Improving 2D Diffusion Models for 3D Medical Imaging with Inter‑Slice Consistent Stochasticity
Authors: Chenhe Du
Qing Wu
Xuanyu Tian
Jingyi Yu
Hongjiang Wei
Yuyao Zhang
Venue: ICLR 2026 Poster (2026)
Keywords: diffusion models
inverse problems
CT reconstruction
3D
medical imaging
Primary area: applications to computer vision, audio, language, and other modalities

Abstract: 3D medical imaging is in high demand and essential for clinical diagnosis and scientific research. Currently, diffusion models have become an effective tool for medical imaging reconstruction thanks to their ability to learn rich, high‑quality data priors.  However, learning the 3D data distribution with diffusion models in medical imaging is challenging, not only due to the difficulties in data collection but also because of the significant computational burden during model training. A common compromise is to train the diffusion model on 2D data priors and reconstruct stacked 2D slices to address 3D medical inverse problems. However, the intrinsic randomness of diffusion sampling causes severe inter‑slice discontinuities of reconstructed 3D volumes. Existing methods often enforce continuity regularizations along the $z$‑axis, which introduces sensitive hyper‑parameters and may lead to over-smoothing results. In this work, we revisit the origin of stochasticity in diffusion sampling and introduce Inter‑Slice Consistent Stochasticity (ISCS), a simple yet effective strategy that encourages inter‑slice consistency during diffusion sampling. Our key idea is to control the consistency of stochastic noise components during diffusion sampling, thereby aligning their sampling trajectories without adding any new loss terms or optimization steps.  Importantly, the proposed ISCS is plug‑and‑play and can be dropped into any 2D‑trained diffusion‑based 3D reconstruction pipeline without additional computational cost. Experiments on several medical imaging problems show that our method can effectively improve the performance of medical 3D imaging problems based on 2D diffusion models. Our findings suggest that controlling inter‑slice stochasticity is a principled and practically attractive route toward high‑fidelity 3D medical imaging with 2D diffusion priors. The code is available at: [https://github.com/duchenhe/ISCS](https://github.com/duchenhe/ISCS).

Published as a conference paper at ICLR 2026
IMPROVING 2D DIFFUSION MODELS FOR 3D MEDICAL IMAGING WITH INTER-SLICE CONSISTENT STOCHAS-
TICITY
Chenhe Du' Qing Wu' Xuanyu Tian'
Jingyi Yu' Hongjiang Wei
Yuyao Zhang"!
'Shanghai University
SShangaai Jiao Tong University
{duchenhe, wuging, tianxy, yujingyi, zhangyy8 jeanrrageeeaaaaattcc.eee...
nongiiang..eiissjtu.eee. weilssjtu.edu.co
ABSTRACT
3D medical imaging is high demand and essential for clinical diagnosis and scientific research. Currently, diffusion models have become an effective tool for medical imaging reconstruction thanks to their ability to learn rich, high-quality data priors. However, learning the 3D data distribution with diffusion models in medical imaging is challenging, not only due to the difficulties in data collection but also because of the significant computational burden during model training. A common compromise is to train the diffusion model on 2D data priors and recon- struct stacked 2D slices address 3D medical inverse problems. However, the intrinsic randomness of diffusion sampling causes severe inter-slice discontinuities of reconstructed 3D volumes, Existing methods often enforce continuity regular- izations along the z-axis, which introduces sensitive prpee--prameters and may lead over-smoothing results. this work, we revisit the origin of stochasticity in diffusion sampling and introduce Inter-Slice Consistent Stochasticity (ISCS), a simple yet effective strategy that encourages inter-slice consistency during dif- fusion sampling. Our key idea is to control the consistency of stochastic noise components during diffusion sampling, thereby aligning their sampling trajectories without adding any loss terms optimization steps. Importantly, the proposed ISCS is plug-and-play and can be dropped into any 2D-trained diffusion-based 3D reconstruction pipeline without additional computational cost. Experiments eral medical imaging problems show that our method can effectively improve the performance of medical 3D imaging problems based on 2D diffusion models. Our findings suggest that controlling inter-slice stochasticity is principled and practi- cally attractive route toward high-fidelit 3D medical imaging with 2D diffusion priors. The code is available at: https: //ggttuubb/////////////////tbtht com/ httr/ducheeeeeee IISCS.
INTRODUCTION
Diffusion models (DMs) (Ho et al., 2020; Song et al., 2020b) have demonstrated the unparalleled ability to learn data distribution across various modalities, achieving remarkable success in both data medical imaging, current DMs have shown effectiveness in
generation and image restoration. modeling the distribution 2D image slices. By leveraging powerful diffusion priors, DMs integrated with conventional optimization frameworks have achieved state-of-the-arr (SOTA) performance in solving inverse problems in medical imaging (Song al., 2021; Jalal et al., 2021; Chung et al., 2022; 2024; Du et al., 2024; Hu et al., 2024; Xiang et al., 2023; Wu et al., 2025; Chen et al., 2025), such as accelerated magnetic resonance imaging (MRI) and undersampled X-ray computed tomography (CT).
In clinical practice, medical data is fundamentally large 3D volumes. While individual 2D slices are crucial for review, a complete and accurate 3D volumetric reconstruction is often essential for critical downstream tasks such as precise tumor volume assessment, surgical planning, and tracking disease progression over time. However, translating the success of 2D DM-based solvers to 3D medical
1 Cooresponding authors.

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Published as a conference paper at ICLR 2026
imaging presents significant practical challenges. Due to the "curse of dimensionality". training DMs directly on high-dimensional volumetric data is often infeasible. The memory, computational, and data requirements for training 3D diffusion prior are prohibitively expensive for most academic and even industrial labs (Pinaya et al., 2022; Guo et al., 2025; Wang et al., 2025). A common and practical workaround is train DM on 2D image slices and then apply this 2D prior in slice-by-slice manner for 3D reconstructions (Chung et al., 2023; 2024; Chung & Ye, 2025).
While this 2D-to-3D approach mitigates the training burden, it introduces critical new problem: The resulting 3D volumes always lack consistency along the third dimension (i.e., z-axis). Because each 2D slice is processed independently during the reverse diffusion process, the intrinsic randomness of the sampling procedure leads to severe inter-slice discontinuities and artifacts, degrading the quality of the final 3D volume. Existing methods have attempted to address this issue through several strategies. The most direct approach involves augmenting the 2D diffusion prior with hand-crafted regularizers, such as Total Variation (TV), to enforce smoothness between adjacent slices (Chung et al., 2024; 2023). While effective, these methods often introduce sensitive hyperparameters that require careful tuning, and can lead to over-smoothing that erases fine details. More sophisticated approaches aim to learn more complete 3D prior, for instance by training models 3D patches (Song et al., 2024) or by combining priors from two perpendicular 2D planes (Lee et al., 2023). Although these methods are more principled, they increase the complexity of the training inference pipeline and may impose constraints on the data, such as requiring cubic volumes.
A similar phenomenon of discontinuity arises in the field of video restoration, where applying pre- trained 2D image DMs to video inverse problems often leads to the lack of temporal coherence across frames. Kwon Ye (2025; 2024) pointed out that this temporal flickering is due to the uncoordinated stochasticity inherent in the diffusion sampling process, and introduced batch-consistent sampling (BCS) alleviate it by synchronizing stochastic noise components across frames.
In this work, we systematically investigate how the same uncoordinated stochasticity becomes the fundamental cause of inter-slice inconsistency when extending 2D diffusion priors to 3D medical reconstruction. Motivated by resulting insights, we propose Inter-Slice Consistent Stochasticity (ISCS), a plug-and-play strategy that explicitly synchronizes the random noise component across adjacent slices using smooth interpolation. This aligns their sampling trajectories to ensure 3D coherence without imposing excessive constraints. Extensive experiments on diverse 3D medical imaging inverse problems, including limited- CT and MRI isotropic super- resolution (SR), demonstrate that ISCS consistently improves reconstruction quality and surpasses existing approaches, all without introducing additional loss terms, hyperparameters, computational overhead.
PRELIMINARIES
Diffusion Models Diffusion models are class of generative models that consist of forward and reverse process (Ho et al., 2020; Song et al., 2020b). The forward process is a fixed Markov chain that gradually adds Gaussian noise to a clean data sample 2o ~ Paata (x) over '' discrete timesteps. At each step i, the transition is defined as:
(xx N(xis / 3,x;-1, Br1),
where {81]T is predefined variance schedule. A key property of this process is that sample x, directly from Xp in a closed form:
g(x; Xo) = (X1i v aax0, (1 - I))
where = 11 3r and o₁ I Ast T, Xy approaches a standard Gaussian distribution.
The reverse process learns to reverse this noising procedure, starting from a random noise sample X1 (00 I) and iteratively generating a clean sample Xg. This is achieved by training neural network en (xx,, l) to predict the noise e that was added to create x,. The network is optimized using a simplified mean squared error objective:
[()) = Ex, xo,e [[le- Ea (VVaxo + VI- oee, t)
(3)
Once trained, the reverse process generates xt-1 from T, by removing the predicted noise. Determin- istic samplers like DDIM can be used to accelerate this generation process (Song al., 2020a).
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Medical Imaging Inverse Problem In general, the forward acquisition process of medical imaging can be formulated as follows:
(4) where X E IR- represents the vectorized high-dimensional image to be recovered, y E IRM is the acquired measurement, A R R is the physical-informed forward model, and E RM denotes the system noise.
y= Ax n,
an inverse problem to reconstruct the unknown image x from the observed measurement y. For many critical applications, such as sparse-view CT or MRI isotropic super-resolution (SR), this problem is severely ill- ill-posed (i.e., M < N), where A non invertible, resulting in the analytical solution being infeasible. A robust approach is to frame the reconstruction within Bayesian framework, seeking Maximum A Posteriori (MAP) estimate the image:
& arg max p(xly) = arg min - x
Ax - A log p(x).
(5)
fidelity term
prior term
This formulation decomposes the objective into two components: a data fidelity term, lly Ax| 2. which enforces consistency with the measurements y, and a prior term, log p(x), which regularizes the solution by constraining it to a plausible data manifold. À is weighting parameter. The power of diffusion models lies in their ability implicitly learn strong, complex data prior p(x) from a training dataset. Instead of defining an explicit regularization function, they integrate this prior through a guided reverse sampling process. The update each step guided by the gradient of the posterior log-likelinn nikel-kklioood, which combines the unconditional score learned by the model Vx, log p (x,) with guidance term derived from the likelihood Vx, log p(y|x;).
DM-based Medical Inverse Problem Solvers The prevailing diffusion- inverse problem solvers (DIS) integrate the data-consistency term derived from the likelihood into the reverse sampling process. To further formalize the reconstruction process, outline general iterative framework for solving inverse problems with a pre-trained diffusion model. The process starts with pure Gaussian noise Xy ~ (O, I) and iteratively refines the solution for each reverse timestep from T down to 1. Each iteration, which aims to generate x from Xt, can be decomposed into three fundamental steps:
(1) Denoising Prediction: We denote the estimate of the clean data, as X which is first predicted from the current noisy state x,. Leveraging Tweedie's formula, this can be achieved using the pre-trained noise prediction network Eg:
1 (x, v1 (x)x(x;)):
E [xo
xx]
Vā,
where āi is the noise schedule parameter at step t. This step effectively projects the noisy data onto the learned data manifold.
(2) Data Fidelity Update:
The predicted clean image X is then corrected to be consistent with the physical measurements y. This is achieved by solving data fidelity problem, yielding an updated estimate Kojt- This step can be expressed as a general optimization problem:
Rof= = arg min l
Az|
11 + A||z - xojell2:
(7)
For many linear inverse problems, this sub- sub-problem has a closed-form solution or can be efficiently solved using a few gradient descent steps.
(3) Re-noising to Timestep t 1: Finally, the data-consistent estimate X is used to generate the next iteration, X;-1- This is accomplished by applying the forward diffusion process to Xoje. effectively injecting a controlled amount of noise corresponding to timestep 1. Taking the DDIM style sampler as an example, this process can be define as:
X = V0r-188pp + VI 11- ā;- 172 37 (x+) +
n
(8)
deterministic noise
stochastic noise
where e <~ I), n is a parameter that controls the strength of the stochastic noise component. This step re-introduces stochasticity and prepares the estimate for the subsequent iteration.
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By iteratively applying these three steps, the reconstruction framework progressively refines the solution, ensuring it simultancously adheres to the learned data prior and remains faithful to the observed measurements, thereby converging high-quality reconstruction.
PROPOSED METHOD
In this section, we first provide a detailed analysis of the problem's origin, identifying uncoordinated stochasticity in the slice-wise diffuusin sampling process the fundamental cause (Sec. $3.1). Then, we introduce our ISCS framework. We present its mechanism for generating correlated noise via Spherical Linear Interpolation (Slerp) and its seamless integration into existing DM-based solvers (Sec. $3.2). A geometric overview of our proposed noise strategy in comparison to conventional methods is illustrated in Fig. 1.
3.1 INTER-SLICE INCONSISTENCY IN 2D DM-BASED 3D RECONSTRUCTION
Slice-wise Approximation of 3D Diffusion Prior The application of DMs 3D medical imaging inverse problems presents fundamental dilemma. Ideally, the denoising network used in the reconstruction framework (Eq. 6) should be 3D model trained on volumetric data. However, the immense computational and data requirements for training high-quality 3D DMs make this approach often infeasible. A common alternative to leverage a powerful, pre-trained 2D DM and apply it in slice-by-slice manner along chosen axis (e.g.. the 2-axis). This procedure effectively approximates the 3D denoising operation as a concatenation of independent 2D operations:
Eg (x+) == (x,,),, cx ................................ ..........x.............. (x(,ss))
where Xt, denotes the i-th slice of the noisy 3D volume X
Root Cause of Inter-Slice Inconsistency While computationally efficient, this slice-wise approach introduces a significant challenge: inter-slice inconsistency. The root cause of this problem is a complex interplay between the highly ill-posed nature of many medical inverse problems and the inherent stochasticity of the diffusion sampling process. Specifically, in these problems, the undersampled measurement data often fails to provide sufficient constraints to uniquely determine the solution. DMs are powerful precisely because they can fill these ambiguous regions with strong, data-driven prior. However, this generative capability is actualized through a reverse process that, detailed in the re-noising step (Eq. 8), repeatedly injects random noise. When this process is applied independently to each 2D slice, the combination of weak data constraints and independent stochasticity becomes highly problematic. The lack of strong guidance from the measurements gives the independently sampled noise for each slice excessive freedom to steer the sampling path. Consequently, the sampling trajectories for adjacent slices become entirely uncorrelated, leading to substantial and arbitrary variations between them. When stacked, the resulting 3D volume inevitably suffers from noticeable structural discontinuities and artifacts along the slice axis, severely degrading its diagnostic and analytical quality.
Limitations of Post-Hoc Regularization A prevalent strategy to mitigate these artifacts is to apply post-hoc regularization, such as Total Variation (TV), in an additional optimization step. While effective at smoothing discontinuities, this remedy often introduces new, undesirable artifacts, such as over-smoothing or cartoon-like textures, which can erase fine diagnostic details and compromise data fidelity. More fundamentally, such methods act external corrective step; they do not address the intrinsic cause of the problem. They merely mask the symptoms of the underlying issue: the uncorrelated nature of the slice-wise diffusion sampling.
Our Motivation This observation motivates our central research question: Is it possible to enhance inter-slice consistency directly within the diffusioon sampling process itself, obviating the need for external, artifact-inducing optimization? We posit that the key lies in redesigning the re-noising step. A direct and intuitive strategy is to impose consistency control on the random perturbations applied across adjacent slices. Specially, instead of allowing the stochastic noise be independent for each slice, we aim to impose a structured correlation on the random perturbations applied across the volume. By coupling the sampling paths of adjacent slices, can fundamentally constrain the
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(a) Independent noise
(b) Identical noise (BCS)
(c) Slerp noise (Ours)
Figure 1: Geometric interpretation of how different noise strategies in the re-noising step affect the stochasticity and resulting consistency in diffusion sampling. (a) Independent Noise (Conventional): Independently sampled noise for each slice, leading uncorrelated sampling paths. (b) Identical
Noise (BCS (Kwon & Ye, 2025)): Applying the same noise to all slices forces identical sampling paths. (c) Slerp Noise (Ours): Our proposed ISCS interpolates noise on the hypersphere, generating smoothly correlated information across slices.
solution space and reduce stochastic inconsistencies, thereby promoting the generation of a coherent and continuous 3D volume directly from the generative process.
3.2 ANTER-SLICE CONSISTENT STOCHASTICITY
Building on our motivation control sampling stochasticity, we introduce novel technique named Inter-Slice Consistent Stochasticity (ISCS). The core principle of ISCS is to replace the independent Gaussian noise injection in the re-noising step (Eq. 8) with structured, smoothly varying noise volume, which we denote as ISCS, This modification ensures that the stochastic perturbations applied to adjacent slices are highly correlated, thereby coupling their reverse sampling trajectories. A key advantage of our approach is its simplicity; it can be seamlessly incorporated into any existing diffusion- based inverse problem solver (as shown in Sec. $2) to enforce inter-slice consistency without introducing additional optimization steps requiring model retraining.
Batch-Consister Sampling & Limitations To construct the noise volume ISCS E R require a mechanism that generates inter-slice correlation while ensuring each slice's noise map still adheres to a standard gaussian distribution. A straightforward approach would be to apply the exact same noise to every slice. This strategy, known as batch-consisten sampling (BCS) (Kwon & Ye, 2025), has proven effective for improving temporal consistency in video inverse problems. However, naively adapting BCS to high-dimensional medical volume reconstruction is problematic. Video restoration often deals with short sequences, e.g., under 16 frames in (Kwon Ye, 2025), where inter-frame changes are minor and dynamics are largely preserved in the measurements (Zhang et al., 2025). In contrast, medical volumes feature a much larger axial dimension (e.g.. more than 300 slices for CT) with potentially significant anatomical variation between slices. Enforcing identical noise in this context is an overly rigid constraint that suppresses anatomical changes and introduces "copying artifacts," " where features are improperly replicated across anatomically distinct slices.
Correlated Noise Generation via Slerp This motivates more nuanced approach. We hold that an ideal noise volume should exhibit a spatially varying correlation structure. Specifically, the correlation should satisfy two key properties: (i) it should be strong between adjacent slices to ensure local consistency, and (ii) it should decay the distance between slices increases, permitting necessary global structural divergence. two independent random noise instances at the boundaries of the volume. An interpolation- strategy is therefore a natural fit. To ensuring that every interpolated state remains a valid sample from the prior (0, Ia), we leverage the concentration of measure phenomenon in high-dimensional spaces (Vershynin, 2018). is a classical result that the probability mass of a high-dimensional isotropic Gaussian concentrates tightly in a thin shell around a hypersphere of radius /d. Formally, the Gaussian Annulus Theorem states that for NO, Ia) and any , > 0, there exists constant
other words, we seek to define smooth trajectory between
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such that:
IP 11112- - 3) exp (-c8²).
(10)
This inequality implies that standard linear interpolation, which traverses the chord of the hypersphere (where ||||| < vd), would yield states deviating from the typical set of the distribution. Consequently, to respect the geometry of the high high-probability manifold, we employ Spherical Linear Interpolation (Slerp). By tracing the geodesic path on the hypersphere surface, Slerp preserves the vector norm and distributional statistics throughout the transition.
The procedure is follows. For 3D volume composed of S slices, we first sample two anchor noise vectors, 21, 2g E "x* from the standard normal distribution (0,, I). These anchors define the start and end points of geodesic path the hypersphere. We then generate the noise map for each intermediate slice ISCS by interpolating along this path:
ISCS = s slerp 28; sin((1 - a;)())
sin(a;
21 + sin(
Zs.
(11)
sin(
where Oz = (1 1) 1) is the normalized position of the i-th slice, and Ω arccos( (2)), 2.) /[|z)]] || [|z]]]) is the angle between the anchor vectors. The resulting of noise maps (e,Scs)s 1i=1 constitutes the correlated noise volume, which varies smoothly along the slice dimension while maintaining inter-slice correlation. At the same time, each individual slice is ensured to follow standard Gaussian distribution I).
Ji=
Integration with Diffusion Samplers The generated noise volume aSCS directly replaces the independently sampled noise in the re-noising step of any diffusion sampler. For instance, in the context of a DDIM-like sampler, the update rule can be formulated as:
x 1oo-1 + V 1- - of co(x.) + ISCS
(12)
Here, Xoje the data-consistent prediction of the clean image, the second term represents the deterministic component of the reverse step, and the final term introduces our inter-slice consistent stochasticity, with o, controlling its magnitude. By construction, this process perturbs each 2D slice with similar yet smoothly distinct randomness, effectively suppressing the uncorrelated uncertainty that leads to inter-slice artifacts and thereby improving the overall consistency of the final result.
Algorithm 2D DIS for 3D medical imaging with ISCS
1: Input: Mcasurements Pre-trained DM eg., Timesteps T,, Noise schedule (ar (or))=o
2: Xy ~N;
3: for t = 1..,.... do
4:
1. Denoising Prediction
5:
Xoj: = E. |xo xx] = Va, (x, V1 0456 (x+))
6:
2. Data Fidelity Update
7:
Sale = arg min ||y - Az| 2 + A|| Izz Xule 1
8:
3. Re-noising via ISCS
9: iscs slerp(Zi, zs; ax), 21, iid. (0,1)
10: XI-1 18111
āt-1 3 (xx) B1
10)
end for
12: return X0
4 EXPERIMENTS
To demonstrate the effectiveness and generalization of the proposed ISCS, we conduct experiments on three typical yet challenging 3D medical imaging inverse problems: (i) sparse-view (SV) CT re- construction, (ii) limited-angle (LA) CT reconstruction, and (iii) MRI isotropic super-resolution (SR). In addition, we conduct ablation study comparing identical noise and Slerp noise to evaluate the advantages of our approach in medical 3D volume reconstruction.

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Table Quantitative results of compared methods and slice-to-slice difference for three 3D medical imaging tasks: SVCT of 30 views, LACT of [O, 100]e, and MRI SR of The best performance highlighted in bold. |ه| denotes the absolute gap between the inter-slice difference of the reconstruction and that of the ground truth (smaller is better; see Sec. C.I for details).
Axial
Coronal
Sagittal
Task
Methods
|A|
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
FDK
23.91
0.323
0.324
23.92
0.414
0.311
23.79
0.348
0.310
0.005584
ADMM-TV
32.94
0.882
0.113
33.67
0.895
0.113
33.72
0.893
0.107
0.001617
DDNM
32.55
0.851
0.076
32.51
0.837
0.227
32.79
0.834
0.200
0,009342
SVCT
DDNM+ISCS
33.97
0.885
0.076
33.53
0.896
0.114
33,97
0.893
0.106
0,001785
DDS
34.76
0.919
0.069
35.12
0.906
0.149
35.33
0.904
0.141
0.005588
DDS+TV
36,26
0.931
0.073
37.08
0.938
0.095
37.50
0.936
0.088
0.002937
DDS+ISCS
36.97
0.937
0.064
37.75
0.944
0.070
38.16
0.942
0.065
0.001835
FDK
15.85
0.381
0.233
16.30
0.453
0.240
16.71
0.413
0.223
0.000898
ADMM-TV
27.27
0.795
0.125
27.85
0.794
0.123
27.83
0.799
0.120
0.000877
DDNM
28.40
0.854
0.076
28.75
0.774
0.245
28.22
0.775
0.235
0.016443
LACT
DDNM+ISCS
30.89
0.898
0.066
31.88
0.906
0.084
31.59
0.908
0.076
0.001899
DDS
29.07
0.885
0.086
29.93
0.829
0.196
29.20
0.830
0.193
0,011592
DDS+TV
31.40
0.898
0.086
33.33
0.906
0.110
32.83
0.909
0.104
0.002566
DDS+ISCS
31.65
0.911
0.071
32.90
0.917
0.082
32.49
0.920
0.077
0.001966
Cubic
38.02
0.925
0.032
36.22
0.908
0.095
36,85
0.904
0.111
0.004168
ADMM-TV
39.34
0.940
0.044
38.27
0.934
0.060
36,86
0.906
0.097
0.005074
DDNM
38.32
0.954
0.051
38.83
0.954
0.039
37.84
0.933
0.068
0,001480
MRI SR
DDNM+ISCS
39.62
0.963
0.019
39.84
0.959
0.022
38.65
0.939
0.045
0.001913
DDS
39.32
0.952
0.038
38.84
0.951
0.027
37.94
0.925
0.082
0.001853
DDS+TV
40.12
0.958
0.031
39.36
0.955
0.038
38.53
0.932
0.075
0.004732
DDS+ISCS
40.33
0.968
0.019
39.84
0.965
0.035
39.35
0.948
0.052
0.002096
4.1 EXPERIMENTAL SETTINGS
CT Dataset & Pre-processing We use the AAPM 2016 low-dose CT grand challenge dataset (Me- Collough et al., 2017), which contains 5936 CT slices from 10 patients. All slices are first resized to 256 x 256. We use 5410 slices from 9 patients for training the diffusion model, and reserve one patient's data (L556) for evaluation. The size of the evaluation volume is 256x 1666226x330 1556x000 We employ torch-race radon' library with cone-beam (CB) geometry to simulate projections. For sparse-view, we sample 30 views uniformly from [0", 360"); for limited-angle, 100 views from [0", 100%). Detailed CBCT geometry setting can be found in the Appendix.
MRI Dataset & Pre-processing We use the public IXI dataset which contains multiple modality human brain scans. For our experiments, we use the we-ghihhted images, The evaluation volume has a size of 256 256 150 with voxel spacing of 1.230. x0.3775 mm3 We first resample the data to isotropic mm3 resolution, then pad a size of 256x 256x 256. To simulate anisotropic scans, we apply 5x downsampling along the z-axis.
Implementation Details For the diffusion prior, we adopt the Variance Exploding (VE) diffusion model Song et al. (2020b), following the architecture in Chung et al. (2023). For the CT reconstruction task, the model is trained on the AAPM dataset described above, while for the MRI isotropic SR task, we use the pretrained checkpoint trained on coronal axis slice provided by Lee et al. (2023). To ensure fair comparison across different DIS methods, we employ 30 NFEs for CT and 20 NFEs for MRI throughout all experiments, all DIS methods use the same pre-trained diffsuion prior.
Methods in Comparison & Metrics For 3D medical inverse problems, we compared two repre- sentative state-of-the-art (SOTA) DIS methods: DDNM (Wang al., 2022) and DDS (Chung et al., 2024). Since our approach is DM-annostic and can be seamlessly integrated into existing frameworks,
"https://brain-dae wwtp:se...lmmmme.t.r...eeo httpes///boaanraeeeeeggeeererrrr
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23.23/0.364
32.13/0.807
36.58/0.888
.7.04/0.933
08.03/0..962
PSNR/SSIM
Axial
22.33/0..63
28.28/0.80
30.34/0.566 569
10000
9000
PSNRUSSIN
Sagittal
DDNMHISCS
DDS+TV
Figure 2: Qualitative results of compared methods on a representative sample for SVCT of 30 views.
The display window set as [-480, 820] HU.
23.2280-584
35.31/0.58
PSNRUSSIM
Axial
30.000 00.0660.883
31. 91.32/0.800
31.60/0.90
30 49/0.600.81
31.58/0.00 8.3/
32.35/0.910
PSNR/SSIM
Sagittal
Cubic
DDNM
DDNM+ISCS
DDS
DDS+TV
DDS+ISCS
Figure 3: Qualitative results of compared methods on representative sample for MRI SR of 5x.
we denote the variants DDNM+ISCS and DDS+ISCS, In addition, we compare with traditional reconstruction baselines: FDK and ADMM-TV for CT reconstruction, and cubic upsampling and ADMM-TV for MRI super-resolution. For quantitative evaluation of reconstructed volumes, we adopt two classical data-fidelity metrics, peak signal-to-nn conall-o--ooieeee ratio (PSNR) and structural similarity index measure (SSIM), and one perceptual metric, LPIPS (Zhang et al., 2018).
4.2
MAIN RESULTS
SVCT and LACT Table shows the quantitative results of the compared methods with and without the proposed ISCS strategy. Incorporating ISCS into both DDNM and DDS yields consistent improvements across all three views, in some cases even surpassing TV regularization that relies on additional optimization steps. The gains are particularly pronounced SSIM and LPIPS for the coronal and sagittal planes, indicating that ISCS effectively mitigates inter-slice discontinuities along the z-axis while preserving structural fidelity. Representative qualitative results on SVCT and LACT are shown in Fig. 2 and Fig. 8. Without any constraint inter-slice continuity, DDNM and DDS produce acceptable reconstructions on axial slices but suffer from severe discontinuities and fragmented artifacts in sagittal views due to independent stochasticity. Although adding TV regularization alleviates these artifacts, introduces blurring and cartoon- like artifacts that degrade fine anatomical details. In contrast, ISCS markedly reduces inter-slice inconsistency in both DDNM
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Table 2: Quantitative results of adopt- ing identical (BCS) and slerp noise (ISCS) during re-noising.
Segittal
Coronal
Noise Type
BCS
ICSC
PSNR
38.00
38.16
Identical Noise
Slerp Noise
Identical Noise
Sterp Noise
Coronal
SSIM
0.937
0.941
LPIPS
0.081
0.074
Figure 4: Qualitative results of adopting identical (BCS) and slerp noise (ISCS) during re-noising, where the red arrows denote the noticeable "copying artifacts". The display window is set as [-480, 820] HU.
PSNR
38.24
38.78
Sagittal
SSIM
0.933
0.937
I.PIPS
0.081
0.073
and DDS without introducing such artifacts, preserving sharp edges and yielding reconstructions that are most consistent with the GT.
MRI Isotropic SR Quantitative comparisons and qualitative visualizations are presented in Table I and Fig. respectively. The compared methods exhibit trends consistent with those observed in the CT task when evaluated with and without the proposed ISCS strategy. It is worth noting that the pretrained DM we adopt was trained on coronal slices, so inter-slice inconsistencies mainly manifest in the axial and sagittal views. The results show that ISCS substantially alleviates these inconsistencies without introducing blurring artifacts. particular, the zoomed sagittal view of the cerebellum in Fig. 3 highlights that, without any inter-slice constraint, both DDNM and DDS produce noticeable streak-like artifacts, whereas TV-based regularization suppresses these artifacts at the cost of oversmoothing structural details. By contrast, incorporating the proposed ISCS yields reconstructions that best preserve fine anatomical structures and are most consistent with the GT.
4.3 DISCUSSIONS
Effectiveness of Correlated Noise Generation via Slerp We examine the impact of the proposed ISCS strategy (Slerp-based noise) and the BCS strategy (Kwon & Ye, 2025) (identical noise) on reconstruction performance Eq. 12. Under the same experimental setting, each strategy is run five times. Quantitative results are reported in Table and visualizations in Fig. 4. The results of BCS exhibit noticeable streak artifacts along the z-axis. This observation is consistent with the analysis in Sec. 3.2, suggesting that in high-ding sigh-iimessional medical volumes, enforcing identical stochasticity across all slices suppresses natural structural variations and leads to replicated artifacts.
0.05
Mean Inter siiee Lifference
DOS
0.4
DOS+ISCS
DOS+TVV
0.04
DUS5+1565
DCS
PSNN (083
28
0.03
26
0.02
DCS
0.
0.01
20
DDS 1SCS
0.1
0.75T
0.5T
0.25T
0.75T
0.5T
0,257
0.757
0.5T
0.257
Inverse Steps
Time
Inverse Steps
Figure 5: Performance curves across the sampling process, where a higher PSNR and lower LPIPS and inter-slice difference reflect improved data fidelity and better inter-slice consistency.
Trajectory of the sampling process Fig. plots the evolution of performance over diffusion time steps 7' (i.e., intermediate reconstructions as - With ISCS, the inter-slice difference drops close to the ground-truth reference early in the trajectory, while PSNR/LPIPS continue to improve thereafter. Compared with the DDS baseline, which maintains larger inter-slice gaps until later steps, ISCS achieves cross-slice coherence earlier and sustains across sampling. This early stabilization may reduce the effective search space and help the sampler converge more reliably.

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5 CONCLUSION
We identify uncoordinated stochasticity in diffusion sampling as a key driver of inter-slice incon- sistency when 2D diffusion priors applied to 3D medical reconstruction. To address this, introduce ISCS, a plug-and-play strategy that correlates per-slice noise via spherical linear inter- polation, aligning sampling trajectories without adding loss terms, hyperparameters, retraining, or extra compute. In our experiments on SVCT, LACT and MRI isotropic SR, ISCS generally yields better quantitative scores and smoother cross-view continuity while largely preserving edges and fine anatomy. We view stochasticity control as practical path to narrow the gap between 2D priors and 3D fidelity, and we plan to explore learned, data-adaptive correlation fields and integration with multi-plane 3D priors.
ACKNOWLEGEMENT
This work was supported by the National Natural Science Foundation of China (Grant No. 6257 22571328) 1328) and, in part, by the National Natural Science Foundation of China (Grant No. W2431046), the MoE Key Lab of Intelligent Perception and Guuann-Machinn Collaboration (ShanghaiTech University), and the Shanghai Frontiers Science Center of Human--entered Artificial Intelligence.
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A
APPENDIX
A.1
USE OF LLMS
We affirm that our work was conducted accordance with the ICLR guidelines regarding the use of large language models (LLMs). LLMs were utilized solely for minor text editing, specifically for correcting spelling and grammar errors. No LLM was used to generate or alter any core technical content, including the research methodology. experimental design, results, conclusions. The ideas, data analysis, and scientific conclusions presented in this paper are the sole product of the authors' original work.
A.2 ADDITIONAL DETAILS OF EXPERIMENT
CT Datasets & Pre-processing To standardize the input data, the Hounsfield Unit (HU) values were clipped to the range |-1000, 1600) and linearly rescaled to [0, 1]. For the cone-beam geometry. we adopt configuration with detector dimensions of 512 x 512, detector spacing of 2 mm both u- and u-directions, oource-t-issceener distance of 700 mm, and source-to-detector distance of 500 mm.
A.2.1 NETWORK TRAINING
VE-form (Song et al., 2020b) diffusion model based on the nesnpp architecture was trained on the AAPM dataset for 70 epochs with a batch size of 16 and a learning rate of 2 x 10-4, using single NVIDIA A100 GPU. The model was optimized with Adam (3) 0.9, 10-8) without weight decay.
A.3 ADDITIONAL DETAILS OF BASELINES
ADMM-TV Following the protocol of Chung al. (2023), the solution is to optimize the following objective:
x arg min |Ax
yll + D||
(13)
x
where D = Dr, Dy. D.). and solved with standard ADMM and CG. Hyper- papper-prrameerss are set identical to Chung et al. (2023).
DDNM (Wang et al., 2022) DDNM enforces measurement consistency through range- null space decomposition. The update rule can be expressed as
E[xp
xx,
(DDNM)
AI-AA) Dø- (x;: + A Aly,
(14)
where At denotes the pseudo-inverse of the measurement operator A. For CT reconstruction, SIRT is adopted as the pseudo-inverse operator for stability.
DDS (Chung et al., 2024) problem:
DDS can be interpreted as solving the following proximal optimization
E3 Exxo
X;, (DDS) ss arg min
? ||y Axol 1 ||x0 Do. (x:))12
(15)
Xo 2
which is equivalent to solving the following linear system:
(>A A A = ry + Dg- (xt),
(16)
typically using the conjugate gradient (CG) method. In our experiments, the number of CG iterations was set to 10, which we found to be the most suitable value based tuning with the validation data.
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B EXTENDED THEORETICAL ANALYSIS
In this section, we deepen the theoretical grounding of the proposed Inter-Slice Consistency Sampling (ISCS). Specifically, we analyze the geometric stability of our stochastic interpolation strategy and discuss the compatibility of ISCS with deterministic sampling trajectories (ODEs).
B.1 GEOMETRIC STABILITY OF RANDOM ANCHOR SELECTION
core component ISCS the generation of spatially correlated noise via interpolation between anchor noise vectors. natural question arises regarding the sensitivity of the method to the random selection of these anchors. Here, we provide theoretical justification for using independent random sampling robust default.
Proposition B.1 (Concentration of Angular Distance in High Dimensions). Let 21, ~ (O La) be two independent rundom vectors RR. As the dimension + oo, the angle ((21, 22) between them converges in probability n
lim P ((0(21;22) d0000
2 2
Ve 0.
(17)
Remark B.1. (Implication for ISCS) Since CT reconstruction typically involves high-dimensional latent spaces (d > 1), any two independently sampled anchor vectors are approximately orthogonal (Rs 90") with high probability. This concentration measure phenomenon implies that the "random" selection of anchors actually yields geometrically consistent interpolation path length across different runs. Consequently, our method is inherently stable and does not require hyperparameter tuning for the angular separation of anchors, a claim validate empirically in Section C.4.
B.2 COMPATIBILITY WITH DETERMINISTIC SAMPLERS
While diffusion models often employ stochastic samplers, ISCS is fundamentally compatible with deterministic ODE solvers (e.g., DDIM with 17 0).
Let the reverse diffusion process be modeled as an ODE dx, = fxx, t)dt. The trajectory of this ODE is uniquely determined by the terminal condition Xy. Although deterministic sampling removes stochasticity from the reverse denoising trajectory, the entire reconstruction process remains fully conditioned on the choice initial latent Xy. By applying ISCS to correlate initial noise volume XT across slices, we enforce that the starting points of the reverse process lie on spatially smooth manifold. Since the subsequent integration steps are deterministic maps, this initial coherence preserved throughout the trajectory. We provide empirical verification of this property in Section C.3.
C ADDITIONAL EMPIRICAL RESULTS
We present comprehensive experiments to evaluate the robustness of ISCS against 3D-aware baselines, its performance under deterministic sampling, and its sensitivity to anchor selection.
C.1 QUANTITATIVE EVALUATION OF INTER-SLICE CONSISTENCY
To provide holistic evaluation beyond standard 2D metries (PSNR, SSIM), we introduce a dedicated metric to quantify inter-slice consistency while accounting for natural anatomical variations.
Metric Definition We define the Slice Difference (SDiff) as the mean absolute difference between adjacent slices along the z-axis:
1 SDiff S-1
Mean [z141 - xz)),
(18)
where S is the total number of slices and x; represents the i-th slice.
Crucially, simply minimizing SDiff is insufficient, as it favors over-smoothed solutions (where SDiff 0) that lack texture. Therefore, evaluate fidelity, report the Absolute Gap ((A)
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between the reconstruction and the Ground Truth (GT):
A
SDDif SDifferl
(19)
A smaller | indicates that the reconstructed volume successfully replicates the natural anatomical coherence of the GT, rather than enforcing artificial smoothness.
Results Analysis As detailed in Table and Table 3, our method consistently achieves the lowest | compared to baselines. This quantitative evidence confirms that ISCS not only mitigates flickering artifacts but also restores 3D coherence level that closely matches real anatomy. avoiding the svor-smog pitfalls common explicit regularization methods.
Table 3: Slice-to-slice difference of compared methods for three 3D medical imaging tasks: SVCT of 30 views, LACT of [o, 100Je, and MRI SR of 5x. SDiff and SDiffcr denote the mean absolute difference between adjacent slices for the reconstruction and ground truth, respectively; SDiff SDiffer measures the signed gap, and A is its absolute value (smaller better).
Slice difference
Task
Methods
SDiff
SDiffar
|
FDK
0,011893
0.006309
0.005584
0.005584
ADMM-TV
0.004692
0.006309
-0.001617
0.001617
DDNM
0.015652
0.006309
0.009342
0.009342
SVCT
DDNM+ISCS
0.004524
0.006309
-0.001785
0.001785
DDS
0.011897
0.006309
0.005588
0.005588
DDS+TV
0.003372
0.006309
-0.002937
0.002937
DDS+ISCS
0.004474
0.006309
-0.001835
0.001835
FDK
0.007208
0.006309
0.000898
0.000898
ADMM-TV
0,005432
0.006309
-0.000877
0.000877
DDNM
0.022753
0.006309
0.016443
0.016443
LACT
DDNM+ISCS
0.004410
0.006309
-0.001899
0.001899
DDS
0.017901
0.006309
0.01
0.011592
DDS+TV
0.003743
0.006309
-0.002566
0.002566
DDS+ISCS
0.004344
0.006309
-0.001966
0.001966
Cubic
0.007766
0.011934
0..004688
0.004168
ADMM-TV
0.006861
0.011934
-0.005074
0.005074
DDNM
0.013414
0.011934
0.001480
0.001480
MRI SR
DDNM+ISCS
0.010021
0,011934
-0.001913
0.001913
DDS
0,013787
0,011934
0.001853
0.001853
DDS+TV 0.007202
0.011934
-0.004732
0.004732
DDS+ISCS
0.009838
0.011934
-0.002096
0.002096
C.2 COMPARISON WITH EXPLICIT 3D-AWARE PRIORS
We compare our method against state-of-the-art 3D-aware diffusion priors, specifically Diffusion- Blend (Song et al., 2024) and TPDM (Lee et al., 2023). While 3D-aware methods generally offer strong performance in ideal settings, results highlight distinct trade-offs regarding flexibility, robustness, and computational complexity.
Experimental Setup To ensure fair comparison, all priors were trained the same AAPM CT dataset (Imm slice thickness). evaluate on two distinct subjects to test generalization:
Subject L506 Un-Distributtinn: Standard Imm thickness (300 x 256 x 256), matching the training distribution.
Subject L221 (Out-of-Distributte Thick 5mm slices (99 x 256 x 256), representing significant domain shift.
Note that TPDM requires cubic volumes (D > 256) for orthogonal consistency checks and thus cannot be applied to Subject 1.221 (D 99).
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Table 4: Quantitative comparison on the SVCT task of 30 views. Higher PSNR/SSIM and lower
LPIPS indicate better performance.
Axial
Coronal
Sagittal
Subject
Method
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
DDS
34.76
0.919
0.069
35.12
0.901
0.149
35.33
0.904
0.141
L506
DDS+ISCS
36.97
0.937
0.064
37.75
0.944
0.070
38.16
0.942
0.065
(1mm)
TPDM
37.59
0.944
0.063
38.40
0.950
0.068
38.64
0.948
0.062
DiftusionBlend
38.22
0.943
0.034
38.95
0.945
0.047
39,29
0.943
0.042
DDS
37.83
0.952
0.045
37.96
0.952
0.055
38.62
0.950
0.045
L221
DDS+ISCS
38.70
0.956
0.045
39.03
0.963
0.037
39,70
0.961
0.031
(5mm)
TPDM
DiffusionBlend
38.84
0.944
0.046
39.05
0.946
0.054
39.44
0.946
0.045
Table 5: Quantitative comparison on the LACT task of [0, 1000". Higher PSNR/SSIM and lower LPIPS indicate better performance.
Axial
Coronal
Sagittal
Subject
Method
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
DDS
29.03
0.885
0.086
29.84
0.828
0.197
29.13
0.829
0.194
1,506
DDS+ISCS
31.65
0.911
0.071
32.90
0.917
0.082
32.49
0.920
0.077
(Imm)
TPDM
30.95
0.912
0.062
32.48
0.920
0.070
32.49
0,924
0.064
DiffusionBlend
31.11
0.915
0.037
33.16
0.917
0.053
32.76
0.922
0.049
DDS
29.15
0.895
0.053
29.94
0.860
0.139
30.12
0.862
0.124
1,221
DDS+ISCS
30.45
0.908
0.042
31.42
0.910
0.053
31.85
0.912
0.046
(5mm)
TPDM
DiffusionBlend
31.10
0.918
0.029
32.94
0.921
0.045
33.02
0.923
0.037
Results Analysis Quantitative comparisons for SVCT and LACT tasks are presented in Table and Table 5, respectively.
1. Performance on Ideal Data:
On Subject 1,506, explicit 3D methods (DiffusionBlend. TPDM) generally outperform the 2D baseline (DDS), confirming the value of 3D priors. However, ISCS significantly narrows this gap, recovering nigh-frrequecy details without requiring 3D architectural changes.
2. Robustness to Domain Shift:
On Subject L221 (5mm slices), the advantage of 3Dawwre methods diminishes due to the mismatch between the training prior (1mm) and test data (5mm). Notably, ISCS achieves comparable or superior performance (e.g., higher SSIM in SVCT), demonstrating that regulating stochasticity offers greater flexibility than enforcing rigid 3D spatial constraints.
While 3D-aware methods offer high performance, they necessitate task-specific network designs, 3D-aware architectures, and additional training, which significantly increases computational cost and engineering complexity. ISCS focuses on different axis of improvement: enhancing 2D priors through sampling-time noise correlation without architectural changes. Crucially, ISCS is orthogonal to 3D-aware methods. principle, ISCS can be integrated into frameworks like DiffusionBlend or TPDM to further enhance their consistency, direction plan to explore in future work.
C.3 ANALYSIS ISCS WITH DETERMINISTIC SAMPLERS
We investigate the interaction between the proposed ISCS and the stochasticity of the sampler (i.e., DDIM parameter 7)).
Effectiveness on Deterministic Samplers (17 0) As discussed in Section B.2, ISCS applicable to deterministic paths by correlating the initialization. We conducted an evaluation the SVCT task with 30 views using DDIM with = 0. As summarized in Table 6, incorporating ISCS into the initialization phase leads to substantial performance gains independent per-slice initialization.
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Improvements particularly pronounced in the Coronal and Sagittal orientations: for instance, Coronal LPIPS decreases from 0.239 to 0.065, and PSNR increases from 32.67 to 37.10. These results demonstrate that ISCS alleviates slice-wise discontinuities even when the sampling dynamics themselves are deterministic.
Necessity of Stochasticity Despite the compatibility with v = 0, further analysis indicates that deterministic sampling is not optimal for the inverse problems considered in this work. Table 7 reports an ablation over 1j values in DDIM. Reconstruction quality improves monotonically as vj increases, with the fully stochastic setting (1) R 1) achieving the best PSNR and SSIM. This observation is consistent with recent findings diffusion- based inverse problems (Kwon & Ye, 2025; Zhu et al., 2023; Nie et al., 2024; Wang al., 2022: Kawar et al., 2022), which emphasize the importance of controlled stochasticity for escaping local minima and recovering high-frequ high-frequency structures. Accordingly, although ISCS remains effective at r) O, the main experiments in the manuscript adopt stochastic sampling to obtain the best overall reconstruction fidelity.
Table 7: Stochasticity Ablation. Per- formance vs. 1/ on SVCT-30. Higher stochasticity yields better reconstruc- tion.
Table 6: ISCS with Deterministic Sampling. Effect of ISCS on initial noise under DDIM n (SVCT-30). Significant improvements in auxiliary views demonstrate successful consistency enforcement.
7
PSNR
SSIM
PSNR
SSIM
LPIPS
0.0
34.48
0.916
Axial
0.1
34.56
0.918
DDIM (1) = 0)
32.30
0.864
0.065
0.2
34.77
0.923
+ ISCS
36.19
0.924
0.053
0.3
35.06
0.927
Coronal
0.4
35.38
0.932
DDIM (17
32.67
0.806
0.239
0.5
35.70
0.936
+ ISCS
37.10
0.935
0.065
0.6
35.99
0.939
0.7
36.26
0.942
Sagittal
0.8
36.52
0.945
DDIM (17
32.93
0.805
0.228
0.9
36.77
0.948
+ +ICC
37.58
0.932
0.059
1.0
37.08
0.951
C.4 STABILITY OF ANCHOR SELECTION IN ISCS
This section analyzes the stability of ISCS with respect to the choice of anchor noise vectors 2s) and random seeds. As shown Proposition B. the angle between two independently sampled Gaussian vectors concentrates sharply around 90" with vanishing variance. Consequently, independent random sampling of anchor vectors naturally yields a consistent path length across runs, implying that the ISCS interpolation manifold is robust variations in and 25-
To further quantify this robustness, we perform an ablation in which the angle between 31 and 2s no longer random but fixed to prescribed values 0 E (30", 60% 90", 120", 150", 175"). For each angular constraint, we generate 10 independent trials on the SVCT-30 task. The results, summarized in Table 8, demonstrate highly consistent performance across the entire angular spectrum. The fluctuations in PSNR, SSIM, and LPIPS remain extremely small, with standard deviations mostly below 0.2 dB. Notably, even the difference between the lowest- and highest perffrrmiprooomngggg... settings (e.g.. 150" vs. 175%) remains under 0.15 dB in the Axial view. These results confirm that ISCS exhibits strong invariance to the anchor angle and random seeds, validating the use of simple independent sampling (yielding 0 x 90" by default) as a robust and parameter-fre design choice.
C.5 SCALABILITY AND GENERALIZATION ASSESSMENT
In this section, critically evaluate the scalability and generalization capabilities of ISCS, focusing on two challenging scenarios: pathological cases with abrupt structural changes and data acquisition with varying slice thicknesses.
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Published as a conference paper at ICLR 2026
Table Stability of Anchor Selection Strategy. Quantitative results (Mean + Std) of ISCS under different anchor angles (10 independent runs each) on SVCT-30 task. The method shows minimal sensitivity the specific geometric configuration of the latent noise.
Axial
Coronal
Sagittal
Angle (0)
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
30
36.84 1 0.14
0.937
0.064
37.66
0.14
0.944
0.068
38.04 1 0.15
0.942
0.063
60
36.83 + 0.33
0.937
0.064
37.65
+015
0.944
0.066
38.06 = 0.16
0.942
0,063
90"
36.84 + 0.07
0.937
0.066
37.69 0.08
0.945
0.0669
38.07 0.09
0.943
0,065
120"
36.86 +: 0.05
0.937
0.067
37.69
0.07
0.945
0.069
38.09 0.08
0.943
0,065
150"
36.79 020
0,936
0.065
37,61 0.29
0.944
0.069
38.00 0.24
0.942
0.064
175'
36.90 + 0.04
0.938
0.065
37.74 + 0.03
0.945
0.069
38.12 0.96
0.943
0.064
C.5.1
PRESERVATION OF PATHOLOGICAL STRUCTURES
common concern with consistency--efforinng methods is the potential risk of over-smoothing. which might obscure critical pathological details such tumors or lesions. It is crucial to distinguish the operating mechanism of ISCS from explicit smoothness priors like Total Variation (TV).
Intuition C.1 (Noise Consistency vs. Intensity Smoothness). Traditional priors (e.g.. TV) operate directly the signal intensity space X, explicitly penalizing high-frequency gradients: miny V 1- This often leads to "cartoon-like" artifacts or the blurring of sharp boundaries, which can be detri- mental for small lesions.
In contrast, ISCS operates in the stochastic sampling trajectory (noise space 2). We enforce consistency on the noise 2,, not on the pixel intensity Xo. The structural details of the reconstruction are primarily determined by the measurement operator and the data consistency term. Consequently, ISCS encourages inter-slice coherence without suppressing the gighffrequenc signal components required to represent abrupt pathological changes.
Validation on DeepLesion Dataset We empirically validated this hypothesis using the DeepLesion dataset. We selected two representative subjects: Case A (1mm slice with large lesion) and Case B (5mm slice with a small lesion). The visual results in Fig. 6 indicate:
Case (Large Lesion, 1 mm): ISCS successfully reconstructed the sharp boundaries and internal texture of the large tumor, demonstrating that Slerp interpolation in noise space does not blur structural transitions.
Case (Small Lesion, mm): We observed that TV regularization, in its effort to enforce inter-slice intensity consistency, nearly obliterated the small tumor. In contrast, ISCS preserved the small lesion with high fidelity, yielding a result closest to the GT.
These results confirm that ISCS is robust in pathological scenarios, avoiding the detail destruction common in strong explicit smoothness regularizers.
C.5.2 ROBUSTNESS TO VARYING SLICE THICKNESS
To evaluate the generalization ISCS across different data acquisition protocols, we conducted experiments on datasets with varying slice thicknesses (non-uniform z-spacing), ranging from thin (3mm) to thick (7.5mm) slices. Specifically, we utilized subjects from the LDCT-PD dataset (3mm, 5mm) and the AbdomenAtlas 1.0 dataset (7 (7.5mm). Crucially, applied the exact same experimental settings and hyperparameters across all cases, without any dataset-specific tuning.
The quantitative results in Table 9 show that ISCS consistently outperforms the DDS baseline across all metrics and axes. This robustness suggests that ISCS is a scalable solution for 3D reconstruction that does not require retraining or extensive hyperparameter tuning for different clinical protocols.
C.6 ADDITIONAL VISUAL RESULTS
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Published as a conference paper at ICLR 2026
FDK
DDS+TV
DDS+ISCS
mm
7UV
5 mm
Figure 6: Qualitative comparison of compared methods for SVCT of 30 views. Two representative subjects with slice thicknesses of 1 mm (top) and 5 mm (bottom) are shown. Cyan boxes mark the lesion regions. The display window is [-175, 275] HU.
Table 9: Quantitative Results under Varying Slice Thicknesses. ISCS demonstrates consistent performance gains over the baseline (DDS) across all slice thicknesses (3mm, 5mm, 7.5mm). The method effectively mitigates inter-slice discontinuities regardless of z-spacing, confirming its robust- ness to variations in acquisition protocols.
Axial
Coronal
Sagittal
Thickness
Method
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
PSNR
SSIM
LPIPS
DDS
36.17
0.945
0.046
37.06
0.932
0.082
36,97
0.932
0.073
3mm
DDS ISCS
37.48
0.951
0.049
38.54
0.956
0.044
38.45
0.956
0.038
DDS
37.83
0.952
0.045
37.96
0.952
0.055
38.62
0.950
0.045
5mm
DDS ISCS
38.70
0.956
0.045
39.03
0.963
0.037
39.70
0.961
0.031
34.97
0.934
0.043
35.34
0.938
0.027
37.15
0.940
0.026
7.5mm
DDS ISCS
36.02
0,941
0.040
36.68
0,950
0,023
38.14
0.951
0.021
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Published as a conference paper at ICLR 2026
Axtal
Sagittal
Coronal
FDK
DDNM
DDNM+ISCS
DDS
DDS+TV
DDS+ISCS
GT
Figure 7: Qualitative results of compared methods on representative sample for SVCT 30 views. The display window is set as [-480, 820] HU.
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Published as a conference paper at ICLR 2026
Axtal
Sagittal
Coronal
FDK
DDNM
DDNM+ISCS
DDS
DDS+TV
DDS+ISCS
GT
Figure 8: Qualitative results of compared methods on representative sample for LACT in [0, 100%). The display window is set as [-480, 820] HU.
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Published as a conference paper at ICLR 2026
Axial
Segittal
Coronal
Cubic
DDNM
DDNM+ISCS
DDS
DDS+TV
DDS+ISCS
GT
Figure 9: Qualitative results of compared methods representative sample for MRI SR of 5x.
21


Reviews:
[{"review_id": "j0Qn6GxieU", "reviewer": "Reviewer_4QC1", "summary": "The paper proposes Inter-Slice Consistent Stochasticity (ISCS) to improve 3D medical reconstructions obtained from 2D diffusion priors. The key idea is to synchronize the stochastic component of the reverse diffusion process across adjacent slices by initializing each slice’s noise via spherical linear interpolation (slerp) between two anchor noise maps. This smoothly correlates randomness across slices, aligning sampling trajectories without adding new loss terms, hyperparameters, retraining, or extra computation, and can be dropped into existing 2D-diffusion-based inverse-problem solvers (e.g., DDNM, DDS) as a plug-and-play component.\n\nExperiments on three tasks: sparse-view CT, limited-angle CT, and MRI isotropic super-resolution—show consistent improvements in PSNR/SSIM and LPIPS over DDNM and DDS baselines, often rivaling or exceeding TV-regularized variants, while qualitatively reducing inter-slice artifacts in coronal/sagitta", "questions": "- Training protocol parity: For the base diffusion models used with DDNM and DDS, were they derived from the same trained prior(s) (same data, architecture, and training protocol), with only the solver differing? A concise statement about identical priors across solvers would clarify fairness.\n\n- Beyond inverse problems: Could ISCS plausibly extend to direct 3D volume generation (e.g., from very sparse or no views) by enforcing correlated stochasticity across slices during unconditional or weakly conditioned sampling? Any preliminary observations or limitations?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- The method is simple, clear, and effective: replacing independent per-slice noise with a slerp-correlated noise volume improves inter-slice consistency without extra training or losses, and integrates directly into standard DDIM-style updates.\n\n- Presentation is generally clear, with a helpful geometric interpretation (independent vs. identical vs. slerp noise) that motivates why smooth correlation avoids both uncorrelated flicker and over-rigid copying artifacts.\n\n- Code is provided.", "weaknesses": "- Several related literature are missed. Di-Fusion (Wu etal., ICLR 2025) and DDM^2 (Xiang etal., ICLR 2023) and many more other papers on inverse problem solving for medical data. Those literature were published on ICLR and for a similar problem, even if not exactly the same. The authors are highly encouraged to discuss those related work in the paper.\n\n- Lack of a dedicated inter-slice consistency metric in the main results. The quantitative tables report PSNR/SSIM/LPIPS only (per view). While the paper includes an “inter-slice difference” trajectory to illustrate coherence during sampling, this analysis is not integrated as a headline metric alongside PSNR/SSIM/LPIPS, making it hard to compare inter-slice consistency at a glance across methods and tasks. A specialized, standardized metric for inter-slice consistency would better highlight the core contribution.\n\n- Insufficient theoretical and practical justification that slerp is the best interpolation choice. The current ablation contrasts identical noise (BCS) vs. slerp and shows slerp avoids “copying artifacts” and slightly improves quantitative metrics. However, other plausible interpolations (e.g., simple linear interpolation in noise space) are not evaluated, leaving open whether slerp is uniquely effective or merely one effective option.\n\n- Comparative breadth. Although comparisons include strong diffusion-based solvers (DDNM, DDS), plus classical baselines (e.g., FDK, ADMM-TV), it would strengthen the evidence to compare against additional medical inverse-problem baselines that may (or may not) benefit from noise design, to more clearly position ISCS’s impact.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "4Gz2ETkPUu", "reviewer": "Reviewer_PqvB", "summary": "This paper addresses a key limitation of using 2D diffusion models (DMs) for 3D medical imaging: stochastic inconsistencies between independently sampled slices, leading to discontinuous 3D volumes. The authors propose Inter-Slice Consistent Stochasticity (ISCS)---a plug-and-play method that enforces inter-slice correlation in the diffusion sampling stage by introducing spherical linear interpolation (Slerp) between noise vectors, ensuring smooth stochastic transitions across slices. The method requires no retraining, extra loss terms, or additional computational cost, and can be integrated into existing diffusion-based inverse solvers (DDNM, DDS). Experiments on sparse-view CT, limited-angle CT, and MRI isotropic SR demonstrate consistent PSNR/SSIM/LPIPS improvements, outperforming TV-regularized baselines.", "questions": "1. How does inter-slice correlation affect posterior sampling convergence or variance reduction? I expect formal proof or (at minimum) quantitative analysis.\n\n2. How does ISCS interact with deterministic samplers (e.g., DDIM with $\\eta = 0$)?\n\n3. How does Slerp interpolation work if abrupt structure changes exist?\n\n4. I strongly suggest including comparisons with recent 3D-aware diffusion priors (e.g., DiffusionBlend [Song et al., NeurIPS '24]) or multi-plane consistency methods.\n\n5. Could Slerp interpolation be extended to spatially adaptive correlation where anatomical gradient drives $\\alpha_i$?\n\n6. How does ISCS perform with very thick slices or anisotropic resolutions?\n\n7. Are there any cases where ISCS causes artifacts or over-correlation (e.g., repetitive patterns)?\n\n8. Is the improvement consistent across random seeds, or does stochastic correlation introduce bias?", "limitations": "", "rating": 6, "confidence": 5, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "1. The paper clearly identifies uncorrelated stochasticity as the fundamental cause of inter-slice artifacts, a well-reasoned observation extending findings from video DMs (Kwon & Ye, 2025) to 3D medical imaging.\n\n2. ISCS is lightweight and does not modify model training or inference pipelines. The Slerp-based correlated noise interpolation is mathematically sound and geometrically intuitive.\n\n3. Strong empirical validations:\n- Demonstrated across three inverse problems (SVCT, LACT, MRI-SR).\n- Improves both fidelity (PSNR/SSIM) and perceptual quality (LPIPS).\n- Outperforms both baseline DIS (DDNM/DDS) and TV-regularized counterparts, maintaining anatomical details without oversmoothing.\n\n4. The plug-and-play property enables easy adoption in other 2D DM-based 3D reconstruction pipelines.", "weaknesses": "1. While geometrically motivated, there is no formal proof or quantitative analysis on how inter-slice correlation affects posterior sampling convergence or variance reduction.\n\n2. Scalability and generalization:\n- The Slerp interpolation assumes smooth anatomical transitions, which may fail in pathological cases (e.g., tumors, lesions) with abrupt structure changes.\n- Performance under varying slice thickness or non-uniform z-spacing is not evaluated.\n\n3. The paper lacks comparison with recent 3D-aware diffusion priors (e.g., DiffusionBlend [Song et al., NeurIPS '24]) or multi-plane consistency methods.\n\n4. Only Slerp vs. identical noise is analyzed. Additional ablations (e.g., interpolation degree, anchor distance, or adaptive correlation strength) would strengthen claims.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "qkn0RJ3ATc", "reviewer": "Reviewer_fFZa", "summary": "This paper addresses the issue of inter-slice inconsistency that arises when solving 3D medical inverse problems using 2D diffusion model-based inverse solvers (DIS). The authors propose a simple yet effective approach in which the noise used during the reverse diffusion denoising process is made slice-wise correlated. Motivated by recent findings showing that spherical linear interpolation (Slerp) is more meaningful than linear interpolation for Gaussian noise, the method samples two anchor noise vectors for the first and last slices, and then generates noise for intermediate slices via Slerp interpolation between these anchors.", "questions": "1. While the method shows that it can replace the widely used TV prior, it would be informative to see how it compares with 3D priors such as TQDM. It is okay to the proposed method does not outperform them.\n2. Implicit slice-wise regularization via noise correlation may underperform explicit regularizers (e.g., TV) under severe degradation where large portions of information must be reconstructed. Does the method maintain performance under such challenging forward models?\n3. Since the proposed approach seems orthogonal to explicit volumetric priors such as 3D TV, can the two be combined for further performance improvement?\n4. If the above comparisons and ablation studies (as suggested in the weakness section) are included, the contribution would be significantly strengthened, and I would be willing to raise my score accordingly.", "limitations": "", "rating": 2, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The main strength of this work lies in its ability to mitigate inter-slice inconsistency—a major challenge in 3D medical inverse problems—without introducing additional priors or complex  modifications. Since the method only modifies the noise structure and introduces no new hyperparameters, it is highly practical and easy to integrate into existing 3D medical reconstruction pipelines.\n2. Experiments across multiple imaging modalities and tasks provide strong evidence that the proposed method can effectively replace the widely used total variation (TV) prior.\n3. The comparison with batch-consistent sampling (BCS) clearly demonstrates the limitations of BCS, specifically the copying artifacts it introduces, and shows that the proposed approach effectively resolves these issues.", "weaknesses": "1. The novelty of the proposed method is somewhat limited because similar structural noise techniques have been explored in video diffusion models for enforcing temporal consistency and reducing flickering artifacts (e.g., [1,2,3]). For instance, [1] also samples noise with inter-frame correlations via noise interpolation. To clearly distinguish the contribution, it is necessary to directly compare the proposed method with these noise prior approaches in the same manner as the comparison against BCS.\n2. The interpolated noise is only used during the re-noising steps. Thus, when using deterministic DDIM sampling ($\\eta=0$), where pure noise is not used, the method cannot be applied. If $\\eta=0$ is rarely used in inverse problems due to degraded performance, the authors should provide supporting evidence or references. Additionally, since the proposed method depends directly on the degree of stochasticity ($\\eta$), an analysis of how $\\eta$ influences reconstruction quality is required.\n3. BCS applies its procedure to the initial noise $x_T$. It seems natural to also apply the interpolated correlated noise to the $x_T$ in the proposed method. The authors should clarify why this was not done.\n4. The angle (distance) between the two anchor noise vectors is randomly determined. If there exists an optimal anchor spacing for a given target volume, performance variance may increase. An ablation analyzing reconstruction quality with respect to anchor angle is needed.\n5. **Minor:** The authors attribute the copying artifacts in medical volumes to domain differences from videos, but this claim lacks supporting evidence. Since prior BCS work does not show temporal-slice artifacts in video, the absence of such artifacts is not demonstrated. If the authors wish to maintain the domain-difference argument, they should show that BCS does *not* produce similar artifacts in video inverse problems; otherwise, the proposed method may be better positioned as a domain-genera**l** solution. Of course, evaluating video inverse problems may be beyond the scope of this paper — this is only a suggested clarification and does not affect the overall contribution.\n6. **Minor:** Line 114: “A is invertible” appears to be a typo; presumably it should be **non-invertible**.\n\n[1] Ge, Songwei, et al. \"Preserve your own correlation: A noise prior for video diffusion models.\" *ICCV*. 2023.\n\n[2] Wu, Tianxing, et al. \"Freeinit: Bridging initialization gap in video diffusion models.\" *ECCV.* 2024.\n\n[3] Chang, Pascal, et al. \"How i warped your noise: a temporally-correlated noise prior for diffusion models.\" ICLR (2024).", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "afR7i9RR5B", "reviewer": "Reviewer_6tkB", "summary": "The authors exploit 2D diffusion models for 3D medical image reconstruction. The diffusion models are trained on xy-slices. \nTo obtain continuity in z-axis the authors apply correlated noise during sampling. They call this method \"Inter-Slice Consistent Stochasticitiy\" (ISCS). ISCS is an easy addition to the sampling pipeline, requiring only a single change in the algorithm.", "questions": "- How does the method depend on the sampling of the initial noise vectors for the first and the last slice? \n- How does this method compare against the temporal correlated noise of [2] and the method in [3] ? \n\n[2] Liu and Vahdat \"On Equivariance and Fast Sampling in Video Diffusion Models Trained with Warped Noise\" (2025)\n\n[3] Chang et al. \"How I warped your noise: a temporally correlated noise prior for diffusion models\"", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "- The paper is well-written and contains careful experiments. Importantly, according to Table 1 ISCS performs better than adding an additional TV-regulariser in the z-axis (which is currently the predominant way of enforcing inter-slice consistency)\n- ISCS is a simple method (i.e., it contains no hyperparameters) which can be easily incorporated into existing code-bases with a few extra lines and comes with only negligible additional computational cost \n\nBased on these points (better performance, simple implementation, no overhead computational cost) I would expect that this method will be well adapted in 3D-sampling tasks and code-bases.", "weaknesses": "- There are some important baselines missing in Table 1: using perpendicular 2d models [1] and batch-consistent sampling (i.e., using the same noise for all slices) \n- There is no comparison against the deterministic DDIM sampler (i.e. setting $\\eta=0$ in Equation (8)). For the case of deterministic samplers, no additional noise has to be added during sampling. \n- With the adoption of flow-based models and deterministic samplers for diffusion models (e.g. PNDM [4]) the proposed method might no longer be relevant. For both flow-based models and deterministic sampler, the main argument for the lack of inter-slice consistency (starting at line 244) does no longer hold, because no noise is added. \n- The authors provide a heuristic motivation why their method should work, but not really any theory. In contrast, using a TV-regulariser on the z-axis ensures consistency between slices (albeit requiring an additional hyperparameter)\n- In line 264 the authors write \"recent studies have demonstrated that random samples from a high-dimensional standard normal distribution tend to concentrate on the surface of a hypersphere\" and cite two works from 2024. However, this is a pretty standard concentration of measure phenomenon and known for a long time.\n\n[4] Liu et. al \"Pseudo Numerical Methods for Diffusion Models in Manifolds\" (2022)\n\n\n\n[1] Lee et al. \"Improving 3d imaging with pre-trained perpendicular 2d diffusion models\"", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)