, 4(5):e210315, 2022. PMID: 36204533. [79]Joana Sousa, Tania Pereira, Inês Neves, Francisco Silva, and Hélder P Oliveira. The influence of a coherent annotation and synthetic addition of lung nodules for lung segmentation in ct scans. Sensors, 22(9):3443, 2022. [80] Tuomas Kynkänniemi, Tero Karras, Samuli Laine, Jaakko Lehtinen, and Timo Aila. Improved precision and recall metric for assessing generative models. Advances in neural information processing systems, 32, 2019. [81]Justin Johnson, Alexandre Alahi, and Li Fei-Fei. Perceptual losses for real-time style transfer and super-resolution. In European conference on computer vision, pages 694–711. Springer, 2016. 31